762:
cut algorithm. Most components of the algorithm, e.g., search tree management, management of linear programming solution, cut pool management, and communication management, are internal to the library and need not be touched by the user. The executables can be built in any number of configurations ranging from completely sequential to fully parallel with independently functioning cut generators, cut pools, and LP solvers. The distributed version currently runs in any environment supported by the
148:(OR) community with a peer-review process and an archive. Papers in operations research journals on mathematical theory often contain supporting numerical results from computational studies. The software implementations, models, and data used to produce the numerical results are typically not published. The status quo impeded researchers needing to reproduce computational results, make fair comparisons, and extend the state of the art.
33:
761:
and pricing algorithms. The user of the library can customize the algorithm in any number of ways by supplying application-specific subroutines for reading in custom data files, generating application-specific cutting planes, or applying custom branching rules, resulting in a customized branch and
781:
files. SYMPHONY does not have an LP-Solver of its own, but can be used with solvers like Clp, Cplex, Xpress through the Osi-interface. Cuts are generated using COIN's cut generation library: CGL. SYMPHONY also has structure specific implementations for problems like the
850:
modeler and solver written in C++. It can read
Stochastic MPS and offers direct interfaces for constructing stochastic programs. It generates the deterministic equivalent linear program, solves it, and provides interfaces to access the scenario solutions.
252:. CLP is primarily meant to be used as a callable library, although a stand-alone executable version can be built. It is designed to be as reliable as any commercial solver, although several times slower, and to be able to tackle very large problems.
171:
software, models, and data. COIN-OR was conceived as an initiative to promote open source in the computational operations research community and to provide the on-line resources and hosting services required to enable others to run their own
105:
179:
The COIN-OR website was launched as an experiment in 2000, in conjunction with 17th
International Symposium on Math Programming in Atlanta, Georgia. In 2007, COIN-OR had 25 application projects, including tools for
1269:
557:
483:
409:
320:
753:
SYMPHONY is a callable library which implements both sequential and parallel versions of branch, cut and price to solve MILPs. A branch, cut and price algorithm is similar to a
66:
639:
605:
1873:
1262:
2113:
1682:
1255:
947:
916:
212:) and more. By 2011, this had grown to 48 projects. COIN-OR is hosted by the Institute for Operations Research and the Management Sciences,
711:). Although it has been a popular choice of open source MIP solver for many years, its performance is now significantly inferior to HiGHS.
2091:
1352:
873:
691:
84:
52:
2084:
1933:
1771:
1731:
1647:
1528:
1347:
1278:
807:
2016:
1953:
1820:
1746:
1667:
1553:
1548:
1483:
1412:
696:
489:
415:
341:
205:
1181:
798:, etc. SYMPHONY also has an interactive shell where the user can enter commands to execute and control the program.
1938:
1854:
1815:
1741:
1657:
1543:
1493:
1357:
1131:
815:
783:
778:
723:
249:
975:
1622:
1503:
1224:
An
Introduction to the COIN-OR Optimization Suite: Open Source Tools for Building and Solving Optimization Models
1057:
1110:
1835:
62:
1210:
1156:
791:
766:
message passing protocol. The same source code can also be compiled for shared-memory architectures using any
1002:
264:
787:
48:
43:
1223:
795:
2031:
847:
1864:
1578:
1317:
241:
189:
1030:
758:
245:
173:
1983:
1923:
1800:
1518:
197:
145:
940:
909:
1435:
1431:
1218:, John Karlof (ed.), CRC Press Operations Research Series, 2005, 253-303. (Working paper version)
747:
735:
720:
674:
611:
577:
230:
181:
156:
1085:
885:
647:
160:
1908:
1790:
1711:
1627:
1498:
754:
2021:
1963:
1903:
1751:
1662:
1558:
881:
835:
2061:
1888:
1780:
1701:
1597:
1453:
731:
727:
670:
2107:
1247:
681:. It can be used as both a stand-alone executable and as a callable library (through
1307:
1297:
889:
831:
811:
774:
2066:
2056:
2006:
1973:
1844:
1825:
1805:
1761:
1756:
1726:
1672:
1642:
1568:
1523:
1407:
1377:
1302:
1292:
646:
with up to millions of variables and/or constraints. Its main algorithm is the
32:
1336:
17:
1185:
104:
1991:
1883:
1696:
1592:
1513:
1448:
1382:
137:
2001:
1898:
1341:
1135:
971:
213:
1051:
1023:"OpenSolver for Excel – The Open Source Optimization Solver for Excel"
2051:
1943:
1928:
1617:
1478:
1422:
1402:
1387:
1106:
877:
830:, to solve linear problems. PuLP is the default optimization tool in
767:
233:
141:
255:
CLP is designed to solve linear programming problems such as :
1160:
678:
237:
2045:
2011:
1996:
1968:
1958:
1948:
1918:
1913:
1893:
1878:
1849:
1810:
1795:
1785:
1736:
1721:
1716:
1706:
1691:
1652:
1637:
1632:
1612:
1587:
1538:
1533:
1508:
1473:
1443:
1397:
1372:
1367:
1326:
996:
865:
827:
743:
700:
209:
193:
167:
Research proposed open source as an analogous yet viable means to
152:
1227:. Optimization Days, Montreal, May 7, 2013. (Presentation slides)
1488:
1362:
1331:
1078:"HiGHS - High-performance parallel linear optimization software"
869:
861:
686:
144:." The open literature (e.g., a research journal) provides the
1251:
763:
164:
26:
1244:
216:, and run by the educational, non-profit COIN-OR Foundation.
1211:
Noncommercial
Software for Mixed-Integer Linear Programming
708:
1077:
1022:
116:
58:
657:, Branch Cut and Price (BCP), COIN-OR Branch and Cut (
136:), is a project that aims to "create for mathematical
1239:
614:
580:
492:
418:
344:
267:
163:
of software development and distribution. A group at
880:
modeling systems. They can also be used from within
130:
2030:
1982:
1863:
1834:
1770:
1681:
1577:
1430:
1421:
1316:
1285:
111:
633:
599:
551:
477:
403:
314:
750:solvers to solve the underlying linear programs.
552:{\displaystyle a_{31}x_{1}+a_{32}x_{2}\leq b_{3}}
478:{\displaystyle a_{21}x_{1}+a_{22}x_{2}\leq b_{2}}
404:{\displaystyle a_{11}x_{1}+a_{12}x_{2}\leq b_{1}}
47:, potentially preventing the article from being
738:(MIPs) over heterogeneous networks. It can use
653:CLP is used in other COIN-OR projects such as
1263:
140:what the open literature is for mathematical
8:
97:
1427:
1270:
1256:
1248:
229:COIN-OR LP (CLP or Clp) is an open-source
103:
96:
67:reliable, independent, third-party sources
619:
613:
585:
579:
543:
530:
520:
507:
497:
491:
469:
456:
446:
433:
423:
417:
395:
382:
372:
359:
349:
343:
311:
305:
295:
282:
272:
266:
85:Learn how and when to remove this message
1216:Integer Programming: Theory and Practice
61:by replacing them with more appropriate
901:
707:, CMPL, OpenSolver for Excel, JuMP, or
315:{\displaystyle c_{1}x_{1}+c_{2}x_{2}\,}
44:too closely associated with the subject
860:COIN-OR solvers are available in the
777:(through the COIN-OR MPS reader) and
248:with none of the restrictions of the
159:, and other projects popularized the
7:
1107:"The MIPLIB2017 Benchmark Instances"
806:PuLP is an LP/IP modeler written in
757:algorithm but additionally includes
2092:Comparison of optimization software
683:A Mathematical Programming Language
2114:Mathematical optimization software
1279:Mathematical optimization software
1001:, COIN-OR Foundation, 2024-01-20,
25:
972:"Benchmark of Simplex LP solvers"
692:General Algebraic Modeling System
1208:J.T. Linderoth and T.K. Ralphs:
42:may rely excessively on sources
31:
1113:from the original on 2021-10-30
1088:from the original on 2024-06-17
1060:from the original on 2024-05-15
1033:from the original on 2024-06-10
1005:from the original on 2024-04-13
978:from the original on 2021-11-11
953:from the original on 2016-04-29
922:from the original on 2008-05-15
673:(CBC or Cbc) is an open-source
1:
2085:List of optimization software
1563:
941:"COIN-OR Annual Report, 2011"
910:"COIN-OR Annual Report, 2007"
730:(SYMPHONY) is an open source
654:
201:
240:. It is published under the
206:algebraic modeling languages
634:{\displaystyle x_{2}\geq 0}
600:{\displaystyle x_{1}\geq 0}
2130:
784:traveling salesman problem
250:GNU General Public License
2079:
1392:
704:
675:mixed integer programming
102:
1607:
1602:
1468:
1463:
1056:, JuMP-dev, 2024-06-19,
823:
819:
792:set partitioning problem
739:
658:
185:
788:vehicle routing problem
734:framework for solving
848:stochastic programming
736:mixed integer programs
635:
601:
567:non-negative variables
553:
479:
405:
316:
814:or LP files and call
796:mixed postman problem
759:cutting-plane methods
636:
602:
554:
480:
406:
332:of the following form
317:
244:so it can be used in
242:Common Public License
190:nonlinear programming
770:compliant compiler.
612:
578:
490:
416:
342:
265:
246:proprietary software
200:(e.g., CBC, Bcp and
174:open-source software
330:problem constraints
198:integer programming
146:operations research
99:
810:. It can generate
748:linear programming
746:, XPRESS or other
677:solver written in
631:
597:
549:
475:
401:
312:
231:linear programming
182:linear programming
2101:
2100:
2075:
2074:
648:simplex algorithm
161:open-source model
127:
126:
95:
94:
87:
16:(Redirected from
2121:
1974:Xpress NonLinear
1909:Gurobi Optimizer
1826:Xpress Optimizer
1791:Gurobi Optimizer
1762:Xpress NonLinear
1757:Xpress Optimizer
1712:Gurobi Optimizer
1673:Xpress Optimizer
1628:Gurobi Optimizer
1569:Xpress Optimizer
1499:Gurobi Optimizer
1428:
1272:
1265:
1258:
1249:
1243:
1242:
1240:Official website
1197:
1196:
1194:
1193:
1184:. Archived from
1178:
1172:
1171:
1169:
1168:
1159:. Archived from
1153:
1147:
1146:
1144:
1143:
1134:. Archived from
1128:
1122:
1121:
1119:
1118:
1103:
1097:
1096:
1094:
1093:
1074:
1068:
1067:
1066:
1065:
1053:jump-dev/JuMP.jl
1048:
1042:
1041:
1039:
1038:
1019:
1013:
1012:
1011:
1010:
993:
987:
986:
984:
983:
968:
962:
961:
959:
958:
952:
945:
937:
931:
930:
928:
927:
921:
914:
906:
755:branch and bound
640:
638:
637:
632:
624:
623:
606:
604:
603:
598:
590:
589:
558:
556:
555:
550:
548:
547:
535:
534:
525:
524:
512:
511:
502:
501:
484:
482:
481:
476:
474:
473:
461:
460:
451:
450:
438:
437:
428:
427:
410:
408:
407:
402:
400:
399:
387:
386:
377:
376:
364:
363:
354:
353:
321:
319:
318:
313:
310:
309:
300:
299:
287:
286:
277:
276:
202:COIN-OR SYMPHONY
123:
120:
118:
107:
100:
90:
83:
79:
76:
70:
35:
27:
21:
2129:
2128:
2124:
2123:
2122:
2120:
2119:
2118:
2104:
2103:
2102:
2097:
2071:
2026:
2022:Octeract Engine
1978:
1964:Octeract Engine
1904:Galahad library
1859:
1830:
1766:
1752:Octeract Engine
1677:
1663:Octeract Engine
1573:
1559:Octeract Engine
1417:
1312:
1281:
1276:
1238:
1237:
1234:
1205:
1203:Further reading
1200:
1191:
1189:
1180:
1179:
1175:
1166:
1164:
1155:
1154:
1150:
1141:
1139:
1130:
1129:
1125:
1116:
1114:
1105:
1104:
1100:
1091:
1089:
1076:
1075:
1071:
1063:
1061:
1050:
1049:
1045:
1036:
1034:
1021:
1020:
1016:
1008:
1006:
995:
994:
990:
981:
979:
970:
969:
965:
956:
954:
950:
943:
939:
938:
934:
925:
923:
919:
912:
908:
907:
903:
899:
857:
844:
804:
773:SYMPHONY reads
717:
667:
661:), and others.
615:
610:
609:
581:
576:
575:
539:
526:
516:
503:
493:
488:
487:
465:
452:
442:
429:
419:
414:
413:
391:
378:
368:
355:
345:
340:
339:
301:
291:
278:
268:
263:
262:
227:
222:
151:The success of
115:
91:
80:
74:
71:
56:
36:
23:
22:
15:
12:
11:
5:
2127:
2125:
2117:
2116:
2106:
2105:
2099:
2098:
2096:
2095:
2088:
2080:
2077:
2076:
2073:
2072:
2070:
2069:
2064:
2059:
2054:
2049:
2043:
2040:
2036:
2034:
2028:
2027:
2025:
2024:
2019:
2014:
2009:
2004:
1999:
1994:
1988:
1986:
1980:
1979:
1977:
1976:
1971:
1966:
1961:
1956:
1951:
1946:
1941:
1936:
1931:
1926:
1921:
1916:
1911:
1906:
1901:
1896:
1891:
1889:Artelys Knitro
1886:
1881:
1876:
1870:
1868:
1861:
1860:
1858:
1857:
1852:
1847:
1841:
1839:
1832:
1831:
1829:
1828:
1823:
1818:
1813:
1808:
1803:
1798:
1793:
1788:
1783:
1781:Artelys Knitro
1777:
1775:
1768:
1767:
1765:
1764:
1759:
1754:
1749:
1744:
1739:
1734:
1729:
1724:
1719:
1714:
1709:
1704:
1702:Artelys Knitro
1699:
1694:
1688:
1686:
1679:
1678:
1676:
1675:
1670:
1665:
1660:
1655:
1650:
1645:
1640:
1635:
1630:
1625:
1620:
1615:
1610:
1605:
1600:
1598:Artelys Knitro
1595:
1590:
1584:
1582:
1575:
1574:
1572:
1571:
1566:
1561:
1556:
1551:
1546:
1541:
1536:
1531:
1526:
1521:
1516:
1511:
1506:
1501:
1496:
1491:
1486:
1481:
1476:
1471:
1466:
1461:
1456:
1454:Artelys Knitro
1451:
1446:
1440:
1438:
1425:
1419:
1418:
1416:
1415:
1410:
1405:
1400:
1395:
1390:
1385:
1380:
1375:
1370:
1365:
1360:
1355:
1350:
1345:
1339:
1334:
1329:
1323:
1321:
1314:
1313:
1311:
1310:
1305:
1300:
1295:
1289:
1287:
1283:
1282:
1277:
1275:
1274:
1267:
1260:
1252:
1246:
1245:
1233:
1232:External links
1230:
1229:
1228:
1219:
1204:
1201:
1199:
1198:
1173:
1148:
1123:
1098:
1069:
1043:
1027:opensolver.org
1014:
988:
963:
932:
900:
898:
895:
894:
893:
856:
853:
843:
840:
803:
800:
732:branch and cut
716:
713:
671:branch and cut
666:
663:
644:
643:
642:
641:
630:
627:
622:
618:
607:
596:
593:
588:
584:
570:
569:
562:
561:
560:
559:
546:
542:
538:
533:
529:
523:
519:
515:
510:
506:
500:
496:
485:
472:
468:
464:
459:
455:
449:
445:
441:
436:
432:
426:
422:
411:
398:
394:
390:
385:
381:
375:
371:
367:
362:
358:
352:
348:
334:
333:
325:
324:
323:
322:
308:
304:
298:
294:
290:
285:
281:
275:
271:
226:
223:
221:
218:
125:
124:
113:
109:
108:
93:
92:
75:September 2018
39:
37:
30:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2126:
2115:
2112:
2111:
2109:
2094:
2093:
2089:
2087:
2086:
2082:
2081:
2078:
2068:
2065:
2063:
2060:
2058:
2055:
2053:
2050:
2047:
2044:
2041:
2039:Artelys Kalis
2038:
2037:
2035:
2033:
2029:
2023:
2020:
2018:
2015:
2013:
2010:
2008:
2005:
2003:
2000:
1998:
1995:
1993:
1990:
1989:
1987:
1985:
1981:
1975:
1972:
1970:
1967:
1965:
1962:
1960:
1957:
1955:
1952:
1950:
1947:
1945:
1942:
1940:
1937:
1935:
1932:
1930:
1927:
1925:
1922:
1920:
1917:
1915:
1912:
1910:
1907:
1905:
1902:
1900:
1897:
1895:
1892:
1890:
1887:
1885:
1882:
1880:
1877:
1875:
1872:
1871:
1869:
1866:
1862:
1856:
1853:
1851:
1848:
1846:
1843:
1842:
1840:
1837:
1833:
1827:
1824:
1822:
1819:
1817:
1814:
1812:
1809:
1807:
1804:
1802:
1799:
1797:
1794:
1792:
1789:
1787:
1784:
1782:
1779:
1778:
1776:
1773:
1769:
1763:
1760:
1758:
1755:
1753:
1750:
1748:
1745:
1743:
1740:
1738:
1735:
1733:
1730:
1728:
1725:
1723:
1720:
1718:
1715:
1713:
1710:
1708:
1705:
1703:
1700:
1698:
1695:
1693:
1690:
1689:
1687:
1684:
1680:
1674:
1671:
1669:
1666:
1664:
1661:
1659:
1656:
1654:
1651:
1649:
1646:
1644:
1641:
1639:
1636:
1634:
1631:
1629:
1626:
1624:
1621:
1619:
1616:
1614:
1611:
1609:
1606:
1604:
1601:
1599:
1596:
1594:
1591:
1589:
1586:
1585:
1583:
1580:
1576:
1570:
1567:
1565:
1562:
1560:
1557:
1555:
1552:
1550:
1547:
1545:
1542:
1540:
1537:
1535:
1532:
1530:
1527:
1525:
1522:
1520:
1517:
1515:
1512:
1510:
1507:
1505:
1502:
1500:
1497:
1495:
1492:
1490:
1487:
1485:
1482:
1480:
1477:
1475:
1472:
1470:
1467:
1465:
1462:
1460:
1457:
1455:
1452:
1450:
1447:
1445:
1442:
1441:
1439:
1437:
1433:
1429:
1426:
1424:
1420:
1414:
1411:
1409:
1406:
1404:
1401:
1399:
1396:
1394:
1391:
1389:
1386:
1384:
1381:
1379:
1376:
1374:
1371:
1369:
1366:
1364:
1361:
1359:
1356:
1354:
1351:
1349:
1346:
1343:
1340:
1338:
1335:
1333:
1330:
1328:
1325:
1324:
1322:
1319:
1315:
1309:
1306:
1304:
1301:
1299:
1296:
1294:
1291:
1290:
1288:
1284:
1280:
1273:
1268:
1266:
1261:
1259:
1254:
1253:
1250:
1241:
1236:
1235:
1231:
1226:
1225:
1220:
1217:
1213:
1212:
1207:
1206:
1202:
1188:on 2014-10-15
1187:
1183:
1177:
1174:
1163:on 2013-12-20
1162:
1158:
1152:
1149:
1138:on 2014-02-28
1137:
1133:
1127:
1124:
1112:
1108:
1102:
1099:
1087:
1083:
1082:www.highs.dev
1079:
1073:
1070:
1059:
1055:
1054:
1047:
1044:
1032:
1028:
1024:
1018:
1015:
1004:
1000:
999:
992:
989:
977:
973:
967:
964:
949:
942:
936:
933:
918:
911:
905:
902:
896:
891:
887:
883:
879:
875:
871:
867:
863:
859:
858:
854:
852:
849:
841:
839:
837:
833:
829:
825:
821:
817:
813:
809:
801:
799:
797:
793:
789:
785:
780:
776:
771:
769:
765:
760:
756:
751:
749:
745:
741:
737:
733:
729:
725:
722:
721:multi-process
714:
712:
710:
706:
702:
698:
694:
693:
688:
684:
680:
676:
672:
664:
662:
660:
656:
651:
649:
628:
625:
620:
616:
608:
594:
591:
586:
582:
574:
573:
572:
571:
568:
564:
563:
544:
540:
536:
531:
527:
521:
517:
513:
508:
504:
498:
494:
486:
470:
466:
462:
457:
453:
447:
443:
439:
434:
430:
424:
420:
412:
396:
392:
388:
383:
379:
373:
369:
365:
360:
356:
350:
346:
338:
337:
336:
335:
331:
327:
326:
306:
302:
296:
292:
288:
283:
279:
273:
269:
260:
259:
258:
257:
256:
253:
251:
247:
243:
239:
235:
232:
224:
219:
217:
215:
211:
207:
203:
199:
195:
191:
187:
183:
177:
175:
170:
166:
162:
158:
154:
149:
147:
143:
139:
135:
131:
122:
114:
110:
106:
101:
89:
86:
78:
68:
64:
60:
54:
50:
46:
45:
40:This article
38:
34:
29:
28:
19:
2090:
2083:
2067:Xpress Kalis
2048:CP Optimizer
1458:
1408:Xpress Mosel
1358:GNU MathProg
1286:Data formats
1222:
1215:
1209:
1190:. Retrieved
1186:the original
1176:
1165:. Retrieved
1161:the original
1151:
1140:. Retrieved
1136:the original
1126:
1115:. Retrieved
1101:
1090:. Retrieved
1081:
1072:
1062:, retrieved
1052:
1046:
1035:. Retrieved
1026:
1017:
1007:, retrieved
998:coin-or/Cmpl
997:
991:
980:. Retrieved
966:
955:. Retrieved
935:
924:. Retrieved
904:
890:SolverStudio
845:
832:SolverStudio
805:
779:GNU MathProg
772:
752:
724:optimization
718:
690:
682:
668:
652:
645:
566:
329:
254:
228:
178:
168:
150:
133:
129:
128:
81:
72:
57:Please help
41:
2057:Mathematica
2007:Mathematica
1845:Mathematica
1806:Mathematica
1727:Mathematica
1643:Mathematica
1524:Mathematica
1494:GLPK/GLPSOL
1378:Mathematica
1293:Mathematica
1221:T. Ralphs:
719:Single- or
328:subject to
236:written in
186:COIN-OR CLP
18:COIN-OR CLP
1192:2014-01-03
1167:2013-11-14
1142:2013-11-14
1132:"SYMPHONY"
1117:2021-11-11
1092:2024-06-20
1064:2024-06-20
1037:2024-06-20
1009:2024-06-20
982:2021-11-11
957:2016-07-05
926:2008-03-28
897:References
886:OpenSolver
176:projects.
59:improve it
49:verifiable
1337:APMonitor
846:SMI is a
695:(GAMS) ,
626:≥
592:≥
537:≤
463:≤
389:≤
261:minimize
63:citations
2108:Category
1992:ANTIGONE
1884:ANTIGONE
1774:, MISOCP
1697:ANTIGONE
1593:ANTIGONE
1564:SYMPHONY
1514:Lp_solve
1449:ANTIGONE
1383:MiniZinc
1318:Modeling
1111:Archived
1086:Archived
1058:archived
1031:Archived
1003:archived
976:Archived
948:Archived
917:Archived
892:add-ins.
884:via the
855:See also
728:networks
715:SYMPHONY
709:MiniZinc
669:COIN-OR
655:SYMPHONY
220:Projects
138:software
119:.coin-or
2002:Couenne
1899:Couenne
1867:, MINLP
1838:, MISDP
1685:, MIQCP
1423:Solvers
1342:ECLiPSe
214:INFORMS
208:(e.g.,
192:(e.g.,
184:(e.g.,
169:publish
134:COIN-OR
112:Website
98:COIN-OR
53:neutral
2052:Gecode
1944:NLPQLP
1929:MIDACO
1618:FortMP
1581:, MIQP
1554:SoPlex
1479:FortMP
1403:TOMLAB
1388:OptimJ
1214:. In:
1157:"PuLP"
878:FortSP
876:, and
826:, and
808:Python
768:OpenMP
234:solver
157:Apache
142:theory
2062:JaCoP
2046:CPLEX
2042:Comet
2012:LINDO
1997:BARON
1969:WORHP
1959:SNOPT
1949:NPSOL
1934:MINOS
1919:LINDO
1914:IPOPT
1894:BARON
1879:APOPT
1850:MOSEK
1811:MOSEK
1796:LINDO
1786:CPLEX
1737:MOSEK
1732:MINOS
1722:LINDO
1717:IPOPT
1707:CPLEX
1692:APOPT
1653:MOSEK
1648:MINOS
1638:LINDO
1633:IPOPT
1623:HiGHS
1613:CPLEX
1588:APOPT
1539:MOSEK
1534:MINTO
1529:MINOS
1509:LINDO
1504:HiGHS
1474:CPLEX
1444:APOPT
1413:ZIMPL
1398:Pyomo
1368:LINDO
1348:Gekko
1327:AIMMS
1320:tools
1182:"SMI"
951:(PDF)
944:(PDF)
920:(PDF)
913:(PDF)
882:Excel
866:AIMMS
836:Excel
828:CPLEX
744:CPLEX
726:over
701:AIMMS
210:Coopr
194:IPOPT
153:Linux
2017:SCIP
1954:SCIP
1924:LOQO
1821:SCIP
1801:LOQO
1772:SOCP
1747:SCIP
1668:SCIP
1549:SCIP
1519:LOQO
1489:GLOP
1436:MILP
1393:PuLP
1363:JuMP
1353:GAMS
1344:-CLP
1332:AMPL
888:and
874:GAMS
870:AMPL
862:JuMP
834:for
816:GLPK
802:PuLP
705:PuLP
689:) ,
687:AMPL
565:and
121:.org
51:and
1939:NAG
1874:AOA
1865:NLP
1855:NAG
1836:SDP
1816:NAG
1742:NAG
1683:QCP
1658:NAG
1608:CLP
1603:CBC
1544:NAG
1484:GCG
1469:CBC
1464:CLP
1459:BCP
1373:OPL
1308:sol
1298:MPS
842:SMI
824:CBC
820:CLP
812:MPS
775:MPS
764:PVM
740:CLP
697:MPL
679:C++
665:CBC
659:CBC
238:C++
225:CLP
204:),
196:),
188:),
165:IBM
117:www
65:to
2110::
2032:CP
1984:GO
1579:QP
1434:,
1432:LP
1303:nl
1109:.
1084:.
1080:.
1029:.
1025:.
974:.
946:.
915:.
872:,
868:,
864:,
838:.
818:,
794:,
790:,
786:,
742:,
703:,
699:,
650:.
522:32
499:31
448:22
425:21
374:12
351:11
155:,
1271:e
1264:t
1257:v
1195:.
1170:.
1145:.
1120:.
1095:.
1040:.
985:.
960:.
929:.
822:/
685:(
629:0
621:2
617:x
595:0
587:1
583:x
545:3
541:b
532:2
528:x
518:a
514:+
509:1
505:x
495:a
471:2
467:b
458:2
454:x
444:a
440:+
435:1
431:x
421:a
397:1
393:b
384:2
380:x
370:a
366:+
361:1
357:x
347:a
307:2
303:x
297:2
293:c
289:+
284:1
280:x
274:1
270:c
132:(
88:)
82:(
77:)
73:(
69:.
55:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
