How to Use the Initial Solution with OMMX Adapters

Some OMMX Adapters support providing initial solutions when executing optimization calculations. Here, we’ll introduce this feature using OMMXPySCIPOptAdapter as an example. By providing an initial solution, the solver does not need to construct an initial feasible solution by itself, which can sometimes improve the performance of optimization calculations.

How to Provide an Initial Solution

The initial solution (initial_state) that can be provided is of type ToState, which can accept both ommx.v1.State and Mapping[int, float].

We’ll demonstrate how to provide an initial solution using the following instance:

from ommx.v1 import Instance, DecisionVariable
from ommx.v1.solution_pb2 import State

x = DecisionVariable.integer(1, lower=0, upper=5)
y = DecisionVariable.integer(2, lower=0, upper=5)

ommx_instance = Instance.from_components(
    decision_variables=[x, y],
    objective=x - y,
    constraints=[x + y <= 5],
    sense=Instance.MAXIMIZE,
)

Example of initial solution using ommx.v1.State

initial_state = State(
    entries={
        1: 3.0,
        2: 2.0,
    }
)

Example of initial solution using Mapping[int, float]

initial_state = {
    1: 3.0,
    2: 2.0,
}

As shown below, you can run the optimization with an initial solution by providing initial_state as an argument to the solve function:

from ommx_pyscipopt_adapter import OMMXPySCIPOptAdapter

solution = OMMXPySCIPOptAdapter.solve(
    ommx_instance=ommx_instance,
    initial_state=initial_state,
)

If you need to tune the solver, you can directly use the OMMXPySCIPOptAdapter class to set solver parameters. In this case, you can also provide initial_state as an argument as shown below:

from ommx_pyscipopt_adapter import OMMXPySCIPOptAdapter

adapter = OMMXPySCIPOptAdapter(
    ommx_instance=ommx_instance,
    initial_state=initial_state,
)

Example Comparison With and Without Initial Solution

Using the roll3000 instance from MIPLIB, let’s compare the performance differences with and without an initial solution. For the initial solution, we’ll use a feasible solution (not an optimal one) that was prepared in advance.

from ommx_pyscipopt_adapter import OMMXPySCIPOptAdapter
from ommx import dataset

# Load the instance
ommx_instance = dataset.miplib2017("roll3000")

Without an initial solution

import time

start = time.perf_counter()
solution = OMMXPySCIPOptAdapter.solve(
    ommx_instance=ommx_instance,
)
duration = time.perf_counter() - start
print(f"Execution Time: {duration}")

Execution Time: 50.796635579000025

With an initial solution

For this tutorial, we’ll use the following initial solution obtained in advance:

initial_state = {257: -1.84297022087776e-14, 703: 0.0, 531: -4.6407322429331543e-14, 1052: -9.621932880084689e-15, 360: 0.0, 175: 0.0, 507: 11.000000000000002, 301: 0.0, 937: 3.0000000000000044, 859: 0.0, 564: -3.1086244689504383e-15, 557: -4.6407322429331543e-14, 205: 0.0, 617: 1.3322676295501878e-14, 162: 0.0, 811: 0.0, 759: 3.1086244689503373e-15, 682: 0.0, 987: 0.0, 1013: 0.0, 536: 0.9999999999998973, 189: 0.0, 540: -4.440892098500626e-15, 1135: 0.0, 1163: 0.0, 526: 0.0, 7: -5.362970457884017e-15, 83: 2.0, 606: 0.0, 677: 1.000000000000089, 935: 0.0, 224: 0.0, 824: -5.551115123115685e-17, 161: 0.0, 671: 0.9999999999999867, 1075: 0.0, 1147: 4.440892098500626e-15, 107: -2.6645352591003757e-15, 807: 0.0, 836: 0.0, 1110: 0.0, 1143: 0.0, 84: 0.0, 368: 4.218847493575595e-14, 639: 0.0, 663: 0.0, 171: 0.0, 423: 3.0000000000001226, 730: 0.0, 21: 0.0, 931: -8.881784197001252e-15, 611: 2.842170943040401e-14, 833: 0.0, 435: 4.000000000000141, 410: 0.0, 505: 3.000000000000361, 198: 0.0, 262: 0.0, 76: 0.0, 620: -8.881784197001252e-15, 616: 0.0, 95: -3.887299665209862e-15, 291: 0.0, 748: 2.842170943040401e-14, 822: 1.1435297153639112e-14, 450: 0.0, 61: 0.0, 1003: 3.999999999999979, 845: 2.000000000000089, 124: 0.9999999999999991, 1031: 0.0, 716: 0.0, 948: 5.999999999999996, 821: 0.0, 493: 0.0, 212: 0.0, 34: 0.0, 136: 2.999999999999928, 20: 1.0000000000000009, 701: -8.881784197001252e-15, 839: 0.0, 246: 0.0, 282: 0.0, 919: 0.0, 418: 0.0, 967: 0.0, 1099: 0.0, 458: 0.0, 342: 0.0, 452: 0.0, 637: 0.0, 233: 3.000000000000105, 138: 0.0, 857: 1.000000000000047, 487: -2.6645352591003757e-15, 275: 0.0, 964: 3.0000000000000124, 447: 1.0, 622: 0.0, 877: 0.0, 242: 0.0, 596: 0.0, 854: -1.865174681370263e-14, 153: 1.0000000000000286, 478: 0.0, 679: 2.9999999999999494, 1125: 0.0, 612: 0.0, 975: 0.0, 943: 0.0, 1009: 0.0, 829: 0.0, 400: 0.0, 321: 0.0, 1054: 1.865174681370263e-14, 1159: 1.9999999999999867, 471: -3.1086244689504383e-15, 797: -2.7533531010703882e-14, 1074: -4.3520742565306136e-14, 714: -3.019806626980426e-14, 1162: 0.0, 299: 0.0, 645: 0.0, 71: 0.0, 858: 5.000000000000172, 306: 1.0, 861: 1.84297022087776e-14, 172: 0.0, 1028: 8.881784197001252e-16, 808: 0.0, 1114: 3.9999999999999725, 134: 4.440892098500626e-14, 646: 0.0, 1080: 10.0, 393: -2.4868995751603507e-14, 55: 0.0, 110: 0.0, 949: 3.0531133177191805e-15, 373: 0.0, 456: 0.0, 856: -4.440892098500625e-16, 708: 0.0, 430: 0.0, 560: 0.0, 1017: 2.930988785010413e-14, 243: 1.887379141862766e-14, 971: 2.0000000000000666, 402: 0.9999999999999574, 37: 0.0, 324: 1.000000000000021, 1030: 0.0, 984: 0.0, 749: 8.881784197001252e-15, 250: 0.0, 472: 0.0, 177: 1.0000000000000315, 82: 7.105427357601002e-15, 333: 0.0, 1096: -1.0725940915768033e-14, 372: 4.884981308350689e-14, 140: 0.0, 652: 0.0, 60: 0.0, 316: 0.0, 785: 0.0, 432: 0.0, 401: 0.0, 513: 0.0, 309: 0.0, 633: 1.9999999999999853, 951: 0.0, 481: 3.7192471324942744e-14, 240: 1.000000000000007, 599: 0.0, 685: 0.0, 610: 0.0, 690: 0.9999999999999996, 500: 0.0, 252: 0.0, 603: 0.0, 853: 1.0000000000000089, 519: 0.0, 827: 2.0, 823: 7.000000000000012, 602: 0.0, 578: 0.0, 1064: -4.3520742565306136e-14, 215: 8.881784197001252e-16, 85: 0.0, 583: 0.0, 650: -8.926193117986259e-14, 517: 0.0, 412: 0.0, 609: 0.0, 1133: 1.9999999999999196, 1079: 0.0, 576: 0.0, 803: 0.0, 832: 0.0, 1066: 4.1744385725905886e-14, 694: 1.0, 408: 0.0, 315: 0.0, 783: 0.0, 1127: 0.0, 998: 0.0, 462: 1.0, 1034: 0.0, 678: 1.687538997430238e-14, 454: 0.0, 511: 0.0, 925: 0.0, 707: -3.647082635893639e-14, 411: 0.0, 618: 0.0, 46: 1.000000000000011, 891: 0.0, 740: 0.0, 121: 0.0, 2: 0.0, 459: 0.9999999999999853, 774: 0.0, 339: 1.0000000000000115, 334: 0.0, 669: -7.993605777301127e-15, 255: 0.0, 390: 0.0, 587: 1.000000000000007, 835: 0.0, 133: -1.7985612998927536e-14, 396: 0.0, 341: 0.0, 382: 2.999999999999912, 428: 0.0, 761: 2.220446049250313e-15, 99: 0.0, 156: 0.0, 589: 198.99999999999935, 621: 1.0000000000000009, 510: -9.386431026376354e-16, 687: 0.0, 1156: 0.0, 915: 2.842170943040401e-14, 1051: 0.0, 328: 0.0, 882: 0.0, 258: -1.84297022087776e-14, 1158: 0.0, 995: 1.9999999999999565, 636: -9.175151694187626e-17, 966: -3.1086244689504383e-15, 199: 0.0, 781: 0.0, 754: 0.0, 249: -2.6645352591003757e-15, 969: 0.0, 985: 0.0, 1055: 0.0, 961: 0.0, 141: 2217.9999999999973, 641: 0.0, 607: 0.0, 973: -3.887299665209862e-15, 630: 2.930988785010413e-14, 444: 1.0, 689: 0.0, 89: 0.0, 41: 0.0, 126: 0.0, 69: 0.0, 343: -5.362970457884017e-15, 1021: 0.0, 466: 1.0, 217: -8.881784197001252e-16, 902: 0.0, 604: 67.00000000000283, 539: 1.0047518372857667e-13, 876: 0.0, 534: 0.0, 414: 0.0, 720: 0.0, 911: 0.0, 1070: 0.0, 23: 0.0, 798: 0.0, 1142: -3.1086244689504383e-15, 791: 0.0, 119: 0.0, 615: 1.0, 795: 1.0, 417: 0.0, 59: -9.2148511043888e-15, 755: 1.0000000000000009, 286: 1.9999999999999485, 760: 0.0, 194: 2.0000000000001297, 139: 0.0, 533: 1.0, 608: 0.0, 463: 1.0000000000000364, 965: 5.000000000000172, 665: 0.0, 886: 0.0, 1145: 0.0, 326: 0.0, 453: 0.0, 1104: -1.5765166949677223e-14, 844: 0.0, 903: 0.0, 144: 0.0, 1023: 0.0, 775: 0.0, 884: 0.0, 739: 0.0, 776: 0.0, 308: -8.881784197001252e-15, 851: 4.218847493575595e-15, 294: 0.0, 247: 0.0, 1062: 1.0000000000000364, 125: 1.0000000000000102, 446: 0.0, 366: 0.0, 64: 0.0, 268: 0.0, 757: 0.0, 168: 0.0, 303: 0.0, 688: -2.6645352591003757e-15, 490: 0.0, 590: 0.0, 195: -3.1086244689504383e-15, 506: 1.3322676295501878e-14, 152: 0.0, 380: 1.0, 421: 1.0, 216: 0.0, 327: 0.0, 1015: 0.0, 312: 0.0, 1032: 0.0, 743: 1.0, 1040: 0.0, 176: 0.0, 376: 0.0, 314: 0.0, 165: 0.0, 159: 0.0, 1071: 1.0, 67: 0.0, 1121: -8.722144284963535e-15, 386: 0.9999999999999867, 696: 1.0000000000000004, 538: 0.0, 214: 0.0, 710: 0.0, 515: 0.0, 1082: -1.1102230246251565e-16, 979: 0.0, 94: -5.2004562015845005e-15, 527: 0.0, 102: 0.0, 982: 0.0, 100: 3.0000000000000124, 123: 0.0, 483: 0.0, 167: 1.0, 537: 0.0, 686: 0.0, 280: 3.9999999999999956, 293: 0.0, 672: 151.9999999999999, 191: 0.0, 896: 0.0, 997: 0.0, 92: 0.0, 873: 0.0, 237: 1.0000000000000102, 26: 0.0, 732: -6.217248937900877e-15, 469: 1.0, 959: 0.0, 485: 3.000000000000033, 974: 0.0, 799: 0.0, 750: 0.0, 43: 1.0, 711: 161.9999999999928, 548: 0.0, 362: 0.0, 787: 0.0, 244: 0.0, 24: 0.0, 96: 1.0000000000000284, 588: 0.0, 908: 0.0, 626: 0.0, 762: 0.9999999999999916, 234: 0.0, 1004: 0.0, 489: 0.0, 379: 2.9999999999998863, 651: 0.0, 623: 1.4210854715202004e-14, 1025: 1.0, 488: 0.0, 940: -2.6513460148478883e-14, 461: 0.0, 862: 0.0, 529: 3.197442310920451e-14, 8: 0.0, 950: 1.0000000000000158, 544: 0.0, 499: 0.0, 27: 29.99999999999986, 613: 0.9999999999998973, 521: 0.0, 993: 0.0, 784: -1.4223963249031613e-16, 10: 0.0, 477: -1.3322676295501877e-15, 747: 9.947598300641403e-14, 929: 0.0, 1018: 0.0, 986: 0.0, 562: 0.0, 185: 0.0, 594: 0.0, 726: 0.0, 129: -2.752545508256288e-16, 1024: 1.0000000000001048, 356: 0.9999999999999707, 201: 0.0, 455: 0.0, 436: 0.9999999999999707, 14: -8.548717289613705e-15, 354: 12889.999999999976, 498: 0.0, 860: 0.0, 643: 0.0, 12: -2.6645352591003757e-15, 468: 32.000000000000014, 605: 1.0000000000000278, 190: 0.0, 359: 0.0, 614: 0.0, 289: 0.0, 1022: 0.0, 434: 0.0, 479: -1.5765166949677223e-14, 572: 1.3322676295501878e-14, 1014: 0.0, 114: 0.0, 737: 0.0, 348: 2.1316282072803006e-14, 265: 0.0, 741: -5.400124791776761e-13, 169: 0.0, 825: 0.0, 1049: 4.440892098500626e-15, 561: 0.0, 1044: 0.0, 358: 0.9999999999999831, 1085: 2.999999999999983, 920: -8.881784197002262e-16, 281: 0.0, 1043: 0.0, 654: 0.0, 901: -1.6241245636507983e-14, 648: 2.9999999999999414, 397: -4.440892098500626e-15, 907: 197.00000000000014, 1124: 0.0, 1063: 1.0, 697: 0.0, 1086: 4.000000000000141, 728: -4.2549297418759124e-14, 403: 0.0, 6: 0.0, 913: 0.0, 228: 1.0047518372857667e-13, 442: 8.881784197001252e-16, 994: 0.0, 208: 0.0, 815: 0.0, 698: 0.0, 518: 0.0, 197: -1.021405182655144e-14, 934: 2.999999999999903, 591: -1.0725940915768033e-14, 439: 0.0, 443: 0.0, 1047: 0.0, 894: -3.7192471324942744e-15, 184: 0.0, 1128: 0.0, 70: 0.0, 492: 0.0, 782: 1.2156942119645464e-14, 516: 0.0, 1151: 0.0, 1097: 95.0, 101: 1.7763568394002505e-14, 976: 0.0, 352: 0.0, 151: 4.3115457266996746e-17, 270: 0.0, 1073: -3.4181831865424275e-16, 751: 0.0, 864: 0.0, 351: 0.0, 939: 0.0, 433: 0.0, 756: -4.440892098500627e-16, 30: 0.0, 166: 1.2156942119645464e-14, 955: 0.0, 241: 0.9999999999999999, 1132: 0.0, 658: 0.0, 1036: 0.0, 887: 279.9999999999998, 866: 4.063416270128073e-14, 311: 0.0, 655: 0.0, 753: 2.0, 35: 0.0, 962: 0.0, 385: -1.1435297153639112e-14, 335: 0.9999999999999987, 1057: 0.0, 674: 1.0000000000000884, 388: 1.0, 921: 1.9999999999999498, 264: 0.0, 972: 8.881784197001252e-15, 75: -8.881784197002262e-16, 15: 0.0, 344: 0.0, 528: 0.0, 780: 0.0, 1134: 0.0, 530: 0.0, 44: 0.0, 135: 2.968534766042603e-14, 771: 0.0, 649: 0.0, 1093: 0.0, 220: 0.0, 898: -3.647082635893639e-14, 305: 0.0, 1140: 0.0, 395: 0.0, 870: -3.019806626980426e-14, 905: 1.0000000000000435, 1008: 0.9999999999999813, 837: -5.2004562015845005e-15, 1011: 1.865174681370263e-14, 63: 0.0, 1006: 0.0, 673: 1.4210854715202004e-14, 960: 0.0, 627: 0.0, 378: 0.0, 399: 0.0, 132: 0.0, 475: 0.0, 319: 0.0, 735: 2.6513460148478883e-14, 4: 0.0, 419: 0.0, 1077: 3.9999999999999485, 582: 1.000000000000011, 550: 0.0, 881: 9.769962616701378e-15, 371: 1.0000000000000469, 676: 0.0, 553: 1.0, 229: 0.0, 155: 0.0, 1060: 0.0, 988: 0.0, 644: 7.993605777301127e-15, 357: 0.0, 638: 0.0, 56: -7.105427357601002e-15, 802: 0.0, 834: 0.0, 1045: 8.881784197001252e-16, 3: 0.0, 496: 0.0, 290: 0.0, 922: 0.0, 186: 0.0, 868: 0.0, 457: 0.0, 480: 0.0, 248: 0.9999999999999981, 1105: 0.0, 661: 2.220446049250313e-14, 106: 0.0, 1103: -8.881784197001252e-15, 1026: 0.0, 266: 1.0000000000000007, 424: 0.0, 956: 0.0, 778: 0.0, 668: 0.0, 325: 0.0, 692: 1.0047518372857667e-13, 952: 8.000000000000055, 323: 1.865174681370263e-14, 695: 0.9999999999999929, 942: 0.0, 374: 2.220446049250313e-15, 188: 0.0, 1107: 0.0, 712: 0.0, 767: 0.0, 150: -2.0261570199409107e-14, 938: 0.9999999999999991, 187: -1.3377022877126888e-14, 543: 0.0, 1102: 1.0000000000000018, 300: 0.0, 916: 1.0000000000000302, 330: -2.6645352591003757e-14, 36: 0.0, 1078: 0.0, 532: 1.0, 888: 30.000000000000682, 1067: 0.0, 347: 0.0, 429: 0.9999999999999999, 448: 0.0, 437: 0.0, 1095: 0.0, 284: 1.0, 431: 0.0, 9: 1.3322676295501878e-14, 725: 1.000000000000089, 1098: 0.0, 451: 1.9999999999999565, 81: 0.0, 667: 1.000000000000011, 570: -8.881784197001252e-16, 779: 9.202150330924782e-17, 54: 0.0, 22: 0.0, 404: 0.0, 235: 0.0, 542: 0.0, 118: 0.0, 805: 0.0, 398: 0.0, 878: 0.0, 226: -1.3377022877126888e-14, 78: 3.999999999999904, 909: -7.993605777301127e-15, 1012: 0.0, 814: 0.0, 524: 3.0000000000000115, 238: 0.0, 566: -2.6645352591003757e-15, 554: 0.0, 675: 0.0, 923: 0.0, 874: 0.0, 559: 0.0, 1154: 0.0, 1089: 1.7763568394002505e-15, 551: 0.0, 391: 0.0, 883: 0.0, 203: 0.0, 285: 1.999999999999993, 269: 0.0, 792: 1.0, 659: 0.0, 160: 2.000000000000005, 279: 0.0, 148: 2.0000000000000187, 702: 7.105427357601002e-15, 80: 0.0, 555: 0.0, 11: 0.0, 958: 0.0, 473: 0.0, 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Execute a solve operation by providing the initial_state:

start = time.perf_counter()
solution = OMMXPySCIPOptAdapter.solve(
    ommx_instance=ommx_instance,
    initial_state=initial_state,
)
duration = time.perf_counter() - start
print(f"Execution Time: {duration}")

Execution Time: 27.394719635

In this example, providing an initial solution reduced the optimization calculation time. Note that providing an initial solution does not always improve performance - it may have no effect or even make performance worse in some cases. Trial and error is required to determine if it helps, but in effective cases, significant performance improvement can be expected.