A Hybrid Particle Swarm Optimization Algorithm Enhanced with Nonlinear Inertial Weight and Gaussian Mutation for Job Shop Scheduling Problems
Abstract
:1. Introduction
2. An Overview of the PSO
3. NGPSO Algorithm
3.1. Nonlinear Inertia Weight Improves the Local Search Capability of PSO (PSO-NIW)
3.2. Gauss Mutation Operation Improves the Global Search Capability of PSO (PSO-GM)
3.3. The Main Process of NGPSO
4. NGPSO for JSSP
4.1. The JSSP Model
4.2. Analysis of the Main Process of the NGPSO in Solving JSSP
5. Experimental Results and Analysis
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Dimension | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
position value | 0.36 | 0.01 | 0.67 | 0.69 | 1.19 | 1.02 |
smallest position value | 2 | 1 | 3 | 4 | 6 | 5 |
Projects | Jobs | Operations Number | ||
---|---|---|---|---|
1 | 2 | 3 | ||
J1 | 3 | 3 | 2 | |
operation time | J2 | 1 | 5 | 3 |
J3 | 3 | 2 | 3 | |
J1 | M1 | M2 | M3 | |
machine sequence | J2 | M1 | M3 | M2 |
J3 | M2 | M1 | M3 |
Instance | OVCK | NGPSO | PSO-NIW | PSO-GM | PSO | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Best | Worst | Avg | Best | Worst | Avg | Best | Worst | Avg | Best | Worst | Avg | ||
FT06 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 |
FT10 | 930 | 930 | 1056 | 955 | 930 | 1118 | 967 | 930 | 1073 | 959 | 932 | 1149 | 977 |
FT20 | 1165 | 1210 | 1311 | 1247 | 1178 | 1253 | 1249 | 1167 | 1313 | 1256 | 1180 | 1274 | 1261 |
LA1 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 | 666 |
LA2 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 |
LA3 | 597 | 597 | 676 | 635 | 597 | 680 | 539 | 609 | 679 | 646 | 624 | 690 | 653 |
LA4 | 590 | 590 | 622 | 609 | 613 | 646 | 627 | 604 | 635 | 618 | 627 | 678 | 634 |
LA5 | 593 | 593 | 593 | 593 | 593 | 593 | 593 | 593 | 593 | 593 | 593 | 593 | 593 |
LA6 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 | 926 |
LA7 | 890 | 890 | 890 | 890 | 890 | 890 | 890 | 890 | 890 | 890 | 890 | 890 | 890 |
LA8 | 863 | 863 | 863 | 863 | 863 | 863 | 863 | 863 | 863 | 863 | 863 | 863 | 863 |
LA9 | 951 | 951 | 951 | 951 | 951 | 951 | 951 | 951 | 951 | 951 | 951 | 951 | 951 |
LA10 | 958 | 958 | 997 | 969 | 963 | 1053 | 998 | 958 | 1022 | 988 | 958 | 1069 | 999 |
LA11 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 | 1222 |
LA12 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 | 1039 |
LA13 | 1150 | 1150 | 1150 | 1150 | 1150 | 1150 | 1150 | 1150 | 1150 | 1150 | 1150 | 1150 | 1150 |
LA14 | 1292 | 1292 | 1292 | 1292 | 1292 | 1292 | 1292 | 1292 | 1292 | 1292 | 1292 | 1292 | 1292 |
LA15 | 1207 | 1207 | 1207 | 1207 | 1207 | 1207 | 1207 | 1207 | 1207 | 1207 | 1207 | 1207 | 1207 |
LA16 | 945 | 945 | 945 | 945 | 945 | 992 | 978 | 945 | 972 | 956 | 962 | 994 | 980 |
LA17 | 784 | 794 | 803 | 798 | 811 | 878 | 849 | 784 | 866 | 833 | 822 | 879 | 836 |
LA18 | 848 | 848 | 999 | 913 | 848 | 1033 | 924 | 848 | 1054 | 933 | 857 | 1088 | 957 |
LA19 | 842 | 842 | 1032 | 905 | 889 | 1087 | 923 | 878 | 1073 | 933 | 891 | 1131 | 946 |
LA20 | 902 | 908 | 1228 | 965 | 1113 | 1342 | 1127 | 1009 | 1304 | 1130 | 1152 | 1385 | 1223 |
LA21 | 1046 | 1183 | 1271 | 1208 | 1190 | 1318 | 1224 | 1046 | 1324 | 1230 | 1201 | 1398 | 1244 |
LA22 | 927 | 927 | 989 | 966 | 936 | 1014 | 979 | 927 | 1112 | 982 | 957 | 1194 | 992 |
LA23 | 1032 | 1032 | 1245 | 1123 | 1109 | 1299 | 1203 | 1097 | 1283 | 1196 | 1100 | 1307 | 1208 |
LA24 | 935 | 968 | 1153 | 983 | 998 | 1184 | 1076 | 935 | 1166 | 1047 | 1003 | 1182 | 1089 |
LA25 | 977 | 977 | 1089 | 994 | 987 | 1145 | 1018 | 980 | 1129 | 1007 | 991 | 1211 | 1014 |
LA26 | 1218 | 1218 | 1443 | 1311 | 1233 | 1489 | 1383 | 1226 | 1442 | 1362 | 1287 | 1459 | 1399 |
LA27 | 1235 | 1394 | 1476 | 1412 | 1423 | 1499 | 1445 | 1403 | 1478 | 1431 | 1396 | 1503 | 1477 |
LA28 | 1216 | 1216 | 1440 | 1381 | 1230 | 1457 | 1390 | 1219 | 1444 | 1387 | 1290 | 1445 | 1379 |
LA29 | 1152 | 1280 | 1397 | 1304 | 1310 | 1429 | 1339 | 1344 | 1450 | 1410 | 1339 | 1557 | 1412 |
LA30 | 1355 | 1335 | 1567 | 1417 | 1404 | 1620 | 1503 | 1396 | 1592 | 1500 | 1428 | 1701 | 1511 |
Instance | OVCK | NGPSO | PSO1 | PSO2 | CSA | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Best | Worst | Avg | Best | Worst | Avg | Best | Worst | Avg | Best | Worst | Avg | ||
ABZ5 | 1234 | 1234 | 1457 | 1311 | 1234 | 1466 | 1323 | 1287 | 1487 | 1344 | 1234 | 1583 | 1447 |
ABZ6 | 943 | 943 | 1219 | 1093 | 943 | 1223 | 1137 | 954 | 1235 | 1120 | 1004 | 1284 | 1121 |
ABZ7 | 656 | 713 | 997 | 862 | 689 | 1087 | 901 | 664 | 1176 | 925 | 985 | 1329 | 1150 |
ABZ8 | 665 | 729 | 1298 | 1031 | 819 | 1470 | 1285 | 927 | 1483 | 1232 | 1199 | 1589 | 1337 |
ABZ9 | 679 | 930 | 1015 | 976 | 985 | 1024 | 990 | 958 | 1016 | 982 | 1008 | 1079 | 1034 |
ORB1 | 1059 | 1174 | 1297 | 1226 | 1214 | 1317 | 1276 | 1177 | 1282 | 1235 | 1232 | 1374 | 1353 |
ORB2 | 888 | 913 | 1038 | 957 | 969 | 1074 | 989 | 943 | 1010 | 970 | 1022 | 1114 | 1070 |
ORB3 | 1005 | 1104 | 1243 | 1172 | 1144 | 1265 | 1181 | 1166 | 1270 | 1192 | 1228 | 1295 | 1267 |
ORB4 | 1005 | 1005 | 1163 | 1140 | 1005 | 1182 | 1066 | 1016 | 1167 | 1078 | 1046 | 1211 | 1132 |
ORB5 | 887 | 887 | 1002 | 987 | 887 | 1028 | 994 | 913 | 1013 | 988 | 877 | 1092 | 997 |
ORB6 | 1010 | 1124 | 1203 | 1170 | 1187 | 1245 | 1221 | 1171 | 1247 | 1213 | 1191 | 1265 | 1222 |
ORB7 | 397 | 397 | 464 | 440 | 435 | 468 | 447 | 397 | 468 | 441 | 458 | 482 | 460 |
ORB8 | 899 | 1020 | 1106 | 1054 | 1018 | 1163 | 1056 | 899 | 1155 | 1080 | 1073 | 1173 | 1085 |
ORB9 | 934 | 980 | 1128 | 1032 | 1012 | 1139 | 1043 | 1021 | 1154 | 1042 | 1011 | 1150 | 1032 |
ORB10 | 944 | 1027 | 1157 | 1048 | 1040 | 1143 | 1067 | 1036 | 1154 | 1063 | 944 | 1204 | 1097 |
LA31 | 1784 | 1784 | 2143 | 1972 | 1784 | 2149 | 1986 | 1849 | 2156 | 1961 | 1872 | 2212 | 2057 |
LA32 | 1850 | 1850 | 2202 | 1987 | 1850 | 2237 | 1996 | 1944 | 2248 | 2002 | 1982 | 2397 | 2123 |
LA33 | 1719 | 1719 | 2001 | 1894 | 1719 | 2035 | 1907 | 1719 | 2022 | 1897 | 1829 | 2155 | 1956 |
LA34 | 1721 | 1721 | 2060 | 1939 | 1878 | 2147 | 1963 | 1721 | 2126 | 1955 | 2060 | 2304 | 2187 |
LA35 | 1888 | 1888 | 2212 | 1986 | 1888 | 2271 | 2010 | 1930 | 2308 | 2039 | 1918 | 2431 | 2181 |
LA36 | 1268 | 1408 | 1665 | 1523 | 1396 | 1691 | 1545 | 1415 | 1703 | 1562 | 1511 | 1775 | 1660 |
LA37 | 1397 | 1515 | 1693 | 1560 | 1524 | 1792 | 1623 | 1551 | 1787 | 1635 | 1613 | 1805 | 1743 |
LA38 | 1196 | 1196 | 1596 | 1388 | 1332 | 1781 | 1569 | 1198 | 1610 | 1454 | 1483 | 1708 | 1624 |
LA39 | 1233 | 1662 | 1799 | 1701 | 1712 | 1725 | 1718 | 1711 | 1825 | 1748 | 1731 | 1833 | 1768 |
LA40 | 1222 | 1222 | 1537 | 1413 | 1289 | 1583 | 1425 | 1244 | 1615 | 1423 | 1453 | 1661 | 1528 |
YN1 | 888 | 1248 | 1346 | 1291 | 1303 | 1411 | 1346 | 1259 | 1395 | 1289 | 1291 | 1426 | 1318 |
YN2 | 909 | 911 | 1208 | 1102 | 927 | 1198 | 1109 | 932 | 1226 | 1117 | 1042 | 1318 | 1207 |
YN3 | 893 | 893 | 1376 | 1189 | 903 | 1344 | 1201 | 893 | 1457 | 1255 | 1003 | 1487 | 1311 |
YN4 | 968 | 984 | 1299 | 1106 | 979 | 1376 | 1137 | 1008 | 1410 | 1124 | 1153 | 1677 | 1329 |
Instance | OVCK | NGPSO | GA | DE | ABC | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Best | Worst | Avg | Best | Worst | Avg | Best | Worst | Avg | Best | Worst | Avg | ||
ABZ5 | 1234 | 1234 | 1457 | 1311 | 1234 | 1460 | 1336 | 1234 | 1465 | 1347 | 1236 | 1572 | 1443 |
ABZ6 | 943 | 943 | 1219 | 1093 | 954 | 1247 | 1142 | 948 | 1179 | 1103 | 992 | 1285 | 1138 |
ABZ7 | 656 | 713 | 997 | 862 | 729 | 1128 | 927 | 720 | 1166 | 918 | 973 | 1239 | 1106 |
ABZ8 | 665 | 729 | 1298 | 1031 | 805 | 1386 | 1242 | 822 | 1384 | 1165 | 748 | 1314 | 1137 |
ABZ9 | 679 | 930 | 1015 | 976 | 988 | 1124 | 1003 | 926 | 1023 | 988 | 944 | 1052 | 989 |
ORB1 | 1059 | 1174 | 1297 | 1226 | 1210 | 1348 | 1296 | 1191 | 1302 | 1244 | 1213 | 1320 | 1306 |
ORB2 | 888 | 913 | 1038 | 957 | 958 | 1064 | 997 | 932 | 1125 | 965 | 947 | 1096 | 988 |
ORB3 | 1005 | 1104 | 1243 | 1172 | 1136 | 1273 | 1201 | 1154 | 1281 | 1203 | 1228 | 1295 | 1267 |
ORB4 | 1005 | 1005 | 1163 | 1140 | 1005 | 1178 | 1057 | 1005 | 1183 | 1135 | 1005 | 1239 | 1142 |
ORB5 | 887 | 887 | 1002 | 987 | 913 | 1125 | 1006 | 887 | 1046 | 994 | 877 | 1092 | 1017 |
ORB6 | 1010 | 1124 | 1203 | 1170 | 1187 | 1349 | 1227 | 1171 | 1247 | 1213 | 1194 | 1277 | 1236 |
ORB7 | 397 | 397 | 464 | 440 | 397 | 479 | 456 | 397 | 468 | 441 | 397 | 471 | 455 |
ORB8 | 899 | 1020 | 1106 | 1054 | 1038 | 1188 | 1068 | 899 | 1149 | 1067 | 1043 | 1164 | 1076 |
ORB9 | 934 | 980 | 1128 | 1032 | 997 | 1158 | 1042 | 1003 | 1184 | 1055 | 1011 | 1150 | 1032 |
ORB10 | 944 | 1027 | 1157 | 1048 | 1024 | 1242 | 1107 | 1026 | 1163 | 1059 | 944 | 1164 | 1147 |
LA31 | 1784 | 1784 | 2143 | 1972 | 1784 | 2216 | 1978 | 1784 | 2177 | 1978 | 1784 | 2241 | 2078 |
LA32 | 1850 | 1850 | 2202 | 1987 | 1862 | 2249 | 2003 | 1935 | 2250 | 2013 | 1903 | 2344 | 2013 |
LA33 | 1719 | 1719 | 2001 | 1894 | 1786 | 2126 | 1923 | 1719 | 2103 | 1914 | 1749 | 2052 | 1948 |
LA34 | 1721 | 1721 | 2060 | 1939 | 1889 | 2155 | 1972 | 1721 | 2140 | 1953 | 1764 | 2054 | 1962 |
LA35 | 1888 | 1888 | 2212 | 1986 | 1888 | 2310 | 2015 | 1926 | 2319 | 2044 | 1902 | 2332 | 2135 |
LA36 | 1268 | 1408 | 1665 | 1523 | 1416 | 1631 | 1566 | 1423 | 1698 | 1557 | 1411 | 1765 | 1650 |
LA37 | 1397 | 1515 | 1693 | 1560 | 1549 | 1812 | 1647 | 1544 | 1767 | 1628 | 1524 | 1783 | 1646 |
LA38 | 1196 | 1196 | 1596 | 1388 | 1211 | 1682 | 1467 | 1214 | 1607 | 1450 | 1196 | 1609 | 1425 |
LA39 | 1233 | 1662 | 1799 | 1701 | 1677 | 1831 | 1782 | 1688 | 1845 | 1732 | 1681 | 1840 | 1746 |
LA40 | 1222 | 1222 | 1537 | 1413 | 1263 | 1602 | 1438 | 1255 | 1602 | 1431 | 1257 | 1610 | 1424 |
YN1 | 888 | 1248 | 1346 | 1291 | 1288 | 1430 | 1351 | 1260 | 1419 | 1292 | 1288 | 1419 | 1306 |
YN2 | 909 | 911 | 1208 | 1102 | 934 | 1201 | 1116 | 946 | 1240 | 1125 | 979 | 1253 | 1126 |
YN3 | 893 | 893 | 1376 | 1189 | 914 | 1355 | 1212 | 893 | 1387 | 1262 | 904 | 1422 | 1218 |
YN4 | 968 | 984 | 1299 | 1106 | 993 | 1384 | 1149 | 993 | 1426 | 1133 | 1082 | 1327 | 1129 |
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Yu, H.; Gao, Y.; Wang, L.; Meng, J. A Hybrid Particle Swarm Optimization Algorithm Enhanced with Nonlinear Inertial Weight and Gaussian Mutation for Job Shop Scheduling Problems. Mathematics 2020, 8, 1355. https://doi.org/10.3390/math8081355
Yu H, Gao Y, Wang L, Meng J. A Hybrid Particle Swarm Optimization Algorithm Enhanced with Nonlinear Inertial Weight and Gaussian Mutation for Job Shop Scheduling Problems. Mathematics. 2020; 8(8):1355. https://doi.org/10.3390/math8081355
Chicago/Turabian StyleYu, Hongli, Yuelin Gao, Le Wang, and Jiangtao Meng. 2020. "A Hybrid Particle Swarm Optimization Algorithm Enhanced with Nonlinear Inertial Weight and Gaussian Mutation for Job Shop Scheduling Problems" Mathematics 8, no. 8: 1355. https://doi.org/10.3390/math8081355