---
jupytext:
  text_representation:
    extension: .md
    format_name: myst
    format_version: 0.13
    jupytext_version: 1.19.1
kernelspec:
  display_name: ommx-update-books (3.9.23)
  language: python
  name: python3
---

# 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:

```{code-cell} ipython3
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`

```{code-cell} ipython3
initial_state = State(
    entries={
        1: 3.0,
        2: 2.0,
    }
)
```

Example of initial solution using `Mapping[int, float]`

```{code-cell} ipython3
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:

```{code-cell} ipython3
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:

```{code-cell} ipython3
from ommx_pyscipopt_adapter import OMMXPySCIPOptAdapter

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

(named-initial-state)=
## Providing Values by Name and Subscripts

Pass a `NamedState` directly to SCIP's `initial_state` argument. The adapter
uses {meth}`~ommx.Instance.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.

```{code-cell} ipython3
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
{meth}`~ommx.Solution.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.

```{code-cell} ipython3
from ommx_pyscipopt_adapter import OMMXPySCIPOptAdapter
from ommx import dataset

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

### Without an initial solution

```{code-cell} ipython3
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:

```{code-cell} ipython3
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, 182: 0.0, 1138: 0.0, 427: 0.0, 231: 3.0000000000000213, 926: 0.0, 895: 0.0, 968: 0.0, 954: 0.0, 389: 0.0, 223: -5.684341886080802e-14, 329: 1.0, 800: 3.730349362740526e-14, 164: 0.0, 1058: 0.0, 1029: 0.0, 773: 0.0, 790: 0.0, 58: 0.0, 597: 0.0, 547: 0.0, 812: 0.0, 1002: -8.750737653510993e-14, 340: 4.999999999999949, 1094: 0.9999999999999973, 625: 2.9999999999999893, 804: 0.9999999999999996, 1088: 1.9999999999999885, 345: 1.000000000000089, 717: 1.000000000000031, 558: 0.0, 304: 0.9999999999999901, 867: 8.000000000000055, 253: 33.00000000000008, 765: 0.0, 1117: 0.0, 927: 2.9999999999999627, 202: 0.0, 1007: 0.0, 1108: 0.0, 355: 0.0, 1150: 0.0, 917: 4.999999999999981, 387: 8.43769498715119e-15, 632: 0.0, 192: 0.0, 1139: 0.0, 1160: 1.9999999999999898, 1141: 0.0, 843: 0.0, 48: 2.999999999999967, 830: 137.99999999999926, 1122: 0.0, 245: -1.0502709812953981e-13, 120: 0.0, 349: 0.0, 17: 9.2148511043888e-15, 642: 0.0, 200: 1.0, 912: 2.0000000000000187, 699: 238.00000000000003, 1129: 0.0, 724: 0.0, 992: 3.064215547965432e-14, 112: 0.0, 416: 187.00000000000009, 684: 0.0, 706: 0.0, 174: 4.000000000000132, 546: 0.0, 97: 0.0, 465: 2.3426113579956395e-16, 298: 0.0, 445: 0.9999999999999902, 733: 1.000000000000089, 1090: 0.0, 86: 0.0, 422: 0.0, 236: 0.0, 318: 8.43769498715119e-15, 232: 0.0, 31: 0.0, 273: 0.0, 810: 0.0, 764: 0.0, 1119: 0.9999999999999971, 1048: 0.0, 872: 15.000000000000012, 818: 0.0, 1101: 0.0, 653: 1.0, 384: 0.0, 297: 0.0, 777: -1.7985612998927536e-14, 145: -2.0261570199409107e-14, 127: -8.881784197001252e-16, 79: 0.0, 953: 0.0, 73: 0.0, 90: -8.881784197001252e-15, 363: 0.0, 502: 0.0, 227: -8.548717289613705e-15, 525: 2601.999999999994, 251: 0.0, 98: 2.842170943040401e-14, 211: 0.0, 13: 0.0, 470: 1.9999999999999947, 108: 0.0, 1136: 0.0, 310: 0.0, 426: 6.999999999999999, 892: 1.0000000000000941, 440: 0.0, 841: -3.7192471324942744e-14, 850: 0.0, 552: 0.0, 584: 1.0, 367: 0.0, 629: 0.0, 494: 0.0, 889: 0.0, 464: 9.325873406851315e-14, 259: 0.0, 375: 0.0, 353: 0.0, 598: 1.0000000000000213, 631: 3.000000000000022, 577: 0.0, 704: 0.0, 93: 0.0, 746: 0.0, 565: -2.6645352591003757e-15, 963: 0.0, 1050: 1.0, 1083: 0.0, 292: 1.000000000000023, 332: 0.0, 1100: 0.0, 693: 0.0, 990: 0.0, 512: 0.0, 601: 2.0000000000000355, 713: -8.903988657493755e-14, 369: 0.0, 0: 8.881784197001252e-16, 1081: 1.3322676295501878e-14, 541: 1.0, 196: 0.0, 681: 0.0, 213: 0.0, 467: 0.0, 474: -8.926193117986259e-14, 50: 0.9999999999999574, 1152: -1.674216321134736e-13, 1137: 1.000000000000105, 885: 2.999999999999928, 786: 1.0000000000000007, 817: 12889.999999999976, 130: 0.0, 137: 1.0, 53: 1.0000000000000315, 495: 0.0, 441: 0.0, 571: 1.865174681370263e-14, 1115: 8.881784197001252e-16, 809: 0.0, 819: -9.769962616701378e-15, 1165: 0.0, 364: 0.0, 261: 74.00000000000007, 535: 0.0, 848: 0.0, 731: 0.0, 945: 0.0, 624: 5.000000000000172, 1106: 0.0, 772: 1.000000000000007, 460: 0.0, 727: 0.0, 1046: 0.0, 394: 0.0, 267: -2.7411935155625904e-15, 842: 0.0, 49: 4.999999999999921, 930: 1.999999999999993, 670: 0.0, 928: 0.0, 924: 0.0, 691: 0.0, 146: 0.0, 25: 0.0, 491: 0.0, 142: 9.947598300641403e-14, 849: 0.0, 932: 0.9999999999999867, 33: 1.0, 1010: 0.9999999999999005, 409: 7.105427357601002e-15, 350: 0.0, 207: 2.0000000000000187, 1084: 0.0, 918: -3.7192471324942744e-15, 1112: 0.0, 1016: 0.0, 1053: 0.0, 508: 1.0047518372857667e-13, 482: 0.0, 944: 0.0, 789: 0.0, 1076: 2.9999999999999813, 52: 1.4210854715202004e-14, 680: -7.438494264988549e-15, 320: -8.548717289613705e-15, 449: -2.4868995751603507e-14, 1037: 0.0, 317: 1.000000000000028, 855: 0.9999999999999973, 277: 0.0, 758: 4.440892098500626e-15, 91: 0.0, 222: 0.0, 29: 0.0, 567: 0.0, 438: -6.078471059822732e-15, 549: 0.9999999999999707, 763: 0.0, 991: 4.440892098500626e-15, 628: 0.0, 1068: 0.0, 936: 0.0, 178: 1.0000000000000002, 256: 0.0, 831: 0.0, 183: -8.881784197001252e-16, 1164: 0.0, 946: 0.0, 580: 0.0, 838: 0.0, 19: 0.0, 18: 3.00000000000004, 88: 0.9999999999999999, 420: -3.552713678800501e-15, 377: 0.0, 425: 4.00000000000001, 662: 1.6105119292618043e-14, 806: 0.0, 370: 0.0, 87: -2.930988785010413e-14, 287: 0.0, 579: 0.0, 154: 0.0, 794: 0.0, 501: 7.000000000000055, 852: 1.0000000000000009, 744: 0.0, 1120: 0.0, 406: 0.9999999999999947, 1157: 0.0, 556: 0.0, 103: 1.000000000000018, 1161: 0.0, 666: 0.0, 705: 0.0, 592: 0.0, 47: 0.0, 128: 144.00000000000003, 977: -8.881784197001252e-15, 57: -1.0658141036401503e-14, 503: 0.0, 1144: 0.0, 900: 0.0, 647: 0.0, 68: 0.0, 595: 0.0, 575: 0.0, 415: 0.0, 288: 0.0, 39: 2.9999999999999956, 381: 0.0, 906: 0.0, 846: 1.0, 218: 1.0, 42: -7.993605777301127e-15, 514: 4.440892098500626e-14, 1091: 337.00000000000006, 664: 0.0, 523: 1.0000000000000226, 193: 4.440892098500626e-15, 74: 0.9999999999998995, 263: 0.0, 1027: 0.0, 593: 0.0, 170: 0.0, 1000: -1.2434497875801753e-14, 338: 1.0000000000000115, 1126: 2.6645352591003757e-15, 113: 0.0, 683: 0.0, 715: 0.0, 486: 0.0, 407: 0.0, 66: 0.0, 1148: 0.0, 914: 0.0, 718: -1.3322676295501877e-15, 115: 0.0, 1155: 0.0, 230: 0.0, 826: 0.0, 278: 1.0000000000000286, 999: 0.0, 947: 0.0, 1118: 0.0, 828: -2.930988785010413e-14, 634: 0.0, 1123: 0.0, 721: 0.0, 117: 0.0, 1116: 0.0, 719: -7.993605777301127e-15, 392: 0.0, 405: 2.0000000000000187, 880: 1.000000000000089, 520: 2.784308972829587e-15, 210: 0.0, 1061: 1.0, 793: 0.0, 504: 0.0, 1072: 0.0, 989: 0.0, 813: 0.0, 1042: 1.9999999999999885, 752: 8.881784197001252e-16, 700: 0.0, 1041: 2.0000000000000204, 413: 1.3322676295501878e-14, 574: 3.0000000000000018, 736: 0.0, 1113: 0.0, 904: 0.0, 173: 0.0, 1056: 5.000000000000033, 295: 1.0000000000000278, 619: 2.0, 5: 0.9999999999999951, 497: 0.0, 635: 1.0, 1065: 0.0, 788: 0.0, 742: 1.0, 1039: 0.9999999999999427, 522: 2.220446049250313e-16, 1038: 0.0, 180: 1.0000000000000469, 729: 0.9999999999999628, 869: 0.0, 820: 1.9999999999999982, 219: 0.0, 981: 8.881784197001252e-16, 1020: 1.000000000000089, 147: 0.0, 933: 0.0, 723: 10.000000000000068, 879: 212.00000000000003, 149: 0.0, 509: 1.0, 72: 0.0, 111: 0.0, 897: 3.7192471324942744e-14, 163: 0.0, 978: 1.000000000000047, 1109: 0.0, 545: 0.9999999999999853, 143: 0.9999999999999947, 337: 0.9999999999999005, 302: 1.999999999999993, 1149: 0.0, 840: 0.0, 283: 2.0000000000000204, 271: 0.0, 1019: 0.0, 769: 1.7763568394002505e-15, 16: 0.9999999999999707, 893: -4.6851411639181606e-14, 1092: 0.0, 331: 0.0, 865: 1.3322676295501878e-14, 1001: 2.0, 660: 0.0, 1111: 1.0, 204: 1.0000000000000187, 383: 0.0, 105: 10.000000000000002, 77: 0.0, 734: 1.0, 45: 0.0, 209: 1.0000000000000382, 657: 0.0, 131: 0.0, 1131: -8.881784197001252e-15, 709: 8.881784197001252e-15, 1: 0.0, 957: -1.84297022087776e-14, 656: 0.0, 476: 0.9999999999999694, 104: 0.0, 296: 0.0, 980: 0.0, 62: 0.0, 1130: 0.0, 847: 5.000000000000135, 1035: 0.0, 1146: 0.0, 361: 3.0000000000000124, 768: 0.0, 157: 0.0, 875: 0.0, 890: 0.0, 109: 3.0000000000000044, 585: 1.0, 28: 0.0, 796: 0.0, 365: 0.0, 983: 7.993605777301127e-15, 586: 0.0, 158: 0.0, 600: 2.0000000000000187, 910: 0.0, 179: 0.0, 65: 0.0, 581: 5.000000000000054, 941: 0.0, 722: -3.785860513971784e-14, 1069: 0.0, 1059: 0.0, 346: 0.0, 181: 1.0000000000000364, 307: -1.865174681370263e-14, 568: 0.0, 38: 1.0, 970: 0.0, 40: 4.440892098500626e-15, 738: 0.0, 276: 0.0, 274: 0.0, 871: 0.0, 272: 1.0, 260: 0.0, 801: 0.0, 239: 1.9999999999998908, 322: 0.0, 206: 0.0, 116: 0.0, 766: 0.0, 816: 0.0, 225: 0.9999999999998995, 770: -6.022959908591474e-15, 563: 0.0, 336: 0.0, 573: -9.386431026376354e-16, 254: 0.0, 122: 0.0, 899: -4.440892098500627e-16, 1087: 0.0, 745: 0.0, 640: 0.0, 313: -4.263256414560601e-14, 1153: 0.0, 996: 0.9999999999999498, 51: 0.0, 1033: 0.0, 863: 0.0, 32: 1.000000000000003, 484: 1.000000000000028, 1005: -1.021405182655144e-14, 569: 9.473903143468002e-15, 221: 0.0}
```

Execute a solve operation by providing the `initial_state`:

```{code-cell} ipython3
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.