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.State and Mapping[int, float].

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

from ommx import DecisionVariable, Instance, Sense, State

x = DecisionVariable.integer(1, lower=0, upper=5, name="x", subscripts=[0])
y = DecisionVariable.integer(2, lower=0, upper=5, name="x", subscripts=[1])

ommx_instance = Instance.from_components(
    decision_variables=[x, y],
    objective=x - y,
    constraints={0: x + y <= 5},
    sense=Sense.Maximize,
)

Example of initial solution using ommx.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,
)

Providing Values by Name and Subscripts#

Pass a NamedState directly to SCIP’s initial_state argument. The adapter uses state_from_named_values() to resolve names and subscripts against the instance being solved. This lets you reuse the same initial values when rebuilding a model assigns different variable IDs.

from ommx import NamedState

initial_values: NamedState = {"x": {(0,): 3.0, (1,): 2.0}}
solution = OMMXPySCIPOptAdapter.solve(ommx_instance, initial_state=initial_values)
assert solution.state.entries == {x.id: 5.0, y.id: 0.0}

# Explicit conversion is also available when you need a State.
initial_state = ommx_instance.state_from_named_values(initial_values)

Subscript keys are tuples: () for a scalar, (i,) for one index, and (i, j) for two indices. You can also pass the output of extract_all_decision_variables() to reuse solution values.

Conversion raises KeyError when a supplied name/subscript pair is unknown and ValueError when it matches multiple variables. Label parameters are ignored; use an ID-keyed state to distinguish variables with identical names and subscripts. Conversion accepts partial mappings and leaves omitted variables out of the resulting state. SCIP initializes omitted solver variables to zero. Keys that collide after string or integer normalization raise ValueError.

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}")

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, 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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, 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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}")

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.

How to Use the Initial Solution with OMMX Adapters

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