Consider a mixed integer linear program with an objective function that includes only integer variables. Objective integrality cuts are known as a class of valid inequalities that can be added to strengthen such a formulation: If the objective coefficients are all integers, then the objective value must be an integer because the variables are required to be integer.
I am wondering whether objective integrality cuts have been implemented in modern solvers? If not, what could be challenging when implementing objective integrality cuts? I am surprised that a commercial solver such as CPLEX does not seem to consider objective integrality cuts (I'm not sure about Gurobi). It is not uncommon for an optimization problem to have integer objective values (e.g., scheduling problems, assembly line balancing problems, etc). In such cases, the integrality cuts could play a significant role in solving the problem faster. Just to give an example, here is the log file for an instance of a real-world course scheduling problem solved by CPLEX 12.10 (the objective is to maximize the number of student-lesson allocations):
Nodes Cuts/
Node Left Objective IInf Best Integer Best Bound ItCnt Gap
* 0+ 0 57.0000 80.0000 40.35%
0 0 64.4321 3783 57.0000 64.4321 18 13.04%
0 0 63.3571 3783 57.0000 Cuts: 297 16536 11.15%
0 0 62.5714 3783 57.0000 Cuts: 744 37274 9.77%
0 0 62.5714 3783 57.0000 Cuts: 472 58784 9.77%
0 0 62.5714 3783 57.0000 Cuts: 400 80695 9.77%
0 0 62.5714 3783 57.0000 Cuts: 50 100726 9.77%
0 0 62.5536 3783 57.0000 Cuts: 405 122147 9.74%
* 0+ 0 60.0000 62.5536 4.26%
0 0 cutoff 60.0000 62.5536 122147 4.26%
0 0 62.5536 3783 60.0000 Cuts: 487 163607 4.26%
Heuristic still looking.
0 2 62.5536 2211 60.0000 62.5536 217531 4.26%
Elapsed time = 237.27 sec. (226054.16 ticks, tree = 0.02 MB, solutions = 2)
1 3 62.5536 2220 60.0000 62.5536 287580 4.26%
2 3 62.5536 2086 60.0000 62.5536 251100 4.26%
3 4 62.5536 2162 60.0000 62.5536 309506 4.26%
.
.
.
2469 1948 62.0000 1506 60.0000 62.5536 4209632 4.26%
Elapsed time = 1212.46 sec. (840425.96 ticks, tree = 35.92 MB, solutions = 2)
2501 1968 62.0000 1126 60.0000 62.5536 4229228 4.26%
2544 1990 62.0000 1025 60.0000 62.5536 4254943 4.26%
2555 2005 61.0000 1483 60.0000 62.5536 4266956 4.26%
Performing restart 1
Repeating presolve.
Tried aggregator 2 times.
MIP Presolve eliminated 463 rows and 676 columns.
MIP Presolve modified 7567 coefficients.
Aggregator did 43 substitutions.
Reduced MIP has 8121 rows, 14050 columns, and 135496 nonzeros.
Reduced MIP has 13853 binaries, 197 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.28 sec. (310.77 ticks)
Tried aggregator 1 time.
Reduced MIP has 8121 rows, 14050 columns, and 135496 nonzeros.
Reduced MIP has 13853 binaries, 197 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.08 sec. (90.85 ticks)
Represolve time = 0.62 sec. (575.33 ticks)
2574 0 62.5000 2516 60.0000 Cuts: 122 4514780 4.17%
2574 0 62.5000 2516 60.0000 Cuts: 528 4534076 4.17%
2574 0 62.2000 2516 60.0000 Cuts: 220 4550193 3.67%
2574 0 62.0000 2516 60.0000 Cuts: 200 4565065 3.33%
2574 0 62.0000 2516 60.0000 Cuts: 240 4582021 3.33%
2574 0 62.0000 2516 60.0000 Cuts: 203 4595338 3.33%
2574 0 62.0000 2516 60.0000 Cuts: 94 4615273 3.33%
2574 0 62.0000 2516 60.0000 Cuts: 212 4629574 3.33%
2574 0 62.0000 2516 60.0000 Cuts: 31 4644396 3.33%
2574 0 62.0000 2516 60.0000 Cuts: 228 4660555 3.33%
2574 0 62.0000 2516 60.0000 Cuts: 103 4674035 3.33%
2574 2 62.0000 1389 60.0000 62.0000 4674035 3.33%
2575 3 62.0000 1826 60.0000 62.0000 4709875 3.33%
2576 4 62.0000 1816 60.0000 62.0000 4747076 3.33%
2577 5 62.0000 1818 60.0000 62.0000 4763581 3.33%
2579 7 62.0000 1977 60.0000 62.0000 4816350 3.33%
2580 4 62.0000 1936 60.0000 62.0000 4728882 3.33%
2582 10 62.0000 2032 60.0000 62.0000 4891825 3.33%
Elapsed time = 1711.68 sec. (1187756.21 ticks, tree = 0.05 MB, solutions = 2)
2583 5 62.0000 1773 60.0000 62.0000 4764410 3.33%
2586 11 62.0000 1604 60.0000 62.0000 4908032 3.33%
.
.
.
6137 1599 61.3333 1125 60.0000 62.0000 12157124 3.33%
6146 1598 61.9079 1424 60.0000 62.0000 12173722 3.33%
6181 1609 61.3647 1111 60.0000 61.9995 12233657 3.33%
6226 1625 61.0000 1003 60.0000 61.9995 12250334 3.33%
6249 1636 infeasible 60.0000 61.9995 12278475 3.33%
6283 1641 infeasible 60.0000 61.9951 12317307 3.33%
Elapsed time = 3963.23 sec. (2538648.23 ticks, tree = 41.58 MB, solutions = 2)
6301 1647 61.5000 1577 60.0000 61.9951 12418694 3.33%
6364 1666 infeasible 60.0000 61.9934 12316289 3.32%
6412 1733 61.7162 1227 60.0000 61.9904 12709071 3.32%
6444 1736 61.0000 1106 60.0000 61.9904 12716961 3.32%
6476 1656 61.7184 1323 60.0000 61.9904 12350981 3.32%
6484 1769 61.7025 1211 60.0000 61.9903 12794727 3.32%
6496 1735 cutoff 60.0000 61.9903 12743643 3.32%
6511 1775 61.3971 941 60.0000 61.9903 12813587 3.32%
6535 1743 61.0000 977 60.0000 61.9903 12757733 3.32%
6569 1779 61.0000 1082 60.0000 61.9903 12830429 3.32%
Elapsed time = 4023.28 sec. (2579373.65 ticks, tree = 43.78 MB, solutions = 2)
6588 1791 61.4419 1166 60.0000 61.9903 12850058 3.32%
6603 1791 61.8181 1268 60.0000 61.9903 12872281 3.32%
6628 1793 61.5922 1131 60.0000 61.9903 12892286 3.32%
6647 1795 61.5000 1150 60.0000 61.9903 12910529 3.32%
6672 1795 61.3736 1376 60.0000 61.9903 12927013 3.32%
6689 1840 61.0000 1093 60.0000 61.9832 13086892 3.31%
6702 1814 61.8944 1642 60.0000 61.9803 12977507 3.30%
6747 1842 cutoff 60.0000 61.9803 13106508 3.30%
6767 1830 61.8605 1587 60.0000 61.9803 13007243 3.30%
6792 1832 61.1159 1134 60.0000 61.9803 13051760 3.30%
Elapsed time = 4078.46 sec. (2620380.80 ticks, tree = 45.21 MB, solutions = 2)
6822 1832 cutoff 60.0000 61.9803 13070729 3.30%
6842 1838 61.0000 1324 60.0000 61.9803 13062044 3.30%
6866 1910 61.8334 1441 60.0000 61.9767 13384490 3.29%
6874 1909 61.5960 1261 60.0000 61.9767 13405032 3.29%
6878 1864 61.2500 1442 60.0000 61.9767 13189519 3.29%
6884 1909 61.5172 1466 60.0000 61.9767 13425013 3.29%
6907 1920 61.8302 1533 60.0000 61.9687 13538726 3.28%
6939 1910 61.0000 944 60.0000 61.9687 13446020 3.28%
6966 1909 61.4766 879 60.0000 61.9687 13459069 3.28%
7001 1915 61.0000 1167 60.0000 61.9687 13472454 3.28%
Elapsed time = 4145.74 sec. (2661009.25 ticks, tree = 47.80 MB, solutions = 2)
7021 1967 cutoff 60.0000 61.9687 13747529 3.28%
7040 1923 61.3571 1135 60.0000 61.9687 13504972 3.28%
7070 1918 cutoff 60.0000 61.9681 13572484 3.28%
7114 1984 61.0000 1237 60.0000 61.9681 13811339 3.28%
7161 1985 61.3571 936 60.0000 61.9681 13791200 3.28%
7195 1990 61.0000 1051 60.0000 61.9655 13802870 3.28%
7241 2037 61.4184 1335 60.0000 61.9655 13856241 3.28%
7273 2041 61.0000 718 60.0000 61.9605 13870340 3.27%
7330 2027 infeasible 60.0000 61.9605 14163653 3.27%
7381 2049 61.4755 1224 60.0000 61.9605 14182949 3.27%
Elapsed time = 4206.36 sec. (2700755.48 ticks, tree = 51.38 MB, solutions = 2)
7398 2062 61.7146 1275 60.0000 61.9605 14200049 3.27%
7429 2012 61.2611 1148 60.0000 61.9605 14005744 3.27%
7436 2052 61.3431 1829 60.0000 61.9605 13906393 3.27%
7449 2070 61.0000 764 60.0000 61.9603 14231211 3.27%
7490 2022 61.2747 1098 60.0000 61.9603 14022232 3.27%
7530 2074 cutoff 60.0000 61.9521 14272106 3.25%
7549 2039 61.7106 1072 60.0000 61.9521 14038477 3.25%
7586 2048 61.8510 1416 60.0000 61.9521 14059524 3.25%
7606 2230 61.0000 1314 60.0000 61.9502 14554729 3.25%
7628 2179 cutoff 60.0000 61.9502 14392664 3.25%
Elapsed time = 4270.14 sec. (2743050.11 ticks, tree = 53.81 MB, solutions = 2)
7648 2120 61.0000 894 60.0000 61.9502 14322353 3.25%
7672 2133 61.8597 1531 60.0000 61.9502 14308142 3.25%
7686 2231 61.9079 1684 60.0000 61.9502 14601680 3.25%
7699 2119 61.8254 1403 60.0000 61.9502 14351175 3.25%
7714 2234 61.0000 998 60.0000 61.9470 14664571 3.25%
7723 2236 61.0000 1212 60.0000 61.9470 14644039 3.25%
7731 2134 61.8674 1343 60.0000 61.9470 14318333 3.25%
7756 2238 61.0000 733 60.0000 61.9463 14674875 3.24%
7776 2255 61.2500 1536 60.0000 61.9463 14725473 3.24%
7786 2256 61.8481 1247 60.0000 61.9463 14735565 3.24%
Elapsed time = 4332.20 sec. (2783199.85 ticks, tree = 56.46 MB, solutions = 2)
7791 2257 cutoff 60.0000 61.9463 14745895 3.24%
7808 2264 61.0000 1198 60.0000 61.9430 14946733 3.24%
7821 2270 61.0000 984 60.0000 61.9430 14950291 3.24%
7860 2290 61.0000 1212 60.0000 61.9430 14776599 3.24%
7875 2295 61.0000 932 60.0000 61.9430 14786495 3.24%
7895 2263 61.0000 1251 60.0000 61.9430 14884742 3.24%
7934 2271 infeasible 60.0000 61.9430 14890638 3.24%
7955 2303 61.7400 1119 60.0000 61.9430 14828629 3.24%
7971 2317 61.0000 905 60.0000 61.9383 15097930 3.23%
7990 2272 61.3033 1703 60.0000 61.9383 15027318 3.23%
Elapsed time = 4388.94 sec. (2822866.25 ticks, tree = 57.50 MB, solutions = 2)
8007 2333 61.0000 867 60.0000 61.9354 15151925 3.23%
8029 2333 61.8355 1319 60.0000 61.9354 15165228 3.23%
8046 2334 61.0000 1299 60.0000 61.9354 15178204 3.23%
8060 2343 61.2530 1273 60.0000 61.9354 15191329 3.23%
8078 2326 61.0000 1075 60.0000 61.9354 15125606 3.23%
8098 2354 61.0000 1058 60.0000 61.9324 15218130 3.22%
8156 2361 61.4800 969 60.0000 61.9324 15232884 3.22%
8188 2266 61.0000 1072 60.0000 61.9324 15065570 3.22%
8217 2352 infeasible 60.0000 61.9304 15355287 3.22%
8241 2354 61.3676 1088 60.0000 61.9303 15369248 3.22%
Elapsed time = 4446.48 sec. (2862230.01 ticks, tree = 60.96 MB, solutions = 2)
8277 2365 61.0924 1171 60.0000 61.9303 15247471 3.22%
8316 2426 61.0000 942 60.0000 61.9261 15559093 3.21%
8336 2400 61.1240 1216 60.0000 61.9261 15508046 3.21%
8367 2401 61.3986 1564 60.0000 61.9261 15517862 3.21%
8416 2357 61.0000 1159 60.0000 61.9261 15407396 3.21%
8469 2372 infeasible 60.0000 61.9261 15396690 3.21%
8506 2369 61.0000 779 60.0000 61.9261 15418228 3.21%
8547 2449 61.8355 1424 60.0000 61.9235 15744339 3.21%
8574 2373 cutoff 60.0000 61.9235 15484108 3.21%
8584 2373 61.3522 1138 60.0000 61.9235 15508231 3.21%
Elapsed time = 4506.51 sec. (2901953.67 ticks, tree = 61.37 MB, solutions = 2)
8620 2487 infeasible 60.0000 61.9189 15913518 3.20%
8642 2512 61.0000 815 60.0000 61.9173 16054147 3.20%
8682 2491 61.0000 693 60.0000 61.9173 15951697 3.20%
8718 2489 infeasible 60.0000 61.9142 15960741 3.19%
8783 2547 61.5657 1450 60.0000 61.9142 16227651 3.19%
8824 2523 infeasible 60.0000 61.9142 16130680 3.19%
8887 2489 61.0000 714 60.0000 61.9142 15813419 3.19%
8920 2494 infeasible 60.0000 61.9142 15834833 3.19%
8980 2492 61.0000 738 60.0000 61.9142 15857991 3.19%
9006 2548 infeasible 60.0000 61.9142 16322787 3.19%
Elapsed time = 4562.09 sec. (2940776.73 ticks, tree = 65.84 MB, solutions = 2)
9025 2547 61.6203 1203 60.0000 61.9142 16235296 3.19%
9050 2500 61.2500 975 60.0000 61.9142 16018633 3.19%
9088 2552 61.8385 1463 60.0000 61.9036 16341978 3.17%
9123 2553 cutoff 60.0000 61.8966 16365088 3.16%
9164 2593 61.6620 1309 60.0000 61.8966 16502662 3.16%
9196 2641 61.0000 1047 60.0000 61.8966 16746483 3.16%
9243 2647 61.5000 913 60.0000 61.8966 16767595 3.16%
9280 2599 61.0000 1102 60.0000 61.8966 16561253 3.16%
9332 2627 61.7113 1186 60.0000 61.8966 16590406 3.16%
9356 2628 61.0930 1225 60.0000 61.8966 16611364 3.16%
Elapsed time = 4625.76 sec. (2981229.66 ticks, tree = 66.86 MB, solutions = 2)
9380 2650 61.2630 1095 60.0000 61.8919 16836200 3.15%
9399 2653 61.0000 1807 60.0000 61.8919 16868094 3.15%
9434 2652 61.0000 1115 60.0000 61.8919 16872831 3.15%
9452 2663 61.7739 989 60.0000 61.8919 16908281 3.15%
9489 2689 61.0000 916 60.0000 61.8919 16922193 3.15%
9515 2676 cutoff 60.0000 61.8825 17184971 3.14%
9536 2676 cutoff 60.0000 61.8825 17197590 3.14%
9559 2653 61.0000 1108 60.0000 61.8674 16989017 3.11%
9596 2655 cutoff 60.0000 61.8674 16997530 3.11%
9631 2692 61.0000 1068 60.0000 61.8674 17219131 3.11%
Elapsed time = 4683.73 sec. (3020301.29 ticks, tree = 67.36 MB, solutions = 2)
9677 2705 infeasible 60.0000 61.8674 17243510 3.11%
9710 2692 61.2222 543 60.0000 61.8674 17047013 3.11%
9730 2711 cutoff 60.0000 61.8674 17281318 3.11%
9736 2713 61.5693 1157 60.0000 61.8674 17293726 3.11%
9741 2718 61.0305 1214 60.0000 61.8674 17301128 3.11%
9760 2762 61.0314 1247 60.0000 61.8451 17579803 3.08%
9787 2817 61.0000 1424 60.0000 61.8451 17774155 3.08%
9820 2797 infeasible 60.0000 61.8451 17700085 3.08%
9837 2766 61.0000 1023 60.0000 61.8363 17608387 3.06%
9847 2833 61.0000 1176 60.0000 61.8363 17815781 3.06%
Elapsed time = 4754.33 sec. (3067906.75 ticks, tree = 70.23 MB, solutions = 2)
9867 2812 61.1667 2051 60.0000 61.8363 17870760 3.06%
9889 2837 cutoff 60.0000 61.8363 17858429 3.06%
9931 2838 61.5000 1075 60.0000 61.8291 17872321 3.05%
9978 2825 61.0000 1209 60.0000 61.8291 17970922 3.05%
10067 2863 61.0000 1335 60.0000 61.8291 17909832 3.05%
10155 2829 infeasible 60.0000 61.8291 17748554 3.05%
10222 2813 cutoff 60.0000 61.8291 17982223 3.05%
10288 2847 infeasible 60.0000 61.8165 18056261 3.03%
10336 2857 61.1795 1001 60.0000 61.8165 18077392 3.03%
10376 2947 infeasible 60.0000 61.8041 18445395 3.01%
Elapsed time = 4810.86 sec. (3107326.40 ticks, tree = 74.47 MB, solutions = 2)
10435 2859 infeasible 60.0000 61.8041 18125171 3.01%
10489 2868 cutoff 60.0000 61.8041 18130255 3.01%
10503 2951 61.4333 1405 60.0000 61.8041 18508519 3.01%
10537 2874 61.0000 648 60.0000 61.8041 18151270 3.01%
10559 2950 cutoff 60.0000 61.8041 18542058 3.01%
10597 3003 cutoff 60.0000 61.7965 18672270 2.99%
10637 2957 61.0000 1077 60.0000 61.7965 18584630 2.99%
10671 2887 61.0000 967 60.0000 61.7965 18183141 2.99%
10691 2883 61.0000 880 60.0000 61.7965 18207587 2.99%
10727 2892 61.2927 1416 60.0000 61.7965 18231150 2.99%
Elapsed time = 4873.31 sec. (3146013.14 ticks, tree = 73.37 MB, solutions = 2)
10774 3047 cutoff 60.0000 61.7760 19014444 2.96%
10826 2963 cutoff 60.0000 61.7760 18665600 2.96%
10845 3013 61.5000 1202 60.0000 61.7701 18746676 2.95%
10862 3054 61.0000 1081 60.0000 61.7701 18883472 2.95%
10904 3069 61.0000 861 60.0000 61.7701 19268861 2.95%
10949 3052 61.0000 1054 60.0000 61.7701 18921892 2.95%
10980 3059 61.3111 1383 60.0000 61.7701 18940213 2.95%
11001 3063 61.0000 848 60.0000 61.7701 19043353 2.95%
11038 3073 61.0000 944 60.0000 61.7654 19067069 2.94%
11059 3058 61.0000 1304 60.0000 61.7654 18971160 2.94%
Elapsed time = 4933.79 sec. (3184940.39 ticks, tree = 76.15 MB, solutions = 2)
11099 3079 61.0000 1048 60.0000 61.7654 18979024 2.94%
11141 3078 cutoff 60.0000 61.7654 19001584 2.94%
11181 3116 61.1591 1047 60.0000 61.7552 19553552 2.93%
11211 3116 61.0000 1263 60.0000 61.7514 19559733 2.92%
11246 3089 61.0000 779 60.0000 61.7514 19458460 2.92%
11291 3132 61.4763 1437 60.0000 61.7514 19575665 2.92%
11318 3130 cutoff 60.0000 61.7514 19597777 2.92%
11357 3138 infeasible 60.0000 61.7514 19771799 2.92%
11398 3141 cutoff 60.0000 61.7453 19780179 2.91%
11451 3100 infeasible 60.0000 61.7453 19503913 2.91%
Elapsed time = 4986.36 sec. (3224179.72 ticks, tree = 76.34 MB, solutions = 2)
11509 3131 cutoff 60.0000 61.7453 19827301 2.91%
11549 3162 61.1432 1142 60.0000 61.7360 19946929 2.89%
11570 3129 61.0000 877 60.0000 61.7360 19663162 2.89%
11634 3165 61.4550 983 60.0000 61.7360 19880048 2.89%
11698 3166 cutoff 60.0000 61.7360 19902554 2.89%
11734 3150 61.0000 1006 60.0000 61.7147 20159523 2.86%
11790 3145 infeasible 60.0000 61.7147 20061632 2.86%
11854 3165 infeasible 60.0000 61.7147 19948884 2.86%
11893 3187 infeasible 60.0000 61.7147 20215485 2.86%
11944 3183 61.4327 1461 60.0000 61.7147 20236691 2.86%
Elapsed time = 5042.58 sec. (3262981.88 ticks, tree = 78.15 MB, solutions = 2)
11977 3147 61.5000 1015 60.0000 61.7147 20121081 2.86%
12027 3184 cutoff 60.0000 61.7066 20277701 2.84%
12083 3176 cutoff 60.0000 61.7066 20300601 2.84%
12124 3161 61.5000 1002 60.0000 61.6967 20771814 2.83%
12154 3148 61.3691 1151 60.0000 61.6967 20381973 2.83%
12194 3158 infeasible 60.0000 61.6967 20580807 2.83%
12250 3150 61.0000 1240 60.0000 61.6919 20842945 2.82%
12303 3141 cutoff 60.0000 61.6919 20449019 2.82%
12364 3197 cutoff 60.0000 61.6835 21017417 2.81%
12387 3206 61.0000 1339 60.0000 61.6835 21154927 2.81%
Elapsed time = 5103.26 sec. (3302444.71 ticks, tree = 78.19 MB, solutions = 2)
12437 3221 infeasible 60.0000 61.6835 21175005 2.81%
12476 3221 61.0000 988 60.0000 61.6835 21199639 2.81%
12508 3166 infeasible 60.0000 61.6835 20892100 2.81%
12516 3162 61.0000 1108 60.0000 61.6835 20909465 2.81%
12549 3186 61.0000 1307 60.0000 61.6667 21301906 2.78%
12608 3158 infeasible 60.0000 61.6590 21568178 2.76%
12698 3247 61.0000 1065 60.0000 61.6590 21277625 2.76%
12755 3186 infeasible 60.0000 61.6590 21513465 2.76%
12781 3181 cutoff 60.0000 61.6494 21535145 2.75%
12844 3188 61.0000 1098 60.0000 61.6494 21381785 2.75%
Elapsed time = 5168.29 sec. (3341418.56 ticks, tree = 76.25 MB, solutions = 2)
12899 3201 cutoff 60.0000 61.6494 21784101 2.75%
12936 3196 cutoff 60.0000 61.6321 21608725 2.72%
12955 3197 infeasible 60.0000 61.6224 21811000 2.70%
12980 3191 61.0000 677 60.0000 61.6224 21833958 2.70%
13003 3165 61.0000 924 60.0000 61.6224 21638900 2.70%
13026 3234 61.0000 1059 60.0000 61.6224 22075653 2.70%
13065 3239 cutoff 60.0000 61.6224 22090956 2.70%
13074 3210 cutoff 60.0000 61.6224 21909136 2.70%
13115 3154 infeasible 60.0000 61.6224 21712230 2.70%
13157 3232 cutoff 60.0000 61.6000 22137303 2.67%
Elapsed time = 5227.01 sec. (3380933.18 ticks, tree = 75.92 MB, solutions = 2)
13170 3225 cutoff 60.0000 61.6000 22153208 2.67%
13183 3222 61.0000 1456 60.0000 61.6000 22164650 2.67%
13206 3215 61.0000 1186 60.0000 61.6000 22296707 2.67%
13237 3165 61.0000 987 60.0000 61.6000 22394542 2.67%
13270 3127 cutoff 60.0000 61.5568 22670998 2.59%
13302 3213 cutoff 60.0000 61.5568 22348758 2.59%
13319 3116 61.0000 1003 60.0000 61.5568 22700891 2.59%
13350 3104 infeasible 60.0000 61.5568 22721876 2.59%
13371 3082 cutoff 60.0000 61.5568 22789932 2.59%
13400 3079 cutoff 60.0000 61.5191 22900534 2.53%
Elapsed time = 5287.62 sec. (3422572.94 ticks, tree = 73.30 MB, solutions = 2)
13416 3064 cutoff 60.0000 61.5000 22968687 2.50%
13448 3079 61.0000 1175 60.0000 61.5000 22927242 2.50%
13460 3074 cutoff 60.0000 61.5000 22940326 2.50%
13471 3058 cutoff 60.0000 61.5000 22994565 2.50%
13495 3041 cutoff 60.0000 61.5000 23026843 2.50%
13524 3047 cutoff 60.0000 61.5000 23023921 2.50%
13561 2997 cutoff 60.0000 61.5000 23146081 2.50%
13595 2979 61.0000 961 60.0000 61.5000 23194905 2.50%
13635 2952 infeasible 60.0000 61.5000 23243440 2.50%
13671 3026 61.0000 1011 60.0000 61.5000 23126969 2.50%
Elapsed time = 5341.50 sec. (3461642.86 ticks, tree = 73.45 MB, solutions = 2)
13685 2949 61.0000 1025 60.0000 61.5000 23284084 2.50%
13702 2943 cutoff 60.0000 61.5000 23295585 2.50%
13735 2951 61.0000 984 60.0000 61.5000 23274270 2.50%
13745 3105 61.0000 1410 60.0000 61.5000 22804004 2.50%
In this case, the optimality gap is set to 2% and the optimization would have terminated earlier if the integrality of the objective function had been considered. I have seen this issue numerous times with more severe delays in the termination due to the solver not considering the integrality cuts. I could resolve this issue manually by introducing an auxiliary integer variable that captures the value of the original objective function in a constraint. However, I am wondering why this has not already been considered in modern solvers (perhaps it has, but it requires a certain configuration/implementation)?
