OMMX Adapterで初期解を利用する方法

OMMX Adapterの中には、最適化計算実行時に初期解を渡す機能をサポートしているものがあります。ここではOMMXPySCIPOptAdapterを例に、この機能を紹介します。初期解を渡すことで、ソルバーが初期実行可能解を自ら構築する必要がなくなり、最適化計算のパフォーマンスが向上することがあります。

初期解を渡す方法

渡すことのできる初期解（initial_state）はToState型であり、これはommx.v1.StateまたはMapping[int, float]の両方の型を受け取ることができます。 以下のインスタンスを用いて、初期解を渡す方法を説明します。

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,
)

ommx.v1.Stateによる初期解の例

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

Mapping[int, float]による初期解の例

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

以下の通り、solve関数にinitial_stateを引数として渡すことで、初期解を渡して最適化計算を実行することができます。

from ommx_pyscipopt_adapter import OMMXPySCIPOptAdapter

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

ソルバーをチューニングして利用したい場合、直接OMMXPySCIPOptAdapterクラスを使うことでソルバーのパラメーター等を設定するケースもあります。この場合においても、以下の通りinitial_stateを引数として渡すことができます。

from ommx_pyscipopt_adapter import OMMXPySCIPOptAdapter

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

初期解の有無による比較の例

MIPLIBのroll3000というインスタンスを例に、初期解を渡す場合と渡さない場合で、どのような違いが生じるかを確認します。 初期解としては、事前に作成しておいた実行可能解（最適解ではない）を与えることとします。

from ommx_pyscipopt_adapter import OMMXPySCIPOptAdapter
from ommx import dataset

# インスタンスの読み込み
ommx_instance = dataset.miplib2017("roll3000")

初期解を渡さない場合

import time

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

実行時間: 50.11402355999999

初期解を渡す場合

初期解（initial_state）として、このチュートリアルでは事前に得られた以下を使用することとします。

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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initial_stateを渡してsolveを実行する

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

実行時間: 27.03826196700001

この例では、初期解を渡すことで、最適化計算に要する時間が短縮されました。 なお、初期解を渡すことで常にパフォーマンスが向上するわけではなく、変動がなかったり、悪化するケースもあります。このため、向上するか否かについて試行錯誤は必要ですが、有効なケースにおいては大きなパフォーマンスの向上が期待できます。