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Clear old FrontierOR files 2701-3600 of 5583

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  1. huisman2005/gurobi_solution_log/large_log_3.jsonl +0 -2
  2. huisman2005/gurobi_solution_log/large_log_4.jsonl +0 -2
  3. huisman2005/gurobi_solution_log/large_log_5.jsonl +0 -1
  4. huisman2005/gurobi_solution_log/tiny_log.jsonl +0 -2
  5. huisman2005/instance/large_instance_1.json +0 -1
  6. huisman2005/instance/large_instance_2.json +0 -1
  7. huisman2005/instance/large_instance_3.json +0 -1
  8. huisman2005/instance/large_instance_4.json +0 -1
  9. huisman2005/instance/large_instance_5.json +0 -1
  10. huisman2005/instance/tiny_instance.json +0 -1014
  11. huisman2005/instance/tiny_instance_2.json +0 -835
  12. huisman2005/instance_schema.json +0 -80
  13. huisman2005/mathematical_formulation.md +0 -65
  14. huisman2005/problem_description.txt +0 -69
  15. huisman2005/solution_logger.py +0 -61
  16. huisman2005/solution_schema.json +0 -11
  17. ji2019/feasibility_check.py +0 -808
  18. ji2019/gurobi_code.py +0 -624
  19. ji2019/gurobi_feasi_result/large_feasi_result_1.json +0 -6
  20. ji2019/gurobi_feasi_result/large_feasi_result_2.json +0 -6
  21. ji2019/gurobi_feasi_result/large_feasi_result_3.json +0 -6
  22. ji2019/gurobi_feasi_result/large_feasi_result_4.json +0 -6
  23. ji2019/gurobi_feasi_result/large_feasi_result_5.json +0 -6
  24. ji2019/gurobi_feasi_result/tiny_feasi_result.json +0 -6
  25. ji2019/gurobi_solution/large_solution_1.json +0 -85
  26. ji2019/gurobi_solution/large_solution_2.json +0 -85
  27. ji2019/gurobi_solution/large_solution_3.json +0 -85
  28. ji2019/gurobi_solution/large_solution_4.json +0 -85
  29. ji2019/gurobi_solution/large_solution_5.json +0 -85
  30. ji2019/gurobi_solution/tiny_solution.json +0 -59
  31. ji2019/gurobi_solution_log/large_log_1.jsonl +0 -25
  32. ji2019/gurobi_solution_log/large_log_2.jsonl +0 -25
  33. ji2019/gurobi_solution_log/large_log_3.jsonl +0 -29
  34. ji2019/gurobi_solution_log/large_log_4.jsonl +0 -23
  35. ji2019/gurobi_solution_log/large_log_5.jsonl +0 -13
  36. ji2019/gurobi_solution_log/tiny_log.jsonl +0 -3
  37. ji2019/instance/large_instance_1.json +0 -1
  38. ji2019/instance/large_instance_11.json.pre_12ships +0 -1253
  39. ji2019/instance/large_instance_2.json +0 -1
  40. ji2019/instance/large_instance_21.json.pre_12ships +0 -1253
  41. ji2019/instance/large_instance_3.json +0 -1
  42. ji2019/instance/large_instance_31.json.pre_12ships +0 -1253
  43. ji2019/instance/large_instance_4.json +0 -1
  44. ji2019/instance/large_instance_41.json.pre_12ships +0 -1253
  45. ji2019/instance/large_instance_5.json +0 -1
  46. ji2019/instance/large_instance_51.json.pre_12ships +0 -1253
  47. ji2019/instance/tiny_instance.json +0 -314
  48. ji2019/instance_schema.json +0 -30
  49. ji2019/mathematical_formulation.md +0 -214
  50. ji2019/problem_description.txt +0 -15
huisman2005/gurobi_solution_log/large_log_3.jsonl DELETED
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- {"time": 2902.585, "objective_value": 1296.0}
 
 
 
huisman2005/gurobi_solution_log/large_log_4.jsonl DELETED
@@ -1,2 +0,0 @@
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- {"time": 3.266, "objective_value": 4496.0}
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- {"time": 3.492, "objective_value": 2285.0}
 
 
 
huisman2005/gurobi_solution_log/large_log_5.jsonl DELETED
@@ -1 +0,0 @@
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- {"time": 522.387, "objective_value": 1698.0}
 
 
huisman2005/gurobi_solution_log/tiny_log.jsonl DELETED
@@ -1,2 +0,0 @@
1
- {"time": 24.747, "objective_value": 6340.0}
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- {"time": 46.171, "objective_value": 2819.0}
 
 
 
huisman2005/instance/large_instance_1.json DELETED
@@ -1 +0,0 @@
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huisman2005/instance/large_instance_2.json DELETED
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huisman2005/instance/large_instance_3.json DELETED
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huisman2005/instance/large_instance_4.json DELETED
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huisman2005/instance/large_instance_5.json DELETED
@@ -1 +0,0 @@
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572
- "trip_id": 69
573
- },
574
- {
575
- "start_time": 1138,
576
- "end_time": 1190,
577
- "start_location": "B",
578
- "end_location": "C",
579
- "trip_id": 70
580
- },
581
- {
582
- "start_time": 1142,
583
- "end_time": 1191,
584
- "start_location": "A",
585
- "end_location": "C",
586
- "trip_id": 71
587
- },
588
- {
589
- "start_time": 1183,
590
- "end_time": 1228,
591
- "start_location": "C",
592
- "end_location": "B",
593
- "trip_id": 72
594
- },
595
- {
596
- "start_time": 1185,
597
- "end_time": 1234,
598
- "start_location": "C",
599
- "end_location": "A",
600
- "trip_id": 73
601
- },
602
- {
603
- "start_time": 1189,
604
- "end_time": 1209,
605
- "start_location": "D",
606
- "end_location": "A",
607
- "trip_id": 74
608
- },
609
- {
610
- "start_time": 1190,
611
- "end_time": 1236,
612
- "start_location": "A",
613
- "end_location": "B",
614
- "trip_id": 75
615
- },
616
- {
617
- "start_time": 1206,
618
- "end_time": 1252,
619
- "start_location": "B",
620
- "end_location": "A",
621
- "trip_id": 76
622
- },
623
- {
624
- "start_time": 1206,
625
- "end_time": 1226,
626
- "start_location": "A",
627
- "end_location": "D",
628
- "trip_id": 77
629
- },
630
- {
631
- "start_time": 1218,
632
- "end_time": 1263,
633
- "start_location": "B",
634
- "end_location": "C",
635
- "trip_id": 78
636
- },
637
- {
638
- "start_time": 1382,
639
- "end_time": 1431,
640
- "start_location": "A",
641
- "end_location": "C",
642
- "trip_id": 79
643
- }
644
- ],
645
- "travel_times": {
646
- "A": {
647
- "A": 0,
648
- "B": 32,
649
- "C": 34,
650
- "D": 14,
651
- "depot_1": 52,
652
- "depot_2": 52
653
- },
654
- "B": {
655
- "A": 32,
656
- "B": 0,
657
- "C": 32,
658
- "D": 21,
659
- "depot_1": 43,
660
- "depot_2": 58
661
- },
662
- "C": {
663
- "A": 34,
664
- "B": 32,
665
- "C": 0,
666
- "D": 35,
667
- "depot_1": 18,
668
- "depot_2": 27
669
- },
670
- "D": {
671
- "A": 14,
672
- "B": 21,
673
- "C": 35,
674
- "D": 0,
675
- "depot_1": 52,
676
- "depot_2": 58
677
- },
678
- "depot_1": {
679
- "A": 52,
680
- "B": 43,
681
- "C": 18,
682
- "D": 52,
683
- "depot_1": 0,
684
- "depot_2": 27
685
- },
686
- "depot_2": {
687
- "A": 52,
688
- "B": 58,
689
- "C": 27,
690
- "D": 58,
691
- "depot_1": 27,
692
- "depot_2": 0
693
- }
694
- },
695
- "distances_km": {
696
- "A": {
697
- "A": 0.0,
698
- "B": 26.4008,
699
- "C": 28.0713,
700
- "D": 11.1803,
701
- "depot_1": 43.0465,
702
- "depot_2": 42.72
703
- },
704
- "B": {
705
- "A": 26.4008,
706
- "B": 0.0,
707
- "C": 25.9422,
708
- "D": 17.2047,
709
- "depot_1": 35.4683,
710
- "depot_2": 48.3322
711
- },
712
- "C": {
713
- "A": 28.0713,
714
- "B": 25.9422,
715
- "C": 0.0,
716
- "D": 29.0689,
717
- "depot_1": 15.0,
718
- "depot_2": 22.4722
719
- },
720
- "D": {
721
- "A": 11.1803,
722
- "B": 17.2047,
723
- "C": 29.0689,
724
- "D": 0.0,
725
- "depot_1": 43.0116,
726
- "depot_2": 48.0833
727
- },
728
- "depot_1": {
729
- "A": 43.0465,
730
- "B": 35.4683,
731
- "C": 15.0,
732
- "D": 43.0116,
733
- "depot_1": 0.0,
734
- "depot_2": 22.1359
735
- },
736
- "depot_2": {
737
- "A": 42.72,
738
- "B": 48.3322,
739
- "C": 22.4722,
740
- "D": 48.0833,
741
- "depot_1": 22.1359,
742
- "depot_2": 0.0
743
- }
744
- },
745
- "deadhead_speed_km_per_hour": 50,
746
- "operational_speeds_km_per_hour": {
747
- "06:00-08:59": 28,
748
- "09:00-12:59": 32,
749
- "13:00-18:59": 30,
750
- "19:00-23:59": 35
751
- },
752
- "frequency_table_minutes": {
753
- "06:00-08:59": 80,
754
- "09:00-12:59": 120,
755
- "13:00-18:59": 80,
756
- "19:00-23:59": 240
757
- },
758
- "duty_types": {
759
- "tripper": {
760
- "type_id": 0,
761
- "num_pieces": 1,
762
- "piece_length_min": 30,
763
- "piece_length_max": 300,
764
- "break_length_min": null,
765
- "duty_length_max": null,
766
- "work_time_max": null,
767
- "start_time_min": null,
768
- "start_time_max": null,
769
- "end_time_max": null
770
- },
771
- "early": {
772
- "type_id": 1,
773
- "num_pieces": 2,
774
- "piece_length_min": 30,
775
- "piece_length_max": 300,
776
- "break_length_min": 45,
777
- "duty_length_max": 585,
778
- "work_time_max": 540,
779
- "start_time_min": null,
780
- "start_time_max": null,
781
- "end_time_max": 990
782
- },
783
- "day": {
784
- "type_id": 2,
785
- "num_pieces": 2,
786
- "piece_length_min": 30,
787
- "piece_length_max": 300,
788
- "break_length_min": 45,
789
- "duty_length_max": 585,
790
- "work_time_max": 540,
791
- "start_time_min": 480,
792
- "start_time_max": null,
793
- "end_time_max": 1094
794
- },
795
- "late": {
796
- "type_id": 3,
797
- "num_pieces": 2,
798
- "piece_length_min": 30,
799
- "piece_length_max": 300,
800
- "break_length_min": 45,
801
- "duty_length_max": 585,
802
- "work_time_max": 540,
803
- "start_time_min": 795,
804
- "start_time_max": null,
805
- "end_time_max": 1170
806
- },
807
- "split": {
808
- "type_id": 4,
809
- "num_pieces": 2,
810
- "piece_length_min": 30,
811
- "piece_length_max": 300,
812
- "break_length_min": 90,
813
- "duty_length_max": 720,
814
- "work_time_max": 540,
815
- "start_time_min": null,
816
- "start_time_max": null,
817
- "end_time_max": null
818
- }
819
- },
820
- "crew_parameters": {
821
- "sign_on_time_depot_minutes": 10,
822
- "sign_off_time_depot_minutes": 5,
823
- "extra_time_non_depot_relief_minutes": 15,
824
- "extra_time_includes_deadhead_to_depot": true,
825
- "max_pieces_per_duty": 2,
826
- "continuous_attendance": true,
827
- "changeovers_allowed": true
828
- },
829
- "vehicle_parameters": {
830
- "each_vehicle_has_own_depot": true,
831
- "unlimited_vehicles_per_depot": true,
832
- "all_depots_can_serve_all_trips": true,
833
- "fictitious_cost_per_minute_empty_outside_depot": 1
834
- }
835
- }
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
huisman2005/instance_schema.json DELETED
@@ -1,80 +0,0 @@
1
- {
2
- "num_trips": "<int> Total number of timed bus trips to be covered across all lines and directions.",
3
- "num_depots": "<int> Number of vehicle depots available in the transit network.",
4
- "num_lines": "<int> Number of bus lines operated in the network.",
5
- "trips_per_line_per_direction": "<int> Number of trips scheduled per line per direction over the planning horizon.",
6
- "speed_type": "<str> Speed profile category that determines which set of time-of-day operational speeds applies.",
7
- "coordinate_area_km": "<list[int], length 2> Width and height in kilometers of the rectangular area in which all locations are placed.",
8
- "locations": {
9
- "{location_name}": "<list[int], length 2> X and Y coordinates in kilometers of the named location (depot or line endpoint)."
10
- },
11
- "depots": [
12
- {
13
- "depot_id": "<int> Zero-based index identifying this depot.",
14
- "name": "<str> Name of this depot matching its key in the locations dictionary.",
15
- "coordinates": "<list[int], length 2> X and Y coordinates in kilometers of this depot."
16
- }
17
- ],
18
- "relief_locations": "<list[str], length num_lines+1 or num_lines> Names of locations where driver changeovers may take place.",
19
- "lines": [
20
- {
21
- "from": "<str> Name of the origin endpoint of this bus line.",
22
- "to": "<str> Name of the destination endpoint of this bus line."
23
- }
24
- ],
25
- "trips": [
26
- {
27
- "trip_id": "<int> Zero-based index identifying this trip, ordered by departure time.",
28
- "start_time": "<int> Departure time of this trip in minutes from midnight.",
29
- "end_time": "<int> Arrival time of this trip in minutes from midnight.",
30
- "start_location": "<str> Name of the origin location where this trip departs.",
31
- "end_location": "<str> Name of the destination location where this trip arrives."
32
- }
33
- ],
34
- "travel_times": {
35
- "{origin}": {
36
- "{destination}": "<int> Deadhead travel time in minutes from origin to destination."
37
- }
38
- },
39
- "distances_km": {
40
- "{origin}": {
41
- "{destination}": "<float> Euclidean distance in kilometers from origin to destination."
42
- }
43
- },
44
- "deadhead_speed_km_per_hour": "<int> Speed in kilometers per hour at which vehicles travel empty between assignments.",
45
- "operational_speeds_km_per_hour": {
46
- "{time_interval}": "<int> In-service vehicle speed in kilometers per hour during this time-of-day interval."
47
- },
48
- "frequency_table_minutes": {
49
- "{time_interval}": "<int> Minutes between consecutive departures on the same line and direction during this time-of-day interval."
50
- },
51
- "duty_types": {
52
- "{duty_type_name}": {
53
- "type_id": "<int> Numeric identifier for this duty type.",
54
- "num_pieces": "<int> Number of consecutive work segments that compose a duty of this type.",
55
- "piece_length_min": "<int> Minimum allowed duration in minutes of each work segment.",
56
- "piece_length_max": "<int> Maximum allowed duration in minutes of each work segment.",
57
- "break_length_min": "<int or null> Minimum required break duration in minutes between work segments, or null if no break applies.",
58
- "duty_length_max": "<int or null> Maximum total span in minutes from sign-on to sign-off, or null if unconstrained.",
59
- "work_time_max": "<int or null> Maximum cumulative working time in minutes within the duty, or null if unconstrained.",
60
- "start_time_min": "<int or null> Earliest allowed duty start time in minutes from midnight, or null if unconstrained.",
61
- "start_time_max": "<int or null> Latest allowed duty start time in minutes from midnight, or null if unconstrained.",
62
- "end_time_max": "<int or null> Latest allowed duty end time in minutes from midnight, or null if unconstrained."
63
- }
64
- },
65
- "crew_parameters": {
66
- "sign_on_time_depot_minutes": "<int> Time in minutes added to duty duration when a driver signs on at a depot.",
67
- "sign_off_time_depot_minutes": "<int> Time in minutes added to duty duration when a driver signs off at a depot.",
68
- "extra_time_non_depot_relief_minutes": "<int> Extra time in minutes added when a driver starts or ends at a non-depot relief location.",
69
- "extra_time_includes_deadhead_to_depot": "<bool> Whether the extra time for non-depot relief includes the deadhead travel time to the depot.",
70
- "max_pieces_per_duty": "<int> Maximum number of consecutive work segments allowed in any single duty.",
71
- "continuous_attendance": "<bool> Whether a driver must remain on the vehicle whenever it is outside the depot.",
72
- "changeovers_allowed": "<bool> Whether a driver may transfer to a different vehicle during a break between work segments."
73
- },
74
- "vehicle_parameters": {
75
- "each_vehicle_has_own_depot": "<bool> Whether each vehicle operates from and returns to a single home depot.",
76
- "unlimited_vehicles_per_depot": "<bool> Whether the fleet size at each depot is unlimited.",
77
- "all_depots_can_serve_all_trips": "<bool> Whether every depot may serve every trip regardless of line.",
78
- "fictitious_cost_per_minute_empty_outside_depot": "<int> Cost rate per minute charged when a vehicle sits idle outside its home depot."
79
- }
80
- }
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
huisman2005/mathematical_formulation.md DELETED
@@ -1,65 +0,0 @@
1
- # Original Formulation: Multiple-Depot Integrated Vehicle and Crew Scheduling Problem (MD-VCSP)
2
-
3
- *Source: Multiple-Depot Integrated Vehicle and Crew Scheduling, Dennis Huisman, Richard Freling, Albert P. M. Wagelmans, 2005 (Transportation Science 39(4), pp. 491–502).*
4
-
5
- The canonical formulation studied by the paper is **MD-VCSP1**, introduced in §2 (“Mathematical Formulation”). Its notation ($y^d_{ij}$, $x^d_k$) is carried into the algorithm of §3 and the computational experiments of §5. The reformulation MD-VCSP2 of §4 (“Alternative Approach”), obtained by substituting out the $y$ variables, is recorded under *Variants*.
6
-
7
- ## Sets and Indices
8
-
9
- - $N=\{1,2,\dots,n\}$: set of trips, numbered by increasing starting time.
10
-
11
- - $E=\{(i,j)\mid i<j,\ i\text{ and }j\text{ compatible},\ i\in N,\ j\in N\}$: set of deadheads.
12
-
13
- - $D$: set of depots.
14
-
15
- - $s^d,\ t^d$: source and sink nodes representing depot $d$.
16
-
17
- - $G^d=(V^d,A^d)$: acyclic directed vehicle-scheduling network for depot $d$, with $V^d=N^d\cup\{s^d,t^d\}$ and $A^d=E^d\cup(s^d\times N^d)\cup(N^d\times t^d)$, where $N^d\subseteq N$ and $E^d\subseteq E$ are the trips and deadheads corresponding to depot $d$.
18
-
19
- - $A^{sd}\subset A^d$: set of *short* arcs (idle time between two consecutive trips is too short for the vehicle to return to the depot).
20
-
21
- - $A^{ld}\subset A^d$: set of *long* arcs (idle time is long enough for the vehicle to return to the depot in between).
22
-
23
- - $K^d$: set of feasible duties corresponding to depot $d$ (exponentially large; generated by column generation).
24
-
25
- - $K^d(i)$: set of duties covering the trip task of trip $i\in N^d$ (each trip corresponds to exactly one trip task).
26
-
27
- - $K^d(i,j)$: set of duties covering the dh-task of short arc $(i,j)\in A^{sd}$.
28
-
29
- - $K^d(i,t^d)$: set of duties covering the dh-task from $el_i$ (end location of trip $i$) to depot $d$.
30
-
31
- - $K^d(s^d,j)$: set of duties covering the dh-task from depot $d$ to $bl_j$ (begin location of trip $j$).
32
-
33
- - $el_i$, $bl_j$: ending location of trip $i$, beginning location of trip $j$.
34
-
35
- ## Parameters
36
-
37
- - $c^d_{ij}$: vehicle cost of arc $(i,j)\in A^d$ (usually a function of travel and idle time; a fixed vehicle cost may be added to arcs $(s^d,i)$ or $(j,t^d)$).
38
-
39
- - $f^d_k$: crew cost of duty $k\in K^d$ (usually a combination of fixed costs such as wages and variable costs such as overtime payment).
40
-
41
- ## Decision Variables
42
-
43
- - $y^d_{ij}\in\{0,1\}$: $1$ if arc $(i,j)$ is used and assigned to depot $d$, $0$ otherwise, for all $d\in D$, $(i,j)\in A^d$.
44
-
45
- - $x^d_k\in\{0,1\}$: $1$ if duty $k$ corresponding to depot $d$ is selected, $0$ otherwise, for all $d\in D$, $k\in K^d$.
46
-
47
- ## Objective
48
-
49
- $$\begin{align}
50
- \min\ & \sum_{d\in D}\sum_{(i,j)\in A^d} c^d_{ij}\,y^d_{ij}
51
- + \sum_{d\in D}\sum_{k\in K^d} f^d_k\,x^d_k \tag{1}
52
- \end{align}$$
53
-
54
- ## Constraints
55
-
56
- $$\begin{align}
57
- \sum_{d\in D}\ \sum_{j:(i,j)\in A^d} y^d_{ij} &= 1, & \forall i\in N \tag{2}\\[2pt]
58
- \sum_{d\in D}\ \sum_{i:(i,j)\in A^d} y^d_{ij} &= 1, & \forall j\in N \tag{3}\\[2pt]
59
- \sum_{i:(i,j)\in A^d} y^d_{ij} - \sum_{i:(j,i)\in A^d} y^d_{ji} &= 0, & \forall d\in D,\ \forall j\in N^d \tag{4}\\[2pt]
60
- \sum_{k\in K^d(i)} x^d_k - \sum_{j:(i,j)\in A^d} y^d_{ij} &= 0, & \forall d\in D,\ \forall i\in N^d \tag{5}\\[2pt]
61
- \sum_{k\in K^d(i,j)} x^d_k - y^d_{ij} &= 0, & \forall d\in D,\ \forall (i,j)\in A^{sd} \tag{6}\\[2pt]
62
- \sum_{k\in K^d(i,t^d)} x^d_k - y^d_{i\,t^d} - \sum_{j:(i,j)\in A^{ld}} y^d_{ij} &= 0, & \forall d\in D,\ \forall i\in N^d \tag{7}\\[2pt]
63
- \sum_{k\in K^d(s^d,j)} x^d_k - y^d_{s^d\,j} - \sum_{i:(i,j)\in A^{ld}} y^d_{ij} &= 0, & \forall d\in D,\ \forall j\in N^d \tag{8}\\[2pt]
64
- x^d_k,\ y^d_{ij} &\in \{0,1\}, & \forall d\in D,\ \forall k\in K^d,\ \forall (i,j)\in A^d \tag{9}
65
- \end{align}$$
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
huisman2005/problem_description.txt DELETED
@@ -1,69 +0,0 @@
1
- # Problem Description
2
-
3
- A public transit company must simultaneously schedule vehicles and crew members to cover a set of timed bus trips across a network served by multiple depots. The instance specifies the total number of trips, each identified by an index and defined by its departure time in minutes from midnight, arrival time in minutes from midnight, origin, and destination, with trips ordered by increasing departure time. The number of depots and their identifiers, names, and geographic positions are given, along with a dictionary of all named locations and their coordinate pairs, placed within a rectangular area in kilometers. The bus lines operated, each with a from and to endpoint, define the route structure, and the number of lines and the number of trips per line per direction characterize the service pattern. A designated set of relief locations identifies where driver changeovers may take place. Travel times in minutes between every pair of locations and corresponding Euclidean distances in kilometers are provided. Vehicles traveling empty between assignments move at a fixed deadhead speed, while in-service operational speeds vary by time-of-day interval. Departure frequencies per line also vary by time-of-day interval, and a speed profile category determines which set of operational speeds applies. Five crew duty types are defined, each keyed by type name, with each type specifying an identifier, how many consecutive work segments it comprises, the minimum and maximum allowed duration of each work segment in minutes, the minimum required break duration between segments if applicable, the maximum total duty span, the maximum cumulative working time within a duty, and optional earliest or latest start or end times for the duty in minutes from midnight. Crew parameters specify the sign-on time when a driver begins at a depot, the sign-off time when ending at a depot, the extra time penalty when starting or ending at a non-depot relief location, whether that extra time includes the deadhead travel time to the depot, the maximum number of work segments per duty, whether a driver must be continuously present on the vehicle whenever it is outside the depot, and whether a driver may switch to a different vehicle during a break. Vehicle parameters indicate that each vehicle operates from and returns to a single home depot, that the fleet size at each depot is unlimited, that every depot may serve every trip, and a fictitious cost rate per minute that a vehicle sits idle outside its depot.
4
-
5
- The company must assign every trip to exactly one vehicle and every work task to exactly one crew duty such that the vehicle schedules and crew schedules are mutually compatible. Each vehicle starts its day at its home depot, performs a sequence of trips connected by deadhead movements, and returns to the same depot at the end of the day. Two trips are compatible for consecutive service by the same vehicle if the earlier trip ends before the later trip begins and the vehicle can travel from the ending location of the earlier trip to the starting location of the later trip in time. Between two consecutive trips assigned to the same vehicle, if the idle time is long enough for the vehicle to travel from the ending location of the first trip to its home depot and then from the depot to the starting location of the next trip, the vehicle is assumed to return to the depot during that gap; such a connection is called a long arc. Otherwise the vehicle remains outside the depot during the idle period, forming a short arc. Every trip must have exactly one predecessor connection and exactly one successor connection in the overall schedule, where a predecessor or successor may be another trip or the depot source or sink respectively. Within each depot's sub-schedule, the flow is conserved at every trip node: the number of vehicle connections entering a trip from that depot equals the number leaving it for that depot. A trip is assigned to a particular depot if and only if that depot's vehicle schedule contains the arcs adjacent to that trip.
6
-
7
- Crew members are organized into duties, each associated with a single depot, and a duty of a crew member only involves tasks on vehicles from that same depot. There are two kinds of tasks: trip tasks, which correspond one-to-one with trips, and deadhead tasks, which correspond to the vehicle's repositioning movements between consecutive trips or between a trip and its depot. A piece of work is a maximal sequence of consecutive tasks on one vehicle block without a break, bounded by relief points; its feasibility depends solely on its duration falling between the minimum and maximum piece length for the applicable duty type. Each duty consists of at most two pieces of work. When a duty has two pieces, they are separated by a break of at least the minimum break duration specified by the duty type. When a driver signs on at a depot, a sign-on time is added to the duty duration; when signing off at a depot, a sign-off time is added. When a duty begins or ends at a non-depot relief location, the extra time plus the deadhead travel time from that location to the depot is added to the duty duration instead. A duty need not start and end at its home depot, but a driver must be continuously present on the vehicle whenever it is outside the depot. Changeovers are permitted, meaning a driver may transfer to a different vehicle during a break, so the two pieces of work in a duty need not be on the same vehicle.
8
-
9
- The crew schedule must be consistent with the vehicle schedule through the following linkages. A trip task is covered by a duty from a given depot if and only if the corresponding trip is assigned to a vehicle from that depot. For short arcs, the deadhead task between two consecutive trips is covered by a duty if and only if that short arc is used in the vehicle schedule. For deadhead tasks from the end of a trip to the depot, coverage by a duty from depot d is required if and only if either the trip is the last trip of its vehicle (connecting to the depot sink) or the vehicle's next connection from that trip is a long arc, since in both cases the vehicle returns to the depot. Symmetrically, the deadhead task from depot d to the start of a trip is covered if and only if either that trip is the vehicle's first trip from depot d or the vehicle's preceding connection to that trip is a long arc.
10
-
11
- Each duty must conform to one of the five defined duty types. The tripper type consists of a single piece of work with no break. The four normal types — early, day, late, and split — each require exactly two pieces of work with a mandatory break. Each type imposes its own limits on minimum and maximum piece duration, minimum break length, maximum duty span, maximum cumulative working time, and allowable windows for when the duty may start and end.
12
-
13
- The goal is to minimize the total combined cost of vehicle operations and crew duties. Vehicle costs consist of a fixed cost for each vehicle used plus a variable cost that accrues at the fictitious cost rate for every minute a vehicle is idle outside its depot. Crew costs combine fixed components such as wages with variable components such as overtime. In the standard experimental setting, each vehicle used counts as a cost of one and each driver duty counts as a cost of one, so the objective reduces to minimizing the total number of vehicles plus the total number of drivers.
14
-
15
- # Data Instance Variable Explanation
16
-
17
- - num_trips: total number of bus trips to be covered
18
- - num_depots: number of vehicle/crew depots
19
- - num_lines: number of bus lines operated
20
- - trips_per_line_per_direction: number of trips scheduled per line per direction
21
- - speed_type: speed profile category determining which operational speeds apply
22
- - generation_seed: random seed used to generate this instance
23
- - coordinate_area_km: dimensions of the rectangular geographic area in kilometers, as [width, height]
24
- - locations: dictionary mapping each location name to its coordinate pair [x, y] in kilometers
25
- - depots: list of depot objects, each containing:
26
- - depot_id: integer identifier of the depot
27
- - name: name of the depot (matching a key in locations)
28
- - coordinates: geographic position [x, y] in kilometers
29
- - relief_locations: list of location names where driver changeovers may take place
30
- - lines: list of bus line objects, each containing:
31
- - from: origin endpoint of the line
32
- - to: destination endpoint of the line
33
- - trips: list of trip objects ordered by departure time, each containing:
34
- - trip_id: integer index of the trip
35
- - start_time: departure time in minutes from midnight
36
- - end_time: arrival time in minutes from midnight
37
- - start_location: origin location name
38
- - end_location: destination location name
39
- - travel_times: nested dictionary of travel times in minutes, indexed by [origin][destination]
40
- - distances_km: nested dictionary of Euclidean distances in kilometers, indexed by [origin][destination]
41
- - deadhead_speed_km_per_hour: speed in km/h for empty vehicle repositioning moves
42
- - operational_speeds_km_per_hour: dictionary mapping time-of-day interval strings to in-service speed in km/h
43
- - frequency_table_minutes: dictionary mapping time-of-day interval strings to departure frequency in minutes per line
44
- - duty_types: dictionary of crew duty types keyed by type name, each containing:
45
- - type_id: integer identifier of the duty type
46
- - num_pieces: number of consecutive work segments in a duty of this type
47
- - piece_length_min: minimum allowed duration of each work segment in minutes
48
- - piece_length_max: maximum allowed duration of each work segment in minutes
49
- - break_length_min: minimum required break duration between segments in minutes (null if not applicable)
50
- - duty_length_max: maximum total span of the duty in minutes (null if unconstrained)
51
- - work_time_max: maximum cumulative working time within the duty in minutes (null if unconstrained)
52
- - start_time_min: earliest allowed start time in minutes from midnight (null if unconstrained)
53
- - start_time_max: latest allowed start time in minutes from midnight (null if unconstrained)
54
- - end_time_max: latest allowed end time in minutes from midnight (null if unconstrained)
55
- - crew_parameters: dictionary of crew scheduling parameters containing:
56
- - sign_on_time_depot_minutes: time added when a driver signs on at a depot
57
- - sign_off_time_depot_minutes: time added when a driver signs off at a depot
58
- - extra_time_non_depot_relief_minutes: extra time penalty when starting or ending at a non-depot relief location
59
- - extra_time_includes_deadhead_to_depot: whether the extra time includes deadhead travel time to the depot (boolean)
60
- - max_pieces_per_duty: maximum number of work segments per duty
61
- - continuous_attendance: whether a driver must stay on the vehicle whenever it is outside the depot (boolean)
62
- - changeovers_allowed: whether a driver may switch to a different vehicle during a break (boolean)
63
- - vehicle_parameters: dictionary of vehicle scheduling parameters containing:
64
- - each_vehicle_has_own_depot: whether each vehicle operates from and returns to a single home depot (boolean)
65
- - unlimited_vehicles_per_depot: whether the fleet size at each depot is unlimited (boolean)
66
- - all_depots_can_serve_all_trips: whether every depot may serve every trip (boolean)
67
- - fictitious_cost_per_minute_empty_outside_depot: cost rate per minute for a vehicle idle outside its depot
68
-
69
- # Data Instance
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
huisman2005/solution_logger.py DELETED
@@ -1,61 +0,0 @@
1
- """
2
- Convergence logger for optimization algorithms.
3
-
4
- Records incumbent solutions with timestamps to a JSONL file.
5
- This module is provided to LLM-generated programs — they only need to call
6
- `log(objective_value)` whenever a better feasible solution is found.
7
-
8
- Usage in generated code:
9
- from solution_logger import SolutionLogger
10
- logger = SolutionLogger(log_path, sense="minimize") # or "maximize"
11
- # ... inside algorithm loop:
12
- logger.log(objective_value)
13
- """
14
-
15
- import json
16
- import time
17
-
18
-
19
- class SolutionLogger:
20
- def __init__(self, log_path, sense="minimize"):
21
- """
22
- Args:
23
- log_path: Path to the JSONL output file.
24
- sense: "minimize" or "maximize".
25
- """
26
- self.log_path = log_path
27
- self.sense = sense
28
- self.start_time = time.time()
29
- self.best_obj = None
30
- self.min_interval = 0.1 # seconds, avoid excessive writes
31
-
32
- self._last_log_time = 0.0
33
- # Clear the file
34
- with open(self.log_path, "w") as f:
35
- pass
36
-
37
- def log(self, objective_value):
38
- """Record a new incumbent if it improves on the best known."""
39
- if objective_value is None:
40
- return
41
-
42
- # Check if this is an improvement
43
- if self.best_obj is not None:
44
- if self.sense == "minimize" and objective_value >= self.best_obj:
45
- return
46
- if self.sense == "maximize" and objective_value <= self.best_obj:
47
- return
48
-
49
- elapsed = time.time() - self.start_time
50
-
51
- # Throttle writes
52
- if self.best_obj is not None and elapsed - self._last_log_time < self.min_interval:
53
- self.best_obj = objective_value
54
- return
55
-
56
- self.best_obj = objective_value
57
- self._last_log_time = elapsed
58
-
59
- with open(self.log_path, "a") as f:
60
- f.write(json.dumps({"time": round(elapsed, 3),
61
- "objective_value": objective_value}) + "\n")
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
huisman2005/solution_schema.json DELETED
@@ -1,11 +0,0 @@
1
- {
2
- "objective_value": "<int> Total number of vehicles plus crew duties used to cover all trips.",
3
- "vehicle_schedule": "<dict, key: '{depot_name}'> Mapping from each depot name to a list of vehicle trip chains, where each chain is the ordered sequence of trip IDs covered by one vehicle that starts and returns to that depot.",
4
- "crew_schedule": [
5
- {
6
- "depot": "<str> Name of the home depot from which this crew duty operates.",
7
- "type": "<str> Duty type name governing the work rules applied to this duty.",
8
- "trips": "<list[int]> Ordered sequence of trip IDs covered by this crew duty."
9
- }
10
- ]
11
- }
 
 
 
 
 
 
 
 
 
 
 
 
ji2019/feasibility_check.py DELETED
@@ -1,808 +0,0 @@
1
- #!/usr/bin/env python3
2
- """
3
- Feasibility checker for the Lock and Quay Co-scheduling Problem (LQCP).
4
- Based on: Ji et al. (2019), "Exact and heuristic methods for optimizing
5
- lock-quay system in inland waterway", EJOR 277, 740-755.
6
-
7
- Checks hard constraints from the mathematical formulation (Eqs. 5-57),
8
- numbered 1-53 in top-to-bottom order of the formulation section.
9
-
10
- Constraint 54 (objective consistency): a Tier C anti-gaming check that
11
- recomputes the objective (Eq. 1: T_1 + T_2 + penalty) from the solution
12
- variables and rejects solutions whose reported objective_value disagrees.
13
- """
14
-
15
- import argparse
16
- import json
17
- import math
18
-
19
- tol = 1e-5
20
- eps = 1e-5
21
-
22
-
23
- def load_json(path):
24
- with open(path, 'r') as f:
25
- return json.load(f)
26
-
27
-
28
- def check_geq(lhs, rhs):
29
- """For >= constraint: violation = max(0, rhs - lhs)."""
30
- return max(0.0, rhs - lhs)
31
-
32
-
33
- def check_leq(lhs, rhs):
34
- """For <= constraint: violation = max(0, lhs - rhs)."""
35
- return max(0.0, lhs - rhs)
36
-
37
-
38
- def check_eq(lhs, rhs):
39
- """For = constraint: violation = |lhs - rhs|."""
40
- return abs(lhs - rhs)
41
-
42
-
43
- def record_violation(violations, magnitudes, violated_set,
44
- constraint_idx, message, lhs, rhs, violation_amount):
45
- normalizer = max(abs(rhs), eps)
46
- ratio = violation_amount / normalizer
47
- violated_set.add(constraint_idx)
48
- violations.append(message)
49
- magnitudes.append({
50
- "constraint": constraint_idx,
51
- "lhs": float(lhs),
52
- "rhs": float(rhs),
53
- "raw_excess": float(violation_amount),
54
- "normalizer": float(normalizer),
55
- "ratio": float(ratio)
56
- })
57
-
58
-
59
- def main():
60
- parser = argparse.ArgumentParser(
61
- description="Feasibility checker for LQCP (Ji et al., 2019)")
62
- parser.add_argument("--instance_path", type=str, required=True,
63
- help="Path to JSON file containing the data instance.")
64
- parser.add_argument("--solution_path", type=str, required=True,
65
- help="Path to JSON file containing the candidate solution.")
66
- parser.add_argument("--result_path", type=str, required=True,
67
- help="Path to write the JSON feasibility result.")
68
- args = parser.parse_args()
69
-
70
- instance = load_json(args.instance_path)
71
- solution = load_json(args.solution_path)
72
-
73
- # ================================================================
74
- # Parse instance data
75
- # ================================================================
76
- n = instance["num_ships"]
77
- m = instance["num_berths"]
78
- W = instance["chamber_width_W"]
79
- L = instance["chamber_length_L"]
80
- Du = instance["lockage_duration_Du"]
81
- MT = instance["min_time_between_lockages_MT"]
82
- sc = instance["lock_start_availability_sc"]
83
- C_max = instance["C_max"]
84
-
85
- ships = instance["ships"]
86
- w = [s["width"] for s in ships]
87
- l_len = [s["length"] for s in ships]
88
- a = [s["arrival_time"] for s in ships]
89
- Pe = [s["transshipment_penalty"] for s in ships]
90
- MR = [s["mooring_set_MR"] for s in ships]
91
- B_eligible = [s["eligible_berths_B"] for s in ships]
92
-
93
- berths_data = instance["berths"]
94
- s_k = [b["start_availability_sk"] for b in berths_data]
95
- e_k_val = instance.get("berth_end_availability_ek", 1000.0)
96
- e_k = [e_k_val] * m
97
- t_ik = instance["handling_times"] # t_ik[i][k]
98
-
99
- # SL and SB: not in instance data; paper experiments use all ships eligible
100
- # for both modes, so SL = SB = empty.
101
- SL = []
102
- SB = []
103
-
104
- N = list(range(n))
105
- Q = list(range(n)) # |Q| = n
106
- P = list(range(n)) # |P| = n
107
-
108
- # ================================================================
109
- # Parse solution — handle both efficient and gurobi formats
110
- # ================================================================
111
- u = {}
112
- for k_str, v in solution["modes"].items():
113
- u[int(k_str)] = int(round(v))
114
-
115
- lock_ships = [i for i in N if u[i] == 0]
116
- trans_ships = [i for i in N if u[i] == 1]
117
-
118
- is_efficient = "lockage_structure" in solution
119
- is_gurobi = "lockage_assignments" in solution
120
-
121
- # f[i,q]: 1 if ship i is transferred by lockage q
122
- f = {}
123
- for i in N:
124
- for q in Q:
125
- f[i, q] = 0
126
-
127
- # z[q]: 1 if lockage q is used
128
- z = {}
129
- for q in Q:
130
- z[q] = 0
131
-
132
- # C_q_val[q]: completion time of lockage q
133
- C_q_val = {}
134
-
135
- # c[i]: completion/departure time of ship i
136
- c = {}
137
-
138
- # delta[i,p,k]: 1 if ship i assigned to p-th order of berth k
139
- delta = {}
140
- for i in N:
141
- for p_val in P:
142
- for k in range(m):
143
- delta[i, p_val, k] = 0
144
-
145
- if is_efficient:
146
- # --- Efficient solution format ---
147
- lockage_structure = solution["lockage_structure"]
148
- for q_idx, ships_in_lockage in enumerate(lockage_structure):
149
- if ships_in_lockage:
150
- z[q_idx] = 1
151
- for ship_i in ships_in_lockage:
152
- f[ship_i, q_idx] = 1
153
-
154
- lock_ct = solution.get("lock_completion_times", {})
155
- for k_str, v in lock_ct.items():
156
- c[int(k_str)] = v
157
-
158
- # Derive C_q from lockage structure
159
- for q_idx, ships_in_lockage in enumerate(lockage_structure):
160
- if ships_in_lockage:
161
- for si in ships_in_lockage:
162
- if si in c:
163
- C_q_val[q_idx] = c[si]
164
- break
165
-
166
- # For transshipment ships: c_i = a_i (from constraints 29-30)
167
- for i in trans_ships:
168
- c[i] = a[i]
169
-
170
- # Berth assignments: {ship_str: berth_k}
171
- berth_asgn = solution.get("berth_assignments", {})
172
- berth_ships_map = {}
173
- for k_str, berth_k in berth_asgn.items():
174
- ship_i = int(k_str)
175
- if berth_k not in berth_ships_map:
176
- berth_ships_map[berth_k] = []
177
- berth_ships_map[berth_k].append(ship_i)
178
-
179
- # Assign orders by arrival time within each berth
180
- for berth_k, ship_list in berth_ships_map.items():
181
- ship_list.sort(key=lambda i: a[i])
182
- for order_p, ship_i in enumerate(ship_list):
183
- delta[ship_i, order_p, berth_k] = 1
184
-
185
- elif is_gurobi:
186
- # --- Gurobi solution format ---
187
- lockage_asgn = solution.get("lockage_assignments", {})
188
- for k_str, q_val in lockage_asgn.items():
189
- ship_i = int(k_str)
190
- q = int(q_val)
191
- f[ship_i, q] = 1
192
- z[q] = 1
193
-
194
- lock_ct = solution.get("lockage_completion_times", {})
195
- for k_str, v in lock_ct.items():
196
- C_q_val[int(k_str)] = v
197
-
198
- comp_times = solution.get("completion_times", {})
199
- for k_str, v in comp_times.items():
200
- c[int(k_str)] = v
201
-
202
- berth_asgn = solution.get("berth_assignments", {})
203
- for k_str, val in berth_asgn.items():
204
- ship_i = int(k_str)
205
- if isinstance(val, dict):
206
- berth_k = val["berth"]
207
- order_p = val["order"]
208
- delta[ship_i, order_p, berth_k] = 1
209
-
210
- # ================================================================
211
- # Feasibility checking
212
- # ================================================================
213
- violations = []
214
- magnitudes = []
215
- violated_set = set()
216
-
217
- # ------------------------------------------------------------------
218
- # Constraints 1-5 (paper Eqs. 5-9): Ship placement and non-overlap
219
- # Require position variables (x_i, y_i) and auxiliary binaries (lt, b)
220
- # which are not present in either solution format. CANNOT CHECK.
221
- # ------------------------------------------------------------------
222
-
223
- # ------------------------------------------------------------------
224
- # Constraint 6 (paper Eq. 10): sum_q f_{iq} = 1 - u_i, for all i
225
- # Each lock-mode ship assigned to exactly one lockage.
226
- # ------------------------------------------------------------------
227
- for i in N:
228
- lhs = sum(f[i, q] for q in Q)
229
- rhs = 1 - u[i]
230
- va = check_eq(lhs, rhs)
231
- if va > tol:
232
- record_violation(violations, magnitudes, violated_set, 6,
233
- f"Constraint 6 (Eq.10): Ship {i}: sum(f_iq)={lhs} != 1-u_i={rhs}",
234
- lhs, rhs, va)
235
-
236
- # ------------------------------------------------------------------
237
- # Constraint 7 (paper Eq. 11): f_{iq} <= z_q, for all i, q
238
- # A ship can only be transferred by a used lockage.
239
- # ------------------------------------------------------------------
240
- for i in N:
241
- for q in Q:
242
- lhs = f[i, q]
243
- rhs_val = z[q]
244
- va = check_leq(lhs, rhs_val)
245
- if va > tol:
246
- record_violation(violations, magnitudes, violated_set, 7,
247
- f"Constraint 7 (Eq.11): Ship {i} assigned to lockage {q} but z_{q}={rhs_val}",
248
- lhs, rhs_val, va)
249
-
250
- # ------------------------------------------------------------------
251
- # Constraints 8-19 (paper Eqs. 12-23): Mooring constraints
252
- # Require ml, mr, x, y variables — not in solution. CANNOT CHECK.
253
- # ------------------------------------------------------------------
254
-
255
- # ------------------------------------------------------------------
256
- # Constraint 20 (paper Eq. 24): Each lock-mode ship must moor
257
- # Requires ml, mr variables — CANNOT CHECK.
258
- # ------------------------------------------------------------------
259
-
260
- # ------------------------------------------------------------------
261
- # Constraint 21 (paper Eq. 25): Prevent both unattached
262
- # Requires ml, mr variables — CANNOT CHECK.
263
- # ------------------------------------------------------------------
264
-
265
- # ------------------------------------------------------------------
266
- # Constraint 22 (paper Eq. 26): ml+mr <= v
267
- # Requires ml, mr, v variables — CANNOT CHECK.
268
- # ------------------------------------------------------------------
269
-
270
- # ------------------------------------------------------------------
271
- # Constraints 23-24 (paper Eqs. 27-28): f and v consistency
272
- # Require v variable — CANNOT CHECK.
273
- # ------------------------------------------------------------------
274
-
275
- # ------------------------------------------------------------------
276
- # Constraints 25-26 (paper Eqs. 29-30): v <= 1-u_i, v <= 1-u_j
277
- # Require v variable — CANNOT CHECK.
278
- # ------------------------------------------------------------------
279
-
280
- # ------------------------------------------------------------------
281
- # Constraint 27 (paper Eq. 31): c_i >= C_max*(f_{iq}-1) + C_q
282
- # ------------------------------------------------------------------
283
- for i in N:
284
- if i not in c:
285
- continue
286
- for q in Q:
287
- if q not in C_q_val:
288
- continue
289
- rhs_val = C_max * (f[i, q] - 1) + C_q_val[q]
290
- lhs = c[i]
291
- va = check_geq(lhs, rhs_val)
292
- if va > tol:
293
- record_violation(violations, magnitudes, violated_set, 27,
294
- f"Constraint 27 (Eq.31): Ship {i}, lockage {q}: "
295
- f"c_i={lhs:.2f} < C_max*(f_iq-1)+C_q={rhs_val:.2f}",
296
- lhs, rhs_val, va)
297
-
298
- # ------------------------------------------------------------------
299
- # Constraint 28 (paper Eq. 32): c_i <= C_max*(1-f_{iq}) + C_q
300
- # ------------------------------------------------------------------
301
- for i in N:
302
- if i not in c:
303
- continue
304
- for q in Q:
305
- if q not in C_q_val:
306
- continue
307
- rhs_val = C_max * (1 - f[i, q]) + C_q_val[q]
308
- lhs = c[i]
309
- va = check_leq(lhs, rhs_val)
310
- if va > tol:
311
- record_violation(violations, magnitudes, violated_set, 28,
312
- f"Constraint 28 (Eq.32): Ship {i}, lockage {q}: "
313
- f"c_i={lhs:.2f} > C_max*(1-f_iq)+C_q={rhs_val:.2f}",
314
- lhs, rhs_val, va)
315
-
316
- # ------------------------------------------------------------------
317
- # Constraint 29 (paper Eq. 33): c_i >= C_max*(u_i-1) + a_i
318
- # ------------------------------------------------------------------
319
- for i in N:
320
- if i not in c:
321
- continue
322
- rhs_val = C_max * (u[i] - 1) + a[i]
323
- lhs = c[i]
324
- va = check_geq(lhs, rhs_val)
325
- if va > tol:
326
- record_violation(violations, magnitudes, violated_set, 29,
327
- f"Constraint 29 (Eq.33): Ship {i}: c_i={lhs:.2f} < "
328
- f"C_max*(u_i-1)+a_i={rhs_val:.2f}",
329
- lhs, rhs_val, va)
330
-
331
- # ------------------------------------------------------------------
332
- # Constraint 30 (paper Eq. 34): c_i <= C_max*(1-u_i) + a_i
333
- # ------------------------------------------------------------------
334
- for i in N:
335
- if i not in c:
336
- continue
337
- rhs_val = C_max * (1 - u[i]) + a[i]
338
- lhs = c[i]
339
- va = check_leq(lhs, rhs_val)
340
- if va > tol:
341
- record_violation(violations, magnitudes, violated_set, 30,
342
- f"Constraint 30 (Eq.34): Ship {i}: c_i={lhs:.2f} > "
343
- f"C_max*(1-u_i)+a_i={rhs_val:.2f}",
344
- lhs, rhs_val, va)
345
-
346
- # ------------------------------------------------------------------
347
- # Constraint 31 (paper Eq. 35): C_{q+1} - C_q >= MT, for q < |Q|-1
348
- # Applied between consecutive lockage indices with known C_q values.
349
- # ------------------------------------------------------------------
350
- for q in range(n - 1):
351
- if q in C_q_val and (q + 1) in C_q_val:
352
- lhs = C_q_val[q + 1] - C_q_val[q]
353
- rhs_val = MT
354
- va = check_geq(lhs, rhs_val)
355
- if va > tol:
356
- record_violation(violations, magnitudes, violated_set, 31,
357
- f"Constraint 31 (Eq.35): Lockages {q},{q+1}: "
358
- f"C_diff={lhs:.2f} < MT={rhs_val}",
359
- lhs, rhs_val, va)
360
-
361
- # ------------------------------------------------------------------
362
- # Constraint 32 (paper Eq. 36): C_q - Du >= sc, for all q
363
- # Lockage cannot start before chamber is available.
364
- # ------------------------------------------------------------------
365
- for q in Q:
366
- if z[q] == 1 and q in C_q_val:
367
- lhs = C_q_val[q] - Du
368
- rhs_val = sc
369
- va = check_geq(lhs, rhs_val)
370
- if va > tol:
371
- record_violation(violations, magnitudes, violated_set, 32,
372
- f"Constraint 32 (Eq.36): Lockage {q}: "
373
- f"C_q-Du={lhs:.2f} < sc={rhs_val}",
374
- lhs, rhs_val, va)
375
-
376
- # ------------------------------------------------------------------
377
- # Constraint 33 (paper Eq. 37): C_q - Du >= f_{iq}*a_i
378
- # Lockage cannot start before all assigned ships have arrived.
379
- # ------------------------------------------------------------------
380
- for i in N:
381
- for q in Q:
382
- if f[i, q] == 1 and q in C_q_val:
383
- lhs = C_q_val[q] - Du
384
- rhs_val = a[i]
385
- va = check_geq(lhs, rhs_val)
386
- if va > tol:
387
- record_violation(violations, magnitudes, violated_set, 33,
388
- f"Constraint 33 (Eq.37): Ship {i}, lockage {q}: "
389
- f"C_q-Du={lhs:.2f} < a_i={rhs_val}",
390
- lhs, rhs_val, va)
391
-
392
- # ------------------------------------------------------------------
393
- # Constraint 34 (paper Eq. 38): z_q <= sum_i f_{iq}
394
- # A lockage is used only if at least one ship is assigned.
395
- # ------------------------------------------------------------------
396
- for q in Q:
397
- lhs = z[q]
398
- rhs_val = sum(f[i, q] for i in N)
399
- va = check_leq(lhs, rhs_val)
400
- if va > tol:
401
- record_violation(violations, magnitudes, violated_set, 34,
402
- f"Constraint 34 (Eq.38): Lockage {q}: z_q={lhs} > sum(f_iq)={rhs_val}",
403
- lhs, rhs_val, va)
404
-
405
- # ------------------------------------------------------------------
406
- # Constraint 35 (paper Eq. 39): c_i - c_j <= C_max*(u_i+u_j), i < j
407
- # FCFS restriction.
408
- # ------------------------------------------------------------------
409
- for i in N:
410
- for j in N:
411
- if i < j and i in c and j in c:
412
- lhs = c[i] - c[j]
413
- rhs_val = C_max * (u[i] + u[j])
414
- va = check_leq(lhs, rhs_val)
415
- if va > tol:
416
- record_violation(violations, magnitudes, violated_set, 35,
417
- f"Constraint 35 (Eq.39 FCFS): Ships {i},{j}: "
418
- f"c_i-c_j={lhs:.2f} > C_max*(u_i+u_j)={rhs_val:.2f}",
419
- lhs, rhs_val, va)
420
-
421
- # ------------------------------------------------------------------
422
- # Constraint 36 (paper Eq. 40): z_{q+1} <= z_q, for q < n-1
423
- # Used lockages are ordered (no gaps).
424
- # ------------------------------------------------------------------
425
- for q in range(n - 1):
426
- lhs = z[q + 1]
427
- rhs_val = z[q]
428
- va = check_leq(lhs, rhs_val)
429
- if va > tol:
430
- record_violation(violations, magnitudes, violated_set, 36,
431
- f"Constraint 36 (Eq.40): z_{q+1}={lhs} > z_{q}={rhs_val}",
432
- lhs, rhs_val, va)
433
-
434
- # ------------------------------------------------------------------
435
- # Constraint 37 (paper Eq. 41): C_q <= C_{q+1}, for q < n-1
436
- # Lockage completion times are non-decreasing.
437
- # ------------------------------------------------------------------
438
- for q in range(n - 1):
439
- if q in C_q_val and (q + 1) in C_q_val:
440
- lhs = C_q_val[q]
441
- rhs_val = C_q_val[q + 1]
442
- va = check_leq(lhs, rhs_val)
443
- if va > tol:
444
- record_violation(violations, magnitudes, violated_set, 37,
445
- f"Constraint 37 (Eq.41): C_{q}={lhs:.2f} > C_{q+1}={rhs_val:.2f}",
446
- lhs, rhs_val, va)
447
-
448
- # ------------------------------------------------------------------
449
- # Constraint 38 (paper Eq. 42):
450
- # sum_{q<l} (f_{iq} - f_{jq}) >= -(u_i + u_j), for i<j, l in Q
451
- # Ordering in lockage assignments.
452
- # ------------------------------------------------------------------
453
- for i in N:
454
- for j in N:
455
- if i < j:
456
- for l_idx in Q:
457
- if l_idx == 0:
458
- continue # empty sum = 0 >= -(u_i+u_j) always true
459
- lhs = sum(f[i, q] - f[j, q] for q in Q if q < l_idx)
460
- rhs_val = -(u[i] + u[j])
461
- va = check_geq(lhs, rhs_val)
462
- if va > tol:
463
- record_violation(violations, magnitudes, violated_set, 38,
464
- f"Constraint 38 (Eq.42): Ships {i},{j}, l={l_idx}: "
465
- f"sum(f_diff)={lhs} < -(u_i+u_j)={rhs_val}",
466
- lhs, rhs_val, va)
467
-
468
- # ------------------------------------------------------------------
469
- # Constraint 39 (paper Eq. 43): u_i = 0, for i in SL
470
- # Ships that can only pass through lock.
471
- # ------------------------------------------------------------------
472
- for i in SL:
473
- lhs = u[i]
474
- rhs_val = 0
475
- va = check_eq(lhs, rhs_val)
476
- if va > tol:
477
- record_violation(violations, magnitudes, violated_set, 39,
478
- f"Constraint 39 (Eq.43): Ship {i} in SL but u_i={lhs} != 0",
479
- lhs, rhs_val, va)
480
-
481
- # ------------------------------------------------------------------
482
- # Constraint 40 (paper Eq. 48): u_i = 1, for i in SB
483
- # Ships that can only be transshipped.
484
- # ------------------------------------------------------------------
485
- for i in SB:
486
- lhs = u[i]
487
- rhs_val = 1
488
- va = check_eq(lhs, rhs_val)
489
- if va > tol:
490
- record_violation(violations, magnitudes, violated_set, 40,
491
- f"Constraint 40 (Eq.48): Ship {i} in SB but u_i={lhs} != 1",
492
- lhs, rhs_val, va)
493
-
494
- # ------------------------------------------------------------------
495
- # Constraint 41 (paper Eq. 44):
496
- # sum_{k in B(i)} sum_p delta_{ipk} = u_i, for all i
497
- # Each transshipment-mode ship assigned to exactly one berth.
498
- # ------------------------------------------------------------------
499
- for i in N:
500
- lhs = sum(delta[i, p_val, k] for k in B_eligible[i] for p_val in P)
501
- rhs_val = u[i]
502
- va = check_eq(lhs, rhs_val)
503
- if va > tol:
504
- record_violation(violations, magnitudes, violated_set, 41,
505
- f"Constraint 41 (Eq.44): Ship {i}: sum(delta)={lhs} != u_i={rhs_val}",
506
- lhs, rhs_val, va)
507
-
508
- # ------------------------------------------------------------------
509
- # Constraint 42 (paper Eq. 45):
510
- # sum_i delta_{ipk} <= 1, for k in M, p in P
511
- # Each berth serves at most one ship per service order.
512
- # ------------------------------------------------------------------
513
- for k in range(m):
514
- for p_val in P:
515
- lhs = sum(delta[i, p_val, k] for i in N)
516
- rhs_val = 1
517
- va = check_leq(lhs, rhs_val)
518
- if va > tol:
519
- record_violation(violations, magnitudes, violated_set, 42,
520
- f"Constraint 42 (Eq.45): Berth {k}, order {p_val}: "
521
- f"sum(delta)={lhs} > 1",
522
- lhs, rhs_val, va)
523
-
524
- # ------------------------------------------------------------------
525
- # Constraint 43 (paper Eq. 46): Idle time constraint at berth
526
- # sum_{j,l<p} (t_jk*delta_jlk + omega_jlk) + omega_ipk
527
- # - (a_i - s_k)*delta_ipk >= 0
528
- # for k in M, i in N(k), p in P
529
- #
530
- # Since omega is not in the solution, we derive omega from the
531
- # schedule. omega_ipk = max(0, a_i - berth_free_time) when
532
- # delta_ipk=1. The constraint is satisfied iff for each ship at its
533
- # assigned berth position, the berth is free at or before the ship's
534
- # arrival, or the ship waits (omega >= 0 is always true).
535
- # We verify the schedule consistency: each ship at its berth starts
536
- # at or after its arrival time (no time travel).
537
- # ------------------------------------------------------------------
538
- for k in range(m):
539
- # Collect ships assigned to berth k, sorted by order
540
- berth_ships_ordered = []
541
- for i in N:
542
- for p_val in P:
543
- if delta[i, p_val, k] == 1:
544
- berth_ships_ordered.append((p_val, i))
545
- berth_ships_ordered.sort()
546
-
547
- current_time = s_k[k]
548
- for order_p, ship_i in berth_ships_ordered:
549
- # N(k) check: only ships with a_i >= s_k are in constraint scope
550
- if a[ship_i] >= s_k[k]:
551
- # The cumulative berth time up to this position
552
- cumulative = current_time - s_k[k]
553
- rhs_val = (a[ship_i] - s_k[k]) # (a_i - s_k) * delta_ipk with delta=1
554
- # omega_ipk = max(0, a[ship_i] - current_time)
555
- omega_ipk = max(0.0, a[ship_i] - current_time)
556
- lhs = cumulative + omega_ipk
557
- va = check_geq(lhs, rhs_val)
558
- if va > tol:
559
- record_violation(violations, magnitudes, violated_set, 43,
560
- f"Constraint 43 (Eq.46): Ship {ship_i}, berth {k}, "
561
- f"order {order_p}: schedule time={lhs:.2f} < "
562
- f"(a_i-s_k)={rhs_val:.2f}",
563
- lhs, rhs_val, va)
564
-
565
- start = max(current_time, a[ship_i])
566
- current_time = start + t_ik[ship_i][k]
567
-
568
- # ------------------------------------------------------------------
569
- # Constraint 44 (paper Eq. 47): Berth availability time
570
- # sum_i sum_p (t_ik*delta_ipk + omega_ipk) <= e_k - s_k
571
- # Equivalent to: last ship finishes by e_k.
572
- # ------------------------------------------------------------------
573
- for k in range(m):
574
- berth_ships_ordered = []
575
- for i in N:
576
- for p_val in P:
577
- if delta[i, p_val, k] == 1:
578
- berth_ships_ordered.append((p_val, i))
579
- berth_ships_ordered.sort()
580
-
581
- if not berth_ships_ordered:
582
- continue
583
-
584
- # Compute total used time = sum of (handling + idle)
585
- current_time = s_k[k]
586
- total_used = 0.0
587
- for order_p, ship_i in berth_ships_ordered:
588
- start = max(current_time, a[ship_i])
589
- idle = start - current_time
590
- handling = t_ik[ship_i][k]
591
- total_used += handling + idle
592
- current_time = start + handling
593
-
594
- lhs = total_used
595
- rhs_val = e_k[k] - s_k[k]
596
- va = check_leq(lhs, rhs_val)
597
- if va > tol:
598
- record_violation(violations, magnitudes, violated_set, 44,
599
- f"Constraint 44 (Eq.47): Berth {k}: total_time={lhs:.2f} > "
600
- f"available={rhs_val:.2f}",
601
- lhs, rhs_val, va)
602
-
603
- # ------------------------------------------------------------------
604
- # Constraint 45 (paper Eq. 49): u_i in {0,1}
605
- # ------------------------------------------------------------------
606
- for i in N:
607
- if u[i] not in (0, 1):
608
- va = min(abs(u[i] - 0), abs(u[i] - 1))
609
- record_violation(violations, magnitudes, violated_set, 45,
610
- f"Constraint 45 (Eq.49): Ship {i}: u_i={u[i]} not binary",
611
- float(u[i]), float(round(u[i])), va)
612
-
613
- # ------------------------------------------------------------------
614
- # Constraints 46-48 (paper Eqs. 50-52): lt, b, ml, mr binarity
615
- # Variables not in solution — CANNOT CHECK.
616
- # ------------------------------------------------------------------
617
-
618
- # ------------------------------------------------------------------
619
- # Constraint 49 (paper Eq. 53): v, z binary
620
- # v not in solution; check z only.
621
- # ------------------------------------------------------------------
622
- for q in Q:
623
- if z[q] not in (0, 1):
624
- va = min(abs(z[q] - 0), abs(z[q] - 1))
625
- record_violation(violations, magnitudes, violated_set, 49,
626
- f"Constraint 49 (Eq.53): z_{q}={z[q]} not binary",
627
- float(z[q]), float(round(z[q])), va)
628
-
629
- # ------------------------------------------------------------------
630
- # Constraint 50 (paper Eq. 54): 0 <= c_i <= C_max, 0 <= C_q <= C_max
631
- # ------------------------------------------------------------------
632
- for i in N:
633
- if i in c:
634
- if c[i] < -tol:
635
- va = abs(c[i])
636
- record_violation(violations, magnitudes, violated_set, 50,
637
- f"Constraint 50 (Eq.54): Ship {i}: c_i={c[i]:.2f} < 0",
638
- c[i], 0.0, va)
639
- if c[i] > C_max + tol:
640
- va = c[i] - C_max
641
- record_violation(violations, magnitudes, violated_set, 50,
642
- f"Constraint 50 (Eq.54): Ship {i}: c_i={c[i]:.2f} > C_max={C_max}",
643
- c[i], float(C_max), va)
644
-
645
- for q in Q:
646
- if q in C_q_val:
647
- if C_q_val[q] < -tol:
648
- va = abs(C_q_val[q])
649
- record_violation(violations, magnitudes, violated_set, 50,
650
- f"Constraint 50 (Eq.54): Lockage {q}: C_q={C_q_val[q]:.2f} < 0",
651
- C_q_val[q], 0.0, va)
652
- if C_q_val[q] > C_max + tol:
653
- va = C_q_val[q] - C_max
654
- record_violation(violations, magnitudes, violated_set, 50,
655
- f"Constraint 50 (Eq.54): Lockage {q}: C_q={C_q_val[q]:.2f} > C_max={C_max}",
656
- C_q_val[q], float(C_max), va)
657
-
658
- # ------------------------------------------------------------------
659
- # Constraint 51 (paper Eq. 55): f_{iq} in {0,1}
660
- # ------------------------------------------------------------------
661
- for i in N:
662
- for q in Q:
663
- if f[i, q] not in (0, 1):
664
- va = min(abs(f[i, q] - 0), abs(f[i, q] - 1))
665
- record_violation(violations, magnitudes, violated_set, 51,
666
- f"Constraint 51 (Eq.55): f_{i},{q}={f[i,q]} not binary",
667
- float(f[i, q]), float(round(f[i, q])), va)
668
-
669
- # ------------------------------------------------------------------
670
- # Constraint 52 (paper Eq. 56): x_i, y_i non-negative integer
671
- # Variables not in solution — CANNOT CHECK.
672
- # ------------------------------------------------------------------
673
-
674
- # ------------------------------------------------------------------
675
- # Constraint 53 (paper Eq. 57): delta binary, omega >= 0
676
- # omega is derived (always >= 0 by construction); check delta.
677
- # ------------------------------------------------------------------
678
- for i in N:
679
- for p_val in P:
680
- for k in range(m):
681
- if delta[i, p_val, k] not in (0, 1):
682
- va = min(abs(delta[i, p_val, k] - 0),
683
- abs(delta[i, p_val, k] - 1))
684
- record_violation(violations, magnitudes, violated_set, 53,
685
- f"Constraint 53 (Eq.57): delta_{i},{p_val},{k}="
686
- f"{delta[i,p_val,k]} not binary",
687
- float(delta[i, p_val, k]),
688
- float(round(delta[i, p_val, k])), va)
689
-
690
- # ------------------------------------------------------------------
691
- # Constraint 54 (objective consistency — Tier C anti-gaming check):
692
- # Recompute the objective from the solution variables and reject the
693
- # solution when the reported objective_value disagrees.
694
- #
695
- # obj = T_1 + T_2 + penalty (Eq. 1)
696
- # T_1 = sum_{i in N} (c_i - a_i) (Eq. 2)
697
- # T_2 = sum_{k,i,p} [ (n-p+1) t_ik + s_k - a_i ] delta_ipk
698
- # + sum_{k,i,p} (n-p+1) omega_ipk (Eq. 3)
699
- # penalty = sum_{i in N} Pe_i u_i
700
- #
701
- # omega_ipk (berth idle time) is not in the solution; it is
702
- # reconstructed as the minimum feasible berth idle — the value any
703
- # objective-minimizing solver uses, and exactly the reconstruction
704
- # constraints 43/44 already rely on. This makes the recompute an
705
- # exact, full recompute: it reproduces gurobi_code.py's objective
706
- # bit-for-bit on all five Gurobi reference solutions (diff = 0).
707
- #
708
- # The check is purely additive: it only ever adds constraint index
709
- # 54 (the next unused index after the 1-53 formulation constraints).
710
- # ------------------------------------------------------------------
711
- reported_obj = solution.get("objective_value")
712
- try:
713
- reported = float(reported_obj) if reported_obj is not None else None
714
- except (TypeError, ValueError):
715
- reported = None
716
- if reported is not None:
717
- try:
718
- # Only recompute when every ship has a completion time; a
719
- # partial recompute would be unreliable, so skip silently.
720
- if all(i in c for i in N):
721
- # T_1: total delay (completion - arrival) over all ships.
722
- T_1 = sum(c[i] - a[i] for i in N)
723
-
724
- # T_2: weighted berth delay with min-idle omega.
725
- T_2 = 0.0
726
- for k in range(m):
727
- berth_ships_ordered = []
728
- for i in N:
729
- for p_val in P:
730
- if delta[i, p_val, k] == 1:
731
- berth_ships_ordered.append((p_val, i))
732
- berth_ships_ordered.sort()
733
-
734
- berth_time = s_k[k]
735
- for order_p, ship_i in berth_ships_ordered:
736
- weight = n - order_p + 1
737
- T_2 += weight * t_ik[ship_i][k] + s_k[k] - a[ship_i]
738
- omega_ipk = max(0.0, a[ship_i] - berth_time)
739
- T_2 += weight * omega_ipk
740
- berth_time = max(berth_time, a[ship_i]) \
741
- + t_ik[ship_i][k]
742
-
743
- # Transshipment-mode penalty term.
744
- penalty = sum(Pe[i] * u[i] for i in N)
745
-
746
- true_obj = T_1 + T_2 + penalty
747
- abs_diff = abs(reported - true_obj)
748
- # 0.1% relative tolerance with a 1e-3 absolute floor.
749
- obj_tol = max(1e-3, 1e-3 * abs(true_obj))
750
- if abs_diff > obj_tol:
751
- record_violation(violations, magnitudes, violated_set, 54,
752
- f"Constraint 54 (objective consistency): reported "
753
- f"objective_value={reported} differs from recomputed "
754
- f"T1+T2+penalty={true_obj} "
755
- f"(T1={T_1}, T2={T_2}, penalty={penalty}, "
756
- f"|diff|={abs_diff:.6g}, tol={obj_tol:.3g})",
757
- reported, true_obj, abs_diff)
758
- except Exception:
759
- # A recompute failure must never crash the checker or alter
760
- # any constraint verdict — skip the obj check instead.
761
- pass
762
-
763
- # ================================================================
764
- # Build and write result
765
- # ================================================================
766
- feasible = len(violated_set) == 0
767
-
768
- # Aggregate violation messages by constraint index
769
- constraint_messages = {}
770
- for msg in violations:
771
- # Extract constraint index from message
772
- for ci in violated_set:
773
- prefix = f"Constraint {ci} "
774
- if msg.startswith(prefix):
775
- if ci not in constraint_messages:
776
- constraint_messages[ci] = []
777
- constraint_messages[ci].append(msg)
778
- break
779
-
780
- # Create aggregated violations list aligned with violated_constraints
781
- sorted_violated = sorted(list(violated_set))
782
- aggregated_violations = []
783
- for ci in sorted_violated:
784
- msgs = constraint_messages.get(ci, [])
785
- if len(msgs) <= 3:
786
- aggregated_violations.append("; ".join(msgs))
787
- else:
788
- aggregated_violations.append(
789
- f"{msgs[0]}; ... ({len(msgs)} total violations for constraint {ci})")
790
-
791
- result = {
792
- "feasible": feasible,
793
- "violated_constraints": sorted_violated,
794
- "violations": aggregated_violations,
795
- "violation_magnitudes": magnitudes if not feasible else []
796
- }
797
-
798
- with open(args.result_path, 'w') as f:
799
- json.dump(result, f, indent=2)
800
-
801
- if feasible:
802
- print("Solution is FEASIBLE.")
803
- else:
804
- print(f"Solution is INFEASIBLE. Violated constraints: {sorted_violated}")
805
-
806
-
807
- if __name__ == "__main__":
808
- main()
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ji2019/gurobi_code.py DELETED
@@ -1,624 +0,0 @@
1
- """
2
- Gurobi MILP implementation for the Lock and Quay Co-scheduling Problem (LQCP).
3
- Based on: Ji et al. (2019), "Exact and heuristic methods for optimizing
4
- lock-quay system in inland waterway", EJOR 277, 740-755.
5
-
6
- Implements the full MILP model (Eqs. 1-57) from the paper.
7
- """
8
-
9
- import argparse
10
- import json
11
- import gurobipy as gp
12
- from gurobipy import GRB
13
- import os as _os, sys as _sys
14
- # Walk up from this file's directory to find repo root (containing scripts/).
15
- _repo = _os.path.dirname(_os.path.abspath(__file__))
16
- while _repo != _os.path.dirname(_repo) and not _os.path.isdir(_os.path.join(_repo, 'scripts', 'utils')):
17
- _repo = _os.path.dirname(_repo)
18
- if _os.path.isdir(_os.path.join(_repo, 'scripts', 'utils')):
19
- _sys.path.insert(0, _repo)
20
- try:
21
- from scripts.utils.gurobi_log_helper import install_gurobi_logger
22
- except ImportError:
23
- def install_gurobi_logger(log_path): # no-op fallback when scripts/ unavailable
24
- pass
25
-
26
-
27
- def load_instance(instance_path):
28
- """Load instance data from JSON file."""
29
- with open(instance_path, 'r') as f:
30
- data = json.load(f)
31
- return data
32
-
33
-
34
- def build_and_solve_model(data, time_limit):
35
- """Build and solve the LQCP MILP model."""
36
-
37
- # ----- Extract data -----
38
- n = data["num_ships"]
39
- m = data["num_berths"]
40
- W = data["chamber_width_W"]
41
- L = data["chamber_length_L"]
42
- Du = data["lockage_duration_Du"]
43
- MT = data["min_time_between_lockages_MT"]
44
- sc = data["lock_start_availability_sc"]
45
- C_max = data["C_max"]
46
-
47
- ships = data["ships"]
48
- berths = data["berths"]
49
- handling_times = data["handling_times"] # handling_times[i][k]
50
-
51
- # Ship properties
52
- w = {i: ships[i]["width"] for i in range(n)}
53
- l = {i: ships[i]["length"] for i in range(n)}
54
- a = {i: ships[i]["arrival_time"] for i in range(n)}
55
- Pe = {i: ships[i]["transshipment_penalty"] for i in range(n)}
56
- MR = {i: ships[i]["mooring_set_MR"] for i in range(n)}
57
- B_eligible = {i: ships[i]["eligible_berths_B"] for i in range(n)}
58
-
59
- # Berth properties
60
- s_k = {k: berths[k]["start_availability_sk"] for k in range(m)}
61
- # Berth end availability
62
- e_k_val = data.get("berth_end_availability_ek", 1000.0)
63
- e_k = {k: e_k_val for k in range(m)}
64
-
65
- # Handling times t[i][k]
66
- t = {}
67
- for i in range(n):
68
- for k in range(m):
69
- t[i, k] = handling_times[i][k]
70
-
71
- # Sets
72
- N = list(range(n))
73
- M = list(range(m))
74
- Q = list(range(n)) # |Q| = n (upper bound on lockages)
75
- P = list(range(n)) # |P| = n (service orders)
76
-
77
- # N(k) = {i in N : a_i >= s_k} — ships arriving after berth k becomes available
78
- N_k = {}
79
- for k in M:
80
- N_k[k] = [i for i in N if a[i] >= s_k[k]]
81
-
82
- # P(p) = {l in P : l < p} — service orders before p
83
- # Used inline below
84
-
85
- # **NOT SPECIFIED IN PAPER**: Sets SL and SB are not explicitly defined in the
86
- # instance data. The paper states "all ships can choose both modes" in experiments.
87
- # Inferred assumption: SL = empty, SB = empty (all ships can choose either mode).
88
- SL = []
89
- SB = []
90
-
91
- # ----- Create model -----
92
- model = gp.Model("LQCP")
93
- model.setParam("Threads", 1)
94
- model.setParam("TimeLimit", time_limit)
95
- model.setParam("OutputFlag", 1)
96
-
97
- # ----- Decision variables -----
98
- # u_i: mode chosen by ship i (1=transshipment, 0=lock)
99
- u = model.addVars(N, vtype=GRB.BINARY, name="u")
100
-
101
- # x_i, y_i: position of ship i in lock chamber
102
- x = model.addVars(N, vtype=GRB.INTEGER, lb=0, name="x")
103
- y = model.addVars(N, vtype=GRB.INTEGER, lb=0, name="y")
104
-
105
- # lt_{ij}: ship i completely to the left of ship j
106
- lt = model.addVars(N, N, vtype=GRB.BINARY, name="lt")
107
-
108
- # b_{ij}: ship i completely behind ship j
109
- b = model.addVars(N, N, vtype=GRB.BINARY, name="b")
110
-
111
- # ml_{ij}, mr_{ij}: mooring variables
112
- ml = {}
113
- mr = {}
114
- for i in N:
115
- for j in MR[i]:
116
- ml[i, j] = model.addVar(vtype=GRB.BINARY, name=f"ml_{i}_{j}")
117
- mr[i, j] = model.addVar(vtype=GRB.BINARY, name=f"mr_{i}_{j}")
118
-
119
- # ml_{i,n+1}: ship i moors to chamber's right side
120
- ml_right = model.addVars(N, vtype=GRB.BINARY, name="ml_right")
121
- # mr_{i,0}: ship i moors to chamber's left side
122
- mr_left = model.addVars(N, vtype=GRB.BINARY, name="mr_left")
123
-
124
- # z_q: whether lockage q is used
125
- z = model.addVars(Q, vtype=GRB.BINARY, name="z")
126
-
127
- # f_{iq}: ship i transferred by lockage q
128
- f = model.addVars(N, Q, vtype=GRB.BINARY, name="f")
129
-
130
- # v_{ij}: ships i and j in the same lockage (i < j)
131
- v = {}
132
- for i in N:
133
- for j in N:
134
- if i < j:
135
- v[i, j] = model.addVar(vtype=GRB.BINARY, name=f"v_{i}_{j}")
136
-
137
- # c_i: departure/completion time of ship i
138
- c = model.addVars(N, lb=0, ub=C_max, vtype=GRB.CONTINUOUS, name="c")
139
-
140
- # C_q: completion time of lockage q
141
- C = model.addVars(Q, lb=0, ub=C_max, vtype=GRB.CONTINUOUS, name="C_lock")
142
-
143
- # delta_{ipk}: ship i assigned to p-th order of berth k
144
- delta = model.addVars(N, P, M, vtype=GRB.BINARY, name="delta")
145
-
146
- # omega_{ipk}: idle time of berth k before arrival of ship i at p-th order
147
- omega = model.addVars(N, P, M, lb=0, vtype=GRB.CONTINUOUS, name="omega")
148
-
149
- model.update()
150
-
151
- # ----- Objective function (Eq. 1, 2, 4) -----
152
- # T_1 = sum_{i in N} (c_i - a_i)
153
- T_1 = gp.quicksum(c[i] - a[i] for i in N)
154
-
155
- # T_2 (linearized, Eq. 4):
156
- # T_2 = sum_{k in M} sum_{i in N} sum_{p in P}
157
- # { sum_{j in N} sum_{l in P(p)} (t_{jk} * delta_{jlk} + omega_{jlk})
158
- # + omega_{ipk} + t_{ik} + s_k - a_i } * delta_{ipk}
159
- #
160
- # This is nonlinear due to delta_{ipk} multiplying sum terms that also contain delta.
161
- # The paper says Eq. (4) is the linearized version. Looking more carefully at Eq. (4),
162
- # the entire expression inside { } is multiplied by delta_{ipk}, making it quadratic.
163
- #
164
- # **INFERRED ASSUMPTION**: We use Eq. (3) which is the equivalent nonlinear form:
165
- # T_2 = sum_{k in M} sum_{i in N} sum_{p in P} {(n - p + 1) * t_{ik} + s_k - a_i} * delta_{ipk}
166
- # + sum_{k in M} sum_{i in N} sum_{p in P} (n - p + 1) * omega_{ipk}
167
- # This is actually linear since delta_{ipk} multiplies constants and omega_{ipk} is
168
- # multiplied by a constant.
169
-
170
- T_2 = gp.quicksum(
171
- ((n - p + 1) * t[i, k] + s_k[k] - a[i]) * delta[i, p, k]
172
- for k in M for i in N for p in P
173
- ) + gp.quicksum(
174
- (n - p + 1) * omega[i, p, k]
175
- for k in M for i in N for p in P
176
- )
177
-
178
- # Penalty term
179
- penalty = gp.quicksum(Pe[i] * u[i] for i in N)
180
-
181
- model.setObjective(T_1 + T_2 + penalty, GRB.MINIMIZE)
182
-
183
- # ----- Constraints -----
184
-
185
- # --- Ship Placement Sub-problem (Constraints 5-30) ---
186
-
187
- # (5) Non-overlap: lt_{ij} + lt_{ji} + b_{ij} + b_{ji} + (1-f_{iq}) + (1-f_{jq}) >= 1
188
- # for i < j, q in Q
189
- for i in N:
190
- for j in N:
191
- if i < j:
192
- for q in Q:
193
- model.addConstr(
194
- lt[i, j] + lt[j, i] + b[i, j] + b[j, i]
195
- + (1 - f[i, q]) + (1 - f[j, q]) >= 1,
196
- name=f"nonoverlap_{i}_{j}_{q}"
197
- )
198
-
199
- # (6) x_i + w_i <= x_j + W*(1 - lt_{ij}), for i != j
200
- for i in N:
201
- for j in N:
202
- if i != j:
203
- model.addConstr(
204
- x[i] + w[i] <= x[j] + W * (1 - lt[i, j]),
205
- name=f"lt_x_{i}_{j}"
206
- )
207
-
208
- # (7) y_i + l_i <= y_j + L*(1 - b_{ij}), for i != j
209
- for i in N:
210
- for j in N:
211
- if i != j:
212
- model.addConstr(
213
- y[i] + l[i] <= y[j] + L * (1 - b[i, j]),
214
- name=f"b_y_{i}_{j}"
215
- )
216
-
217
- # (8) x_i + w_i <= W
218
- for i in N:
219
- model.addConstr(x[i] + w[i] <= W, name=f"dim_x_{i}")
220
-
221
- # (9) y_i + l_i <= L
222
- for i in N:
223
- model.addConstr(y[i] + l[i] <= L, name=f"dim_y_{i}")
224
-
225
- # (10) sum_{q in Q} f_{iq} = 1 - u_i
226
- for i in N:
227
- model.addConstr(
228
- gp.quicksum(f[i, q] for q in Q) == 1 - u[i],
229
- name=f"lockage_assign_{i}"
230
- )
231
-
232
- # (11) f_{iq} <= z_q
233
- for i in N:
234
- for q in Q:
235
- model.addConstr(f[i, q] <= z[q], name=f"lockage_used_{i}_{q}")
236
-
237
- # Mooring constraints (12)-(15): ship i moors to LEFT of ship j
238
- for i in N:
239
- for j in MR[i]:
240
- # (12) y_j - y_i <= (1 - ml_{ij}) * L
241
- model.addConstr(
242
- y[j] - y[i] <= (1 - ml[i, j]) * L,
243
- name=f"ml_y1_{i}_{j}"
244
- )
245
- # (13) y_i - y_j <= l_j - l_i + (1 - ml_{ij}) * L
246
- model.addConstr(
247
- y[i] - y[j] <= l[j] - l[i] + (1 - ml[i, j]) * L,
248
- name=f"ml_y2_{i}_{j}"
249
- )
250
- # (14) x_j - x_i <= w_i + (1 - ml_{ij}) * W
251
- model.addConstr(
252
- x[j] - x[i] <= w[i] + (1 - ml[i, j]) * W,
253
- name=f"ml_x1_{i}_{j}"
254
- )
255
- # (15) x_j - x_i >= w_i - (1 - ml_{ij}) * W
256
- model.addConstr(
257
- x[j] - x[i] >= w[i] - (1 - ml[i, j]) * W,
258
- name=f"ml_x2_{i}_{j}"
259
- )
260
-
261
- # (16)-(17): Ship i adjacent to chamber's right side (sp_{n+1}: x_{n+1}=W)
262
- for i in N:
263
- # (16) x_{n+1} - x_i <= w_i + (1 - ml_{i,n+1}) * W
264
- # x_{n+1} = W, so: W - x_i <= w_i + (1 - ml_right[i]) * W
265
- model.addConstr(
266
- W - x[i] <= w[i] + (1 - ml_right[i]) * W,
267
- name=f"mlright_x1_{i}"
268
- )
269
- # (17) x_{n+1} - x_i >= w_i - (1 - ml_{i,n+1}) * W
270
- # W - x_i >= w_i - (1 - ml_right[i]) * W
271
- model.addConstr(
272
- W - x[i] >= w[i] - (1 - ml_right[i]) * W,
273
- name=f"mlright_x2_{i}"
274
- )
275
-
276
- # Mooring constraints (18)-(21): ship i moors to RIGHT of ship j
277
- for i in N:
278
- for j in MR[i]:
279
- # (18) y_j - y_i <= (1 - mr_{ij}) * L
280
- model.addConstr(
281
- y[j] - y[i] <= (1 - mr[i, j]) * L,
282
- name=f"mr_y1_{i}_{j}"
283
- )
284
- # (19) y_i - y_j <= l_j - l_i + (1 - mr_{ij}) * L
285
- model.addConstr(
286
- y[i] - y[j] <= l[j] - l[i] + (1 - mr[i, j]) * L,
287
- name=f"mr_y2_{i}_{j}"
288
- )
289
- # (20) x_j - x_i <= -w_j + (1 - mr_{ij}) * W
290
- model.addConstr(
291
- x[j] - x[i] <= -w[j] + (1 - mr[i, j]) * W,
292
- name=f"mr_x1_{i}_{j}"
293
- )
294
- # (21) x_j - x_i >= -w_j - (1 - mr_{ij}) * W
295
- model.addConstr(
296
- x[j] - x[i] >= -w[j] - (1 - mr[i, j]) * W,
297
- name=f"mr_x2_{i}_{j}"
298
- )
299
-
300
- # (22)-(23): Ship i adjacent to chamber's left side (sp_0: x_0=0)
301
- for i in N:
302
- # (22) x_0 - x_i <= -w_i + (1 - mr_{i,0}) * W
303
- # x_0 = 0: -x_i <= -w_i + (1 - mr_left[i]) * W
304
- model.addConstr(
305
- -x[i] <= -w[i] + (1 - mr_left[i]) * W,
306
- name=f"mrleft_x1_{i}"
307
- )
308
- # (23) x_0 - x_i >= -w_i - (1 - mr_{i,0}) * W
309
- # -x_i >= -w_i - (1 - mr_left[i]) * W
310
- model.addConstr(
311
- -x[i] >= -w[i] - (1 - mr_left[i]) * W,
312
- name=f"mrleft_x2_{i}"
313
- )
314
-
315
- # (24) Each lock-mode ship must moor to another ship or chamber side
316
- # sum_{j in MR_i} (ml_{ij} + mr_{ij}) + mr_{i,0} + ml_{i,n+1} >= 1 - u_i
317
- # Note: The paper has "sum_{t in TP} ml_{i,n+1}" but this is just ml_{i,n+1}.
318
- for i in N:
319
- model.addConstr(
320
- gp.quicksum(ml[i, j] + mr[i, j] for j in MR[i])
321
- + mr_left[i] + ml_right[i] >= 1 - u[i],
322
- name=f"moor_required_{i}"
323
- )
324
-
325
- # (25) Prevent two ships of same length both unattached
326
- # ml_{ij} + mr_{ji} <= 1, for i in N, j in MR_i
327
- for i in N:
328
- for j in MR[i]:
329
- if (j, i) in mr: # mr_{ji} exists if i in MR[j]
330
- model.addConstr(
331
- ml[i, j] + mr[j, i] <= 1,
332
- name=f"no_both_unattached_{i}_{j}"
333
- )
334
-
335
- # (26) Two ships not in same lockage cannot moor: ml_{ij} + mr_{ij} <= v_{ij}
336
- for i in N:
337
- for j in MR[i]:
338
- if i < j and (i, j) in v:
339
- model.addConstr(
340
- ml[i, j] + mr[i, j] <= v[i, j],
341
- name=f"moor_same_lockage_a_{i}_{j}"
342
- )
343
- elif j < i and (j, i) in v:
344
- model.addConstr(
345
- ml[i, j] + mr[i, j] <= v[j, i],
346
- name=f"moor_same_lockage_b_{i}_{j}"
347
- )
348
-
349
- # (27) f_{iq} - f_{jq} <= 1 - v_{ij}, for i < j, q in Q
350
- for i in N:
351
- for j in N:
352
- if i < j:
353
- for q in Q:
354
- model.addConstr(
355
- f[i, q] - f[j, q] <= 1 - v[i, j],
356
- name=f"same_lockage1_{i}_{j}_{q}"
357
- )
358
-
359
- # (28) f_{jq} - f_{iq} <= 1 - v_{ij}, for i < j, q in Q
360
- for i in N:
361
- for j in N:
362
- if i < j:
363
- for q in Q:
364
- model.addConstr(
365
- f[j, q] - f[i, q] <= 1 - v[i, j],
366
- name=f"same_lockage2_{i}_{j}_{q}"
367
- )
368
-
369
- # (29) v_{ij} < 1 - u_i => v_{ij} <= 1 - u_i - epsilon
370
- # Since v is binary and u is binary, v_{ij} < 1 - u_i means v_{ij} + u_i <= 0 when u_i=1
371
- # Equivalent to: v_{ij} <= 1 - u_i (since strict < with integers means <=)
372
- # Actually with binary: v_{ij} < 1 - u_i. If u_i = 0, v_{ij} < 1 so v_{ij} = 0 doesn't help.
373
- # If u_i = 0, v_{ij} can be 0. If u_i = 1, v_{ij} < 0 impossible.
374
- # The paper uses strict inequality. For binary variables, v_{ij} < 1-u_i is equivalent
375
- # to v_{ij} <= -u_i when u_i=1 (impossible for v>=0), so v_{ij} + u_i <= 0.
376
- # But if u_i = 0, v_{ij} < 1 which is v_{ij} = 0 for binary.
377
- # Actually re-reading: this should just be v_{ij} <= 1 - u_i for practical purposes.
378
- for i in N:
379
- for j in N:
380
- if i < j:
381
- model.addConstr(
382
- v[i, j] <= 1 - u[i],
383
- name=f"v_mode1_{i}_{j}"
384
- )
385
-
386
- # (30) v_{ij} <= 1 - u_j
387
- for i in N:
388
- for j in N:
389
- if i < j:
390
- model.addConstr(
391
- v[i, j] <= 1 - u[j],
392
- name=f"v_mode2_{i}_{j}"
393
- )
394
-
395
- # --- Lockage Scheduling Sub-problem (Constraints 31-42) ---
396
-
397
- # (31) c_i >= C_max*(f_{iq} - 1) + C_q
398
- for i in N:
399
- for q in Q:
400
- model.addConstr(
401
- c[i] >= C_max * (f[i, q] - 1) + C[q],
402
- name=f"comp_time_lb_{i}_{q}"
403
- )
404
-
405
- # (32) c_i <= C_max*(1 - f_{iq}) + C_q
406
- for i in N:
407
- for q in Q:
408
- model.addConstr(
409
- c[i] <= C_max * (1 - f[i, q]) + C[q],
410
- name=f"comp_time_ub_{i}_{q}"
411
- )
412
-
413
- # (33) c_i >= C_max*(u_i - 1) + a_i
414
- for i in N:
415
- model.addConstr(
416
- c[i] >= C_max * (u[i] - 1) + a[i],
417
- name=f"trans_comp_lb_{i}"
418
- )
419
-
420
- # (34) c_i <= C_max*(1 - u_i) + a_i
421
- for i in N:
422
- model.addConstr(
423
- c[i] <= C_max * (1 - u[i]) + a[i],
424
- name=f"trans_comp_ub_{i}"
425
- )
426
-
427
- # (35) C_{q+1} - C_q >= MT, for q < |Q|
428
- for q in Q:
429
- if q < n - 1:
430
- model.addConstr(
431
- C[q + 1] - C[q] >= MT,
432
- name=f"min_interval_{q}"
433
- )
434
-
435
- # (36) C_q - Du >= sc
436
- for q in Q:
437
- model.addConstr(C[q] - Du >= sc, name=f"chamber_avail_{q}")
438
-
439
- # (37) C_q - Du >= f_{iq} * a_i
440
- for i in N:
441
- for q in Q:
442
- model.addConstr(
443
- C[q] - Du >= f[i, q] * a[i],
444
- name=f"ship_arrival_{i}_{q}"
445
- )
446
-
447
- # (38) z_q <= sum_{i in N} f_{iq}
448
- for q in Q:
449
- model.addConstr(
450
- z[q] <= gp.quicksum(f[i, q] for i in N),
451
- name=f"lockage_scheduled_{q}"
452
- )
453
-
454
- # (39) FCFS: c_i - c_j <= C_max*(u_i + u_j), for i < j
455
- for i in N:
456
- for j in N:
457
- if i < j:
458
- model.addConstr(
459
- c[i] - c[j] <= C_max * (u[i] + u[j]),
460
- name=f"fcfs_{i}_{j}"
461
- )
462
-
463
- # (40) z_{q+1} <= z_q
464
- for q in Q:
465
- if q < n - 1:
466
- model.addConstr(z[q + 1] <= z[q], name=f"lock_order_z_{q}")
467
-
468
- # (41) C_q <= C_{q+1}
469
- for q in Q:
470
- if q < n - 1:
471
- model.addConstr(C[q] <= C[q + 1], name=f"lock_order_C_{q}")
472
-
473
- # (42) sum_{q < l, q in Q} (f_{iq} - f_{jq}) >= -(u_i + u_j), for i < j, l in Q
474
- for i in N:
475
- for j in N:
476
- if i < j:
477
- for l_idx in Q:
478
- model.addConstr(
479
- gp.quicksum(f[i, q] - f[j, q] for q in Q if q < l_idx)
480
- >= -(u[i] + u[j]),
481
- name=f"lock_order_f_{i}_{j}_{l_idx}"
482
- )
483
-
484
- # --- Mode Fixing Constraints (43, 48) ---
485
- # (43) u_i = 0 for i in SL
486
- for i in SL:
487
- model.addConstr(u[i] == 0, name=f"lock_only_{i}")
488
-
489
- # (48) u_i = 1 for i in SB
490
- for i in SB:
491
- model.addConstr(u[i] == 1, name=f"trans_only_{i}")
492
-
493
- # --- BAPD Constraints (44-47) ---
494
-
495
- # (44) sum_{k in B(i)} sum_{p in P} delta_{ipk} = u_i
496
- for i in N:
497
- model.addConstr(
498
- gp.quicksum(delta[i, p, k] for k in B_eligible[i] for p in P) == u[i],
499
- name=f"berth_assign_{i}"
500
- )
501
-
502
- # (45) sum_{i in N} delta_{ipk} <= 1, for k in M, p in P
503
- for k in M:
504
- for p in P:
505
- model.addConstr(
506
- gp.quicksum(delta[i, p, k] for i in N) <= 1,
507
- name=f"berth_capacity_{k}_{p}"
508
- )
509
-
510
- # (46) Idle time constraint at berth
511
- # sum_{j in N} sum_{l in P(p)} (t_{jk} * delta_{jlk} + omega_{jlk})
512
- # + omega_{ipk} - (a_i - s_k) * delta_{ipk} >= 0
513
- # for k in M, i in N(k), p in P
514
- for k in M:
515
- for i in N_k[k]:
516
- for p in P:
517
- model.addConstr(
518
- gp.quicksum(
519
- t[j, k] * delta[j, l_idx, k] + omega[j, l_idx, k]
520
- for j in N for l_idx in P if l_idx < p
521
- )
522
- + omega[i, p, k]
523
- - (a[i] - s_k[k]) * delta[i, p, k] >= 0,
524
- name=f"idle_time_{k}_{i}_{p}"
525
- )
526
-
527
- # (47) Berth availability: sum_{i in N} sum_{p in P} (t_{ik}*delta_{ipk} + omega_{ipk}) <= e_k - s_k
528
- for k in M:
529
- model.addConstr(
530
- gp.quicksum(
531
- t[i, k] * delta[i, p, k] + omega[i, p, k]
532
- for i in N for p in P
533
- ) <= e_k[k] - s_k[k],
534
- name=f"berth_avail_{k}"
535
- )
536
-
537
- # Force delta_{ipk} = 0 for berths not eligible for ship i
538
- for i in N:
539
- for k in M:
540
- if k not in B_eligible[i]:
541
- for p in P:
542
- model.addConstr(delta[i, p, k] == 0,
543
- name=f"ineligible_{i}_{p}_{k}")
544
-
545
- # ----- Solve -----
546
- model.optimize()
547
-
548
- # ----- Extract solution -----
549
- result = {}
550
- if model.SolCount > 0:
551
- result["objective_value"] = model.ObjVal
552
-
553
- # Extract mode decisions
554
- result["modes"] = {str(i): int(round(u[i].X)) for i in N}
555
-
556
- # Extract completion times
557
- result["completion_times"] = {str(i): c[i].X for i in N}
558
-
559
- # Extract lockage assignments for lock-mode ships
560
- lockage_assignments = {}
561
- for i in N:
562
- if round(u[i].X) == 0: # lock mode
563
- for q in Q:
564
- if round(f[i, q].X) == 1:
565
- lockage_assignments[str(i)] = q
566
- break
567
- result["lockage_assignments"] = lockage_assignments
568
-
569
- # Extract lockage completion times
570
- lockage_times = {}
571
- for q in Q:
572
- if round(z[q].X) == 1:
573
- lockage_times[str(q)] = C[q].X
574
- result["lockage_completion_times"] = lockage_times
575
-
576
- # Extract berth assignments for transshipment-mode ships
577
- berth_assignments = {}
578
- for i in N:
579
- if round(u[i].X) == 1: # transshipment mode
580
- for k in B_eligible[i]:
581
- for p in P:
582
- if round(delta[i, p, k].X) == 1:
583
- berth_assignments[str(i)] = {"berth": k, "order": p}
584
- break
585
- result["berth_assignments"] = berth_assignments
586
-
587
- result["solver_status"] = model.Status
588
- result["mip_gap"] = model.MIPGap if hasattr(model, 'MIPGap') else None
589
- else:
590
- result["objective_value"] = None
591
- result["solver_status"] = model.Status
592
- result["error"] = "No feasible solution found within time limit."
593
-
594
- return result
595
-
596
-
597
- def main():
598
- parser = argparse.ArgumentParser(
599
- description="Gurobi MILP solver for LQCP (Ji et al., 2019)"
600
- )
601
- parser.add_argument("--instance_path", type=str, required=True,
602
- help="Path to JSON instance file.")
603
- parser.add_argument("--solution_path", type=str, required=True,
604
- help="Path for output solution JSON file.")
605
- parser.add_argument("--time_limit", type=int, required=True,
606
- help="Maximum solver runtime in seconds.")
607
- parser.add_argument("--log_path", type=str, default=None, help="Path to log incumbent solutions")
608
- args = parser.parse_args()
609
- install_gurobi_logger(args.log_path)
610
-
611
- data = load_instance(args.instance_path)
612
- result = build_and_solve_model(data, args.time_limit)
613
-
614
- with open(args.solution_path, 'w') as f:
615
- json.dump(result, f, indent=2)
616
-
617
- if result["objective_value"] is not None:
618
- print(f"Objective value: {result['objective_value']}")
619
- else:
620
- print("No feasible solution found.")
621
-
622
-
623
- if __name__ == "__main__":
624
- main()
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ji2019/gurobi_feasi_result/large_feasi_result_1.json DELETED
@@ -1,6 +0,0 @@
1
- {
2
- "feasible": true,
3
- "violated_constraints": [],
4
- "violations": [],
5
- "violation_magnitudes": []
6
- }
 
 
 
 
 
 
 
ji2019/gurobi_feasi_result/large_feasi_result_2.json DELETED
@@ -1,6 +0,0 @@
1
- {
2
- "feasible": true,
3
- "violated_constraints": [],
4
- "violations": [],
5
- "violation_magnitudes": []
6
- }
 
 
 
 
 
 
 
ji2019/gurobi_feasi_result/large_feasi_result_3.json DELETED
@@ -1,6 +0,0 @@
1
- {
2
- "feasible": true,
3
- "violated_constraints": [],
4
- "violations": [],
5
- "violation_magnitudes": []
6
- }
 
 
 
 
 
 
 
ji2019/gurobi_feasi_result/large_feasi_result_4.json DELETED
@@ -1,6 +0,0 @@
1
- {
2
- "feasible": true,
3
- "violated_constraints": [],
4
- "violations": [],
5
- "violation_magnitudes": []
6
- }
 
 
 
 
 
 
 
ji2019/gurobi_feasi_result/large_feasi_result_5.json DELETED
@@ -1,6 +0,0 @@
1
- {
2
- "feasible": true,
3
- "violated_constraints": [],
4
- "violations": [],
5
- "violation_magnitudes": []
6
- }
 
 
 
 
 
 
 
ji2019/gurobi_feasi_result/tiny_feasi_result.json DELETED
@@ -1,6 +0,0 @@
1
- {
2
- "feasible": true,
3
- "violated_constraints": [],
4
- "violations": [],
5
- "violation_magnitudes": []
6
- }
 
 
 
 
 
 
 
ji2019/gurobi_solution/large_solution_1.json DELETED
@@ -1,85 +0,0 @@
1
- {
2
- "objective_value": 4496.9,
3
- "modes": {
4
- "0": 1,
5
- "1": 1,
6
- "2": 1,
7
- "3": 1,
8
- "4": 1,
9
- "5": 1,
10
- "6": 1,
11
- "7": 1,
12
- "8": 1,
13
- "9": 1,
14
- "10": 1,
15
- "11": 1
16
- },
17
- "completion_times": {
18
- "0": 57.5,
19
- "1": 57.7,
20
- "2": 219.4,
21
- "3": 254.8,
22
- "4": 266.0,
23
- "5": 322.2,
24
- "6": 393.8,
25
- "7": 423.0,
26
- "8": 433.9,
27
- "9": 473.2,
28
- "10": 589.9,
29
- "11": 689.5
30
- },
31
- "lockage_assignments": {},
32
- "lockage_completion_times": {},
33
- "berth_assignments": {
34
- "0": {
35
- "berth": 0,
36
- "order": 9
37
- },
38
- "1": {
39
- "berth": 6,
40
- "order": 7
41
- },
42
- "2": {
43
- "berth": 5,
44
- "order": 8
45
- },
46
- "3": {
47
- "berth": 0,
48
- "order": 10
49
- },
50
- "4": {
51
- "berth": 6,
52
- "order": 8
53
- },
54
- "5": {
55
- "berth": 5,
56
- "order": 9
57
- },
58
- "6": {
59
- "berth": 0,
60
- "order": 11
61
- },
62
- "7": {
63
- "berth": 6,
64
- "order": 9
65
- },
66
- "8": {
67
- "berth": 5,
68
- "order": 10
69
- },
70
- "9": {
71
- "berth": 5,
72
- "order": 11
73
- },
74
- "10": {
75
- "berth": 6,
76
- "order": 10
77
- },
78
- "11": {
79
- "berth": 6,
80
- "order": 11
81
- }
82
- },
83
- "solver_status": 9,
84
- "mip_gap": 0.3109603429998878
85
- }
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ji2019/gurobi_solution/large_solution_2.json DELETED
@@ -1,85 +0,0 @@
1
- {
2
- "objective_value": 4455.0,
3
- "modes": {
4
- "0": 1,
5
- "1": 1,
6
- "2": 1,
7
- "3": 1,
8
- "4": 1,
9
- "5": 1,
10
- "6": 1,
11
- "7": 1,
12
- "8": 1,
13
- "9": 1,
14
- "10": 1,
15
- "11": 1
16
- },
17
- "completion_times": {
18
- "0": 33.0,
19
- "1": 54.6,
20
- "2": 60.0,
21
- "3": 252.8,
22
- "4": 262.9,
23
- "5": 268.4,
24
- "6": 278.3,
25
- "7": 305.3,
26
- "8": 317.9,
27
- "9": 349.3,
28
- "10": 394.3,
29
- "11": 437.2
30
- },
31
- "lockage_assignments": {},
32
- "lockage_completion_times": {},
33
- "berth_assignments": {
34
- "0": {
35
- "berth": 0,
36
- "order": 8
37
- },
38
- "1": {
39
- "berth": 5,
40
- "order": 8
41
- },
42
- "2": {
43
- "berth": 8,
44
- "order": 8
45
- },
46
- "3": {
47
- "berth": 5,
48
- "order": 9
49
- },
50
- "4": {
51
- "berth": 8,
52
- "order": 9
53
- },
54
- "5": {
55
- "berth": 0,
56
- "order": 9
57
- },
58
- "6": {
59
- "berth": 0,
60
- "order": 10
61
- },
62
- "7": {
63
- "berth": 8,
64
- "order": 10
65
- },
66
- "8": {
67
- "berth": 0,
68
- "order": 11
69
- },
70
- "9": {
71
- "berth": 5,
72
- "order": 10
73
- },
74
- "10": {
75
- "berth": 8,
76
- "order": 11
77
- },
78
- "11": {
79
- "berth": 5,
80
- "order": 11
81
- }
82
- },
83
- "solver_status": 9,
84
- "mip_gap": 0.287698772974011
85
- }
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ji2019/gurobi_solution/large_solution_3.json DELETED
@@ -1,85 +0,0 @@
1
- {
2
- "objective_value": 5365.2,
3
- "modes": {
4
- "0": 1,
5
- "1": 1,
6
- "2": 1,
7
- "3": 1,
8
- "4": 1,
9
- "5": 1,
10
- "6": 1,
11
- "7": 1,
12
- "8": 1,
13
- "9": 1,
14
- "10": 1,
15
- "11": 1
16
- },
17
- "completion_times": {
18
- "0": 341.9,
19
- "1": 450.1,
20
- "2": 522.3,
21
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168
- 8,
169
- 9
170
- ],
171
- "eligible_berths_B": [
172
- 0,
173
- 1,
174
- 2
175
- ]
176
- },
177
- {
178
- "id": 7,
179
- "width": 10.0,
180
- "length": 100.3,
181
- "arrival_time": 61.5,
182
- "transshipment_penalty": 113,
183
- "mooring_set_MR": [
184
- 0,
185
- 1,
186
- 2,
187
- 3,
188
- 4,
189
- 5,
190
- 6,
191
- 8,
192
- 9
193
- ],
194
- "eligible_berths_B": [
195
- 0,
196
- 1,
197
- 2
198
- ]
199
- },
200
- {
201
- "id": 8,
202
- "width": 10.9,
203
- "length": 59.9,
204
- "arrival_time": 77.7,
205
- "transshipment_penalty": 108,
206
- "mooring_set_MR": [
207
- 0,
208
- 1,
209
- 2,
210
- 3,
211
- 4,
212
- 5,
213
- 6,
214
- 7,
215
- 9
216
- ],
217
- "eligible_berths_B": [
218
- 0,
219
- 1,
220
- 2
221
- ]
222
- },
223
- {
224
- "id": 9,
225
- "width": 16.1,
226
- "length": 108.8,
227
- "arrival_time": 96.5,
228
- "transshipment_penalty": 148,
229
- "mooring_set_MR": [
230
- 0,
231
- 1,
232
- 2,
233
- 3,
234
- 4,
235
- 5,
236
- 6,
237
- 7,
238
- 8
239
- ],
240
- "eligible_berths_B": [
241
- 0,
242
- 1,
243
- 2
244
- ]
245
- }
246
- ],
247
- "berths": [
248
- {
249
- "id": 0,
250
- "start_availability_sk": 20.5
251
- },
252
- {
253
- "id": 1,
254
- "start_availability_sk": 27.1
255
- },
256
- {
257
- "id": 2,
258
- "start_availability_sk": 11.5
259
- }
260
- ],
261
- "handling_times": [
262
- [
263
- 141,
264
- 122,
265
- 123
266
- ],
267
- [
268
- 149,
269
- 122,
270
- 131
271
- ],
272
- [
273
- 127,
274
- 138,
275
- 130
276
- ],
277
- [
278
- 123,
279
- 96,
280
- 135
281
- ],
282
- [
283
- 114,
284
- 102,
285
- 119
286
- ],
287
- [
288
- 104,
289
- 112,
290
- 103
291
- ],
292
- [
293
- 113,
294
- 114,
295
- 120
296
- ],
297
- [
298
- 98,
299
- 139,
300
- 108
301
- ],
302
- [
303
- 146,
304
- 94,
305
- 121
306
- ],
307
- [
308
- 138,
309
- 127,
310
- 107
311
- ]
312
- ],
313
- "generation_seed": 1042
314
- }
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ji2019/instance_schema.json DELETED
@@ -1,30 +0,0 @@
1
- {
2
- "num_ships": "<int> Total number of ships arriving at the dam.",
3
- "num_berths": "<int> Total number of berths available at the quay.",
4
- "num_chambers": "<int> Number of parallel lock chambers at the dam.",
5
- "chamber_width_W": "<float> Width of the lock chamber in meters.",
6
- "chamber_length_L": "<float> Length of the lock chamber in meters.",
7
- "lockage_duration_Du": "<float> Fixed duration in minutes required to complete one lockage operation.",
8
- "min_time_between_lockages_MT": "<float> Minimum time in minutes that must elapse between the completion of consecutive lockages.",
9
- "lock_start_availability_sc": "<float> Earliest time in minutes at which the lock chamber becomes available for use.",
10
- "berth_end_availability_ek": "<float> Latest time in minutes at which all berths cease to be available for service.",
11
- "C_max": "<int> Upper bound on the completion time used as a large constant in scheduling constraints.",
12
- "ships": [
13
- {
14
- "id": "<int> Unique identifier of the ship.",
15
- "width": "<float> Width of the ship in meters.",
16
- "length": "<float> Length of the ship in meters.",
17
- "arrival_time": "<float> Time in minutes at which the ship arrives at the coordination point.",
18
- "transshipment_penalty": "<int> Extra cost incurred when the ship chooses to unload cargo at the quay instead of passing through the lock.",
19
- "mooring_set_MR": "<list[int], length num_ships-1> Other ships to which this ship is allowed to moor inside the lock chamber.",
20
- "eligible_berths_B": "<list[int], length num_berths> Berths at which this ship may be served if it chooses the transshipment mode."
21
- }
22
- ],
23
- "berths": [
24
- {
25
- "id": "<int> Unique identifier of the berth.",
26
- "start_availability_sk": "<float> Earliest time in minutes at which the berth becomes available for service."
27
- }
28
- ],
29
- "handling_times": "<list[list[int]], shape [num_ships][num_berths]> Time in minutes required to handle each ship's cargo at each berth."
30
- }
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ji2019/mathematical_formulation.md DELETED
@@ -1,214 +0,0 @@
1
- # Sets and Indices
2
-
3
- - $N$: set of ships, $n = |N|$.
4
-
5
- - $M$: set of berths, $m = |M|$.
6
-
7
- - $SL$: ships that can only pass through the lock.
8
-
9
- - $SB$: ships that can only be transshipped.
10
-
11
- - $Q$: set of lockages, $|Q| = n$.
12
-
13
- - $MR_i \subseteq N$: ships to which ship $i \in N$ may moor.
14
-
15
- - $P$: set of service orders per berth, $|P| = n$.
16
-
17
- - $N(k) = \{i \in N : a_i \geq s_k\}$: ships arriving after berth $k$ is available.
18
-
19
- - $B(i) \subseteq M$: berths that can serve ship $i$.
20
-
21
- - $P(p) = \{l \in P : l < p\}$.
22
-
23
- # Parameters
24
-
25
- - $w_i, l_i$: width and length of ship $i$.
26
-
27
- - $a_i$: arrival time of ship $i$.
28
-
29
- - $W, L$: width and length of the lock chamber.
30
-
31
- - $sc$: start-of-availability time of the chamber.
32
-
33
- - $sp_0 = (0,0)$: chamber’s left side; $sp_{n+1} = (W, 0)$: chamber’s right side.
34
-
35
- - $Du$: duration of a lockage; $MT$: minimal interval between consecutive lockages.
36
-
37
- - $Pe_i$: penalty incurred by ship $i$ when it uses transshipment mode.
38
-
39
- - $t_{ik}$: handling time of ship $i$ at berth $k$.
40
-
41
- - $s_k, e_k$: availability start/end times of berth $k$.
42
-
43
- - $C_{\max}$: upper bound on completion time (a big-$M$ constant).
44
-
45
- # Decision Variables
46
-
47
- - $u_i \in \{0,1\}$: mode chosen by ship $i$ ($1$ = transshipment, $0$ = lock).
48
-
49
- - $x_i, y_i \in \mathbb{Z}_{\geq 0}$: $x$- and $y$-position of ship $i$ in a lockage.
50
-
51
- - $lt_{ij} \in \{0,1\}$: $=1$ iff ship $i$ is entirely left of ship $j$.
52
-
53
- - $b_{ij} \in \{0,1\}$: $=1$ iff ship $i$ is entirely behind ship $j$.
54
-
55
- - $ml_{ij}, mr_{ij} \in \{0,1\}$: $=1$ iff ship $i$ moors on the left/right of ship $j$.
56
-
57
- - $z_q \in \{0,1\}$: $=1$ iff lockage $q$ is used.
58
-
59
- - $f_{iq} \in \{0,1\}$: $=1$ iff ship $i$ is transferred by lockage $q$.
60
-
61
- - $v_{ij} \in \{0,1\}$: $=1$ iff ships $i$ and $j$ travel in the same lockage.
62
-
63
- - $c_i \in [0, C_{\max}]$: departure time of ship $i$.
64
-
65
- - $C_q \in [0, C_{\max}]$: completion time of lockage $q$.
66
-
67
- - $\delta_{ipk} \in \{0,1\}$: $=1$ iff ship $i$ is assigned to the $p$-th order of berth $k$.
68
-
69
- - $\omega_{ipk} \in \mathbb{Z}_{\geq 0}$: idle time of berth $k$ before ship $i$ arrives, when $i$ takes the $p$-th order of $k$.
70
-
71
- # Objective
72
-
73
- $$\begin{align}
74
- \min\quad & T_1 + T_2 + \sum_{i \in N} Pe_i\, u_i, \tag{1}
75
- \end{align}$$ where $$\begin{align}
76
- T_1 &= \sum_{i \in N} (c_i - a_i), \tag{2}\\
77
- T_2 &= \sum_{k \in M}\sum_{i \in N}\sum_{p \in P}
78
- \Bigl\{
79
- \sum_{j \in N}\sum_{l \in P(p)} \bigl(t_{jk}\,\delta_{jlk} + \omega_{jlk}\bigr)
80
- + \omega_{ipk} + t_{ik} + s_k - a_i
81
- \Bigr\}\,\delta_{ipk}. \tag{4}
82
- \end{align}$$ (Constraint (3) is the nonlinear version of $T_2$, linearized as (4).)
83
-
84
- # Constraints: Ship Placement Sub-problem
85
-
86
- $$\begin{align}
87
- & lt_{ij} + lt_{ji} + b_{ij} + b_{ji} + (1 - f_{iq}) + (1 - f_{jq}) \geq 1,
88
- && \forall i<j,\ i,j \in N,\ q \in Q, \tag{5}\\
89
- & x_i + w_i \leq x_j + W(1 - lt_{ij}),
90
- && \forall i \neq j,\ i,j \in N, \tag{6}\\
91
- & y_i + l_i \leq y_j + L(1 - b_{ij}),
92
- && \forall i \neq j,\ i,j \in N, \tag{7}\\
93
- & x_i + w_i \leq W,
94
- && \forall i \in N, \tag{8}\\
95
- & y_i + l_i \leq L,
96
- && \forall i \in N, \tag{9}\\
97
- & \sum_{q \in Q} f_{iq} = 1 - u_i,
98
- && \forall i \in N, \tag{10}\\
99
- & f_{iq} \leq z_q,
100
- && \forall i \in N,\ q \in Q, \tag{11}\\
101
- & y_j - y_i \leq (1 - ml_{ij})\, L,
102
- && \forall i \in N,\ j \in MR_i, \tag{12}\\
103
- & y_i - y_j \leq l_j - l_i + (1 - ml_{ij})\, L,
104
- && \forall i \in N,\ j \in MR_i, \tag{13}\\
105
- & x_j - x_i \leq w_i + (1 - ml_{ij})\, W,
106
- && \forall i \in N,\ j \in MR_i, \tag{14}\\
107
- & x_j - x_i \geq w_i - (1 - ml_{ij})\, W,
108
- && \forall i \in N,\ j \in MR_i, \tag{15}\\
109
- & x_{n+1} - x_i \leq w_i + (1 - ml_{i,n+1})\, W,
110
- && \forall i \in N, \tag{16}\\
111
- & x_{n+1} - x_i \geq w_i - (1 - ml_{i,n+1})\, W,
112
- && \forall i \in N, \tag{17}\\
113
- & y_j - y_i \leq (1 - mr_{ij})\, L,
114
- && \forall i \in N,\ j \in MR_i, \tag{18}\\
115
- & y_i - y_j \leq l_j - l_i + (1 - mr_{ij})\, L,
116
- && \forall i \in N,\ j \in MR_i, \tag{19}\\
117
- & x_j - x_i \leq -\, w_j + (1 - mr_{ij})\, W,
118
- && \forall i \in N,\ j \in MR_i, \tag{20}\\
119
- & x_j - x_i \geq -\, w_j - (1 - mr_{ij})\, W,
120
- && \forall i \in N,\ j \in MR_i, \tag{21}\\
121
- & x_0 - x_i \leq -\, w_i + (1 - mr_{i,0})\, W,
122
- && \forall i \in N, \tag{22}\\
123
- & x_0 - x_i \geq -\, w_i - (1 - mr_{i,0})\, W,
124
- && \forall i \in N, \tag{23}\\
125
- & \sum_{j \in MR_i} (ml_{ij} + mr_{ij}) + mr_{i,0} + ml_{i,n+1}
126
- \geq 1 - u_i,
127
- && \forall i \in N, \tag{24}\\
128
- & ml_{ij} + mr_{ji} \leq 1,
129
- && \forall i \in N,\ j \in MR_i, \tag{25}\\
130
- & ml_{ij} + mr_{ij} \leq v_{ij},
131
- && \forall i \in N,\ j \in MR_i, \tag{26}\\
132
- & f_{iq} - f_{jq} \leq 1 - v_{ij},
133
- && \forall i<j,\ i,j \in N,\ q \in Q, \tag{27}\\
134
- & f_{jq} - f_{iq} \leq 1 - v_{ij},
135
- && \forall i<j,\ i,j \in N,\ q \in Q, \tag{28}\\
136
- & v_{ij} \leq 1 - u_i,
137
- && \forall i<j,\ i,j \in N, \tag{29}\\
138
- & v_{ij} \leq 1 - u_j,
139
- && \forall i<j,\ i,j \in N. \tag{30}
140
- \end{align}$$
141
-
142
- # Constraints: Lockage Scheduling Sub-problem
143
-
144
- $$\begin{align}
145
- & c_i \geq C_{\max}(f_{iq} - 1) + C_q,
146
- && \forall i \in N,\ q \in Q, \tag{31}\\
147
- & c_i \leq C_{\max}(1 - f_{iq}) + C_q,
148
- && \forall i \in N,\ q \in Q, \tag{32}\\
149
- & c_i \geq C_{\max}(u_i - 1) + a_i,
150
- && \forall i \in N, \tag{33}\\
151
- & c_i \leq C_{\max}(1 - u_i) + a_i,
152
- && \forall i \in N, \tag{34}\\
153
- & C_{q+1} - C_q \geq MT,
154
- && \forall q \in Q,\ q < |Q|, \tag{35}\\
155
- & C_q - Du \geq sc,
156
- && \forall q \in Q, \tag{36}\\
157
- & C_q - Du \geq f_{iq}\, a_i,
158
- && \forall i \in N,\ q \in Q, \tag{37}\\
159
- & z_q \leq \sum_{i \in N} f_{iq},
160
- && \forall q \in Q, \tag{38}\\
161
- & c_i - c_j \leq C_{\max}(u_i + u_j),
162
- && \forall i < j, \tag{39}\\
163
- & z_{q+1} \leq z_q,
164
- && \forall q \in Q, \tag{40}\\
165
- & C_q \leq C_{q+1},
166
- && \forall q \in Q, \tag{41}\\
167
- & \sum_{q < l,\ q \in Q}(f_{iq} - f_{jq}) \geq -(u_i + u_j),
168
- && \forall i<j,\ i,j \in N,\ l \in Q. \tag{42}
169
- \end{align}$$
170
-
171
- # Mode Fixing
172
-
173
- $$\begin{align}
174
- & u_i = 0, && \forall i \in SL, \tag{43}\\
175
- & u_i = 1, && \forall i \in SB. \tag{48}
176
- \end{align}$$
177
-
178
- # BAPD (Berth Allocation) Constraints
179
-
180
- $$\begin{align}
181
- & \sum_{k \in B(i)}\sum_{p \in P} \delta_{ipk} = u_i,
182
- && \forall i \in N, \tag{44}\\
183
- & \sum_{i \in N} \delta_{ipk} \leq 1,
184
- && \forall k \in M,\ p \in P, \tag{45}\\
185
- & \sum_{j \in N}\sum_{l \in P(p)}\bigl(t_{jk}\,\delta_{jlk} + \omega_{jlk}\bigr)
186
- + \omega_{ipk} - (a_i - s_k)\,\delta_{ipk} \geq 0,
187
- && \forall k \in M,\ i \in N(k),\ p \in P, \tag{46}\\
188
- & \sum_{i \in N}\sum_{p \in P}\bigl(t_{ik}\,\delta_{ipk} + \omega_{ipk}\bigr)
189
- \leq e_k - s_k,
190
- && \forall k \in M. \tag{47}
191
- \end{align}$$
192
-
193
- # Integrality and Bounds
194
-
195
- $$\begin{align}
196
- & u_i \in \{0,1\},
197
- && \forall i \in N, \tag{49}\\
198
- & lt_{ij},\ b_{ij} \in \{0,1\},
199
- && \forall i \neq j,\ i,j \in N, \tag{50}\\
200
- & ml_{ij},\ mr_{ij} \in \{0,1\},
201
- && \forall i \in N,\ j \in MR_i, \tag{51}\\
202
- & ml_{i,n+1},\ mr_{i,0} \in \{0,1\},
203
- && \forall i \in N, \tag{52}\\
204
- & v_{ij} \in \{0,1\},\quad z_q \in \{0,1\},
205
- && \forall i<j,\ q \in Q, \tag{53}\\
206
- & 0 \leq c_i \leq C_{\max},\quad 0 \leq C_q \leq C_{\max},
207
- && \forall i \in N,\ q \in Q, \tag{54}\\
208
- & f_{iq} \in \{0,1\},
209
- && \forall i \in N,\ q \in Q, \tag{55}\\
210
- & x_i, y_i \in \mathbb{Z}_{\geq 0},
211
- && \forall i \in N, \tag{56}\\
212
- & \delta_{ipk} \in \{0,1\},\quad \omega_{ipk} \geq 0,
213
- && \forall i \in N,\ k \in M,\ p \in P. \tag{57}
214
- \end{align}$$
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ji2019/problem_description.txt DELETED
@@ -1,15 +0,0 @@
1
- # Problem Description
2
-
3
- A set of ships arrives at an inland waterway dam equipped with a lock and a quay. The lock consists of a single rectangular chamber with a known width and length, and the quay is divided into several berths. Each ship has a known width, length, arrival time at a coordination point, and a transshipment penalty reflecting the extra cost and unwillingness associated with choosing to unload cargo at the quay rather than passing through the lock. For each ship, a set of other ships to which it is allowed to moor inside the lock chamber is given, as well as a set of berths at which it may be served if it chooses the transshipment mode. The handling time of each ship at each eligible berth is given. Each berth has a start and end of availability time. The lock chamber has a start of availability time. A fixed duration is required for each lockage, and a minimum time interval must elapse between the completion of one lockage and the completion of the next. Some ships may be restricted to pass only through the lock, and others may be restricted to use only the transshipment mode. A sufficiently large time horizon is given.
4
-
5
- For each ship, the operator must choose one of two modes: lock mode, in which the ship passes through the lock chamber, or transshipment mode, in which the ship's cargo is handled at a quay berth. The number of potential lockages equals the number of ships, serving as an upper bound; each lockage may or may not be used. The number of service order positions at each berth also equals the number of ships. For each lock-mode ship, the operator must assign it to exactly one lockage and determine its position inside the chamber, specified by whole-number x and y coordinates representing the ship's placement within the chamber's width and length. For each transshipment-mode ship, the operator must assign it to exactly one berth and one service order position at that berth. The operator must also determine the completion time of each lockage and the departure time of each ship.
6
-
7
- Ships assigned to the same lockage must not overlap when placed inside the chamber. Specifically, for any two ships in the same lockage, at least one of the following must hold: one ship is entirely to the left of the other in the width direction, or one ship is entirely behind the other in the length direction. If one ship is entirely to the left of another, the first ship's x-coordinate plus its width must not exceed the second ship's x-coordinate. If one ship is entirely behind another, the first ship's y-coordinate plus its length must not exceed the second ship's y-coordinate. Every ship placed in the chamber must fit within the chamber dimensions: its x-coordinate plus its width must not exceed the chamber width, and its y-coordinate plus its length must not exceed the chamber length.
8
-
9
- Each lock-mode ship must be assigned to exactly one lockage. A lockage can only be marked as used if at least one ship is assigned to it, and a ship can only be assigned to a lockage that is used. Each lock-mode ship must be moored to at least one entity: either to the left side of another allowed ship, to the right side of another allowed ship, to the left wall of the chamber, or to the right wall of the chamber. A ship moored to the left side of another ship must be adjacent to it: the mooring ship must be contained within the length span of the ship it moors to, and their x-coordinates must be such that the mooring ship's right edge touches the other ship's left edge. The same adjacency logic applies symmetrically for mooring to the right side, where the mooring ship must be contained within the length span of the ship it moors to, and the other ship's right edge must touch the mooring ship's left edge. For mooring to the chamber's right wall, the ship's right edge must touch the wall, with analogous conditions for the chamber's left wall. If one ship moors to the left side of another, the second ship cannot simultaneously moor to the right side of the first. Two ships that are not assigned to the same lockage cannot moor to each other. Two ships can only be in the same lockage if both choose the lock mode.
10
-
11
- The departure time of a lock-mode ship equals the completion time of the lockage that transfers it. The departure time of a transshipment-mode ship equals its arrival time. The completion time of each lockage minus the lockage duration must be no earlier than the chamber's start of availability time, and also no earlier than the arrival time of every ship assigned to that lockage. The minimum time interval between consecutive lockage completions must be respected. Lockages must be ordered: if a lockage index is used, all lower-indexed lockages must also be used, and completion times must be nondecreasing across lockage indices. A first-come-first-served rule applies to lock-mode ships: among any two ships that both choose the lock mode, the one arriving earlier must depart no later than the one arriving later. Furthermore, for any two lock-mode ships where one arrives earlier, the earlier-arriving ship must be assigned to the same or an earlier lockage than the later-arriving ship.
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- Each transshipment-mode ship must be assigned to exactly one berth and one service order position at that berth. Each service order position at each berth may serve at most one ship. When a ship is assigned to a particular service order at a berth, idle time may be incurred at the berth before the ship's service begins. Specifically, the cumulative handling times and idle times of all ships served at that berth in earlier service orders, plus the idle time before the current ship, must be at least as large as the difference between the ship's arrival time and the berth's start of availability time. The total handling time and idle time across all service orders at a berth must not exceed the berth's total available time window.
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- The goal is to minimize the sum of three components: the total delay of lock-mode ships, where each lock-mode ship's delay is its departure time minus its arrival time; the total delay of transshipment-mode ships, where each such ship's delay accounts for the berth's start time, the cumulative handling and idle times of ships served before it at the same berth, its own handling and idle time, minus its arrival time; and the total transshipment penalty summed over all ships that choose the transshipment mode.