========== [Paper] ========== Tsung-Che Chiang and Hsiao-Jou Lin, A simple and effective evolutionary algorithm for multiobjective flexible job shop scheduling, International Journal of Production Economics, vol. 141, no. 1, pp. 87 - 98, 2013. http://dx.doi.org/10.1016/j.ijpe.2012.03.034 ========== [Benchmark instances] ============= (Mk01-Mk10) Brandimarte, P., Routing and scheduling in a flexible job shop by tabu search, Annals of Operations Research, vol. 41, pp. 157¡V183, 1993. (Kacem4x5, 8x8, 10x7, 10x10, 15x10) Kacem, I., Hammadi, S., Borne, P., Pareto-optimality approach for flexible job shop scheduling problems: Hybridization of evolutionary algorithms and fuzzy logic, Mathematics and Computers in Simulation, vol. 60, pp. 245¡V276, 2002. ========== [Benchmark algorithms] ============= [1] Ho, N.B., Tay, J.C., Solving multiple-objective flexible job shop problems using evolution and local search, IEEE Transactions on Systems, Man, and Cybernetics ¡V Part C, vol. 38, no. 5, pp. 674¡V685, 2008. [2] Xing, L.N., Chen, Y.W., Yang, K.W., An efficient search method for multi-objective flexible job shop scheduling problems, Journal of Intelligent Manufacturing, vol. 20, pp. 283¡V293, 2009. [3] Li, J.Q., Pan, Q.K., Liang, Y.C., An effective hybrid tabu search algorithm for multi-objective flexible job-shop scheduling problems, Computers & Industrial Engineering, vol. 59, pp. 647¡V662, 2010. [4] Bagheri, A., Zandieh, M., Mahdavi, I., Yazdani, M., An artificial immune algorithm for the flexible job-shop scheduling problem, Future Generation Computer Systems, vol. 26, pp. 533¡V541, 2010. [5] Wang, X., Gao, L., Zhang, C., Shao, X., A multi-objective genetic algorithm based on immune and entropy principle for flexible job-shop scheduling problem. International Journal of Advanced Manufacturing Technology, vol. 51, pp. 757¡V767, 2010. [6]Li, J.Q., Pan, Q.K., Gao, K.Z., Pareto-based discrete artificial bee colony algorithm for multi-objective flexible job shop scheduling problems, International Journal of Advanced Manufacturing Technology, vol. 55, pp. 1159¡V1169, 2011. [7] Li, J.Q, Pan, Q.K., Chen, J., A hybrid Pareto-based local search algorithm for multi-objective flexible job shop scheduling problems. International Journal of Production Research, vol. 50, no. 4, pp. 1063¡V1078, 2012. [8] Chiang, T.C. and Lin, H.j., A simple and effective evolutionary algorithm for multiobjective flexible job shop scheduling. International Journal of Production Economics, vol. 141, no. 1, pp. 87 - 98, 2013. ========== [Net set of non-dominated solutions] ========== Each row represents the makespan, total workload, maximum workload of the solution, and the papers that found the solution. Kacem4x5------------------ Totally 4 Pareto optimal solutions: 11 32 10 [2][3][5][6][7][8] 11 34 9 [2][5][7][8] 12 32 8 [2][3][5][6][7][8] 13 33 7 [6][7][8] Kacem8x8------------------ Totally 5 Pareto optimal solutions: 14 77 12 [1][2][3][4][6][7][8] 15 75 12 [1][2][3][5][6][7][8] 15 81 11 [5] 16 73 13 [1][5][6][7][8] 16 77 11 [1][2][7][8] Kacem10x7------------------ Totally 3 Pareto optimal solutions: 11 61 11 [2][3][7][8] 11 62 10 [2][3][7][8] 12 60 12 [2][6][7][8] Kacem10x10------------------ Totally 4 Pareto optimal solutions: 7 42 6 [1][2][3][5][7][8] 7 43 5 [1][3][4][5][6][7][8] 8 41 7 [1][2][5][6][7][8] 8 42 5 [1][2][3][5][6][7][8] Kacem15x10------------------ Totally 2 Pareto optimal solutions: 11 91 11 [1][2][3][5][7][8] 11 93 10 [1][3][7][8] Mk01------------------ Totally 11 Pareto optimal solutions: 40 162 38 [8] 40 164 37 [8] 40 167 36 [3][7][8] 41 160 38 [8] 41 163 37 [8] 42 157 40 [7][8] 42 158 39 [5][8] 42 165 36 [8] 43 155 40 [5][7][8] 44 154 40 [5][8] 45 153 42 [8] Mk02------------------ Totally 8 Pareto optimal solutions: 26 151 26 [3][5][7] 27 145 27 [8] 28 144 28 [8] 29 143 29 [5][7][8] 29 150 26 [8] 30 142 30 [8] 31 141 31 [5][8] 33 140 33 [5][7][8] Mk03------------------ Totally 24 Pareto optimal solutions: 204 850 204 [8] 204 855 199 [5] 204 871 144 [5] 204 882 135 [5] 204 884 133 [5] 210 848 210 [8] 213 844 213 [8] 213 850 199 [5] 221 842 221 [8] 221 847 199 [5] 222 838 222 [8] 230 848 177 [5] 231 834 231 [8] 240 832 240 [8] 249 830 249 [8] 258 828 258 [8] 267 826 267 [8] 276 824 276 [8] 285 822 285 [8] 294 820 294 [8] 303 818 303 [8] 312 816 312 [8] 321 814 321 [8] 330 812 330 [7][8] Mk04------------------ Totally 28 Pareto optimal solutions: 60 390 59 [5] 61 366 61 [3] 61 372 60 [8] 62 360 61 [8] 62 366 60 [8] 63 354 62 [8] 63 357 61 [8] 63 360 60 [8] 64 353 62 [8] 65 348 63 [8] 66 345 63 [5] 67 344 66 [8] 68 352 37 [2] 69 343 67 [8] 72 340 72 [8] 73 350 55 [5] 74 348 55 [5] 74 349 54 [5] 78 337 78 [8] 84 334 84 [8] 90 331 76 [5] 98 330 98 [8] 106 329 106 [8] 114 328 114 [8] 122 327 122 [8] 130 326 130 [8] 138 325 138 [8] 146 324 146 [8] Mk05------------------ Totally 11 Pareto optimal solutions: 172 687 172 [3] 173 683 173 [5][8] 175 682 175 [5][8] 178 680 178 [8] 179 679 179 [5][8] 183 677 183 [5][8] 185 676 185 [5][8] 191 675 191 [8] 197 674 197 [8] 203 673 203 [8] 209 672 209 [8] Mk06------------------ Totally 110 Pareto optimal solutions: 60 441 58 [5] 62 424 55 [5] 65 396 57 [8] 65 397 56 [8] 65 417 54 [5] 66 382 65 [8] 66 383 64 [8] 66 386 62 [8] 66 387 61 [8] 66 388 60 [8] 66 392 58 [8] 66 393 57 [8] 66 395 56 [8] 66 398 55 [8] 67 372 65 [8] 67 374 63 [8] 67 375 62 [8] 67 377 61 [8] 67 379 60 [8] 67 388 59 [8] 67 390 58 [8] 67 391 57 [8] 67 396 55 [8] 68 369 67 [8] 68 370 66 [8] 68 371 65 [8] 68 373 64 [8] 68 389 58 [8] 68 393 56 [8] 69 365 69 [8] 69 367 68 [8] 69 368 67 [8] 69 369 66 [8] 69 370 65 [8] 69 372 64 [8] 69 373 63 [8] 69 376 61 [8] 69 378 60 [8] 69 410 54 [8] 70 364 70 [8] 70 366 68 [8] 70 367 67 [8] 70 392 56 [8] 70 394 55 [8] 70 399 54 [8] 71 362 71 [8] 71 363 70 [8] 71 364 69 [8] 71 372 63 [8] 71 375 61 [8] 72 360 72 [8] 72 361 71 [8] 72 362 70 [8] 72 364 68 [8] 72 368 66 [8] 72 369 65 [8] 72 371 64 [8] 72 374 62 [8] 72 377 60 [8] 73 359 73 [8] 73 366 67 [8] 73 367 66 [8] 74 357 74 [8] 74 359 72 [8] 74 370 64 [8] 75 355 75 [8] 75 358 73 [8] 75 363 69 [8] 76 354 76 [8] 76 356 74 [5] 76 360 71 [8] 76 362 60 [5] 77 353 77 [8] 77 387 59 [8] 77 398 54 [8] 78 352 78 [8] 78 357 73 [8] 78 361 60 [5] 79 350 79 [8] 79 444 52 [8] 80 445 51 [8] 80 446 50 [8] 81 348 81 [8] 81 349 80 [8] 81 351 78 [8] 81 429 53 [8] 81 440 52 [8] 82 347 82 [8] 82 428 53 [8] 82 433 52 [8] 83 346 82 [8] 83 353 76 [8] 84 344 84 [8] 85 343 85 [8] 86 342 86 [8] 87 341 87 [8] 88 339 88 [8] 90 337 90 [8] 91 336 91 [8] 91 443 50 [8] 92 430 52 [8] 92 441 50 [8] 93 335 93 [8] 94 334 94 [8] 94 439 51 [8] 96 333 96 [8] 97 332 97 [8] 99 331 99 [8] 100 330 90 [5] 103 426 53 [8] Mk07------------------ Totally 15 Pareto optimal solutions: 139 693 139 [5] 140 686 138 [5] 143 683 143 [8] 144 673 144 [5][8] 150 669 150 [8] 151 667 151 [5][8] 156 664 156 [8] 157 662 157 [5][8] 161 660 161 [8] 162 659 162 [5][8] 166 657 166 [5][8] 175 655 175 [8] 187 653 187 [8] 202 651 202 [8] 217 649 217 [8] Mk08------------------ Totally 10 Pareto optimal solutions: 523 2524 515 [5] 523 2534 497 [5] 524 2519 524 [5][7][8] 533 2514 533 [7][8] 542 2509 542 [8] 551 2504 551 [8] 560 2499 560 [8] 569 2494 569 [8] 578 2489 578 [5][8] 587 2484 587 [5][8] Mk09------------------ Totally 69 Pareto optimal solutions: 310 2294 301 [3] 310 3514 299 [5] 311 2265 308 [8] 311 2267 304 [8] 311 2271 303 [8] 311 2272 302 [8] 311 2273 301 [8] 311 2274 299 [8] 312 2262 310 [8] 312 2264 308 [8] 312 2266 307 [8] 313 2259 312 [8] 313 2263 309 [8] 313 2265 307 [8] 314 2258 312 [8] 314 2261 310 [8] 315 2255 314 [8] 315 2257 312 [8] 316 2254 315 [8] 317 2256 313 [8] 317 2260 310 [8] 317 2266 304 [8] 319 2252 316 [8] 319 2253 315 [8] 319 2256 312 [8] 320 2249 320 [8] 321 2248 320 [8] 323 2245 322 [8] 323 2247 320 [8] 324 2246 321 [8] 326 2244 323 [8] 327 2243 327 [8] 328 2242 326 [8] 328 2259 308 [5] 329 2239 328 [8] 329 2241 326 [8] 329 2266 301 [5] 330 2240 327 [8] 332 2265 302 [5] 333 2236 333 [8] 333 2238 331 [8] 334 2235 334 [8] 335 2237 332 [8] 337 2234 334 [8] 337 2236 332 [8] 338 2235 333 [8] 339 2233 339 [8] 340 2231 340 [8] 340 2232 339 [8] 341 2230 340 [8] 341 2231 339 [8] 345 2229 342 [8] 346 2226 346 [8] 349 2225 347 [8] 351 2224 348 [8] 354 2223 354 [8] 356 2222 355 [8] 361 2221 360 [8] 366 2220 366 [8] 375 2219 375 [8] 382 2218 382 [8] 388 2217 388 [8] 394 2216 394 [8] 404 2215 404 [8] 414 2214 414 [8] 424 2213 424 [8] 434 2212 434 [8] 444 2211 444 [8] 454 2210 454 [8] Mk10------------------ Totally 142 Pareto optimal solutions: 214 2053 210 [3] 214 2082 204 [5] 217 2064 207 [5] 224 1980 219 [5] 225 1930 209 [8] 225 1937 205 [8] 226 1943 204 [8] 227 1918 215 [8] 228 1913 219 [8] 228 1921 212 [8] 228 1924 210 [8] 229 1913 211 [8] 229 1919 210 [8] 229 1930 208 [8] 229 1933 205 [8] 229 1942 204 [8] 230 1904 219 [8] 230 1929 205 [8] 230 1935 204 [8] 231 1900 215 [8] 231 1906 212 [8] 231 1963 201 [8] 232 1899 217 [8] 232 1913 210 [8] 232 1921 209 [8] 232 1925 207 [8] 232 1956 202 [8] 233 1892 225 [8] 233 1896 215 [8] 233 1902 210 [8] 233 1911 208 [8] 233 1918 207 [8] 233 1952 201 [8] 234 1880 230 [8] 234 1881 220 [8] 234 1889 216 [8] 234 1895 215 [8] 234 1900 212 [8] 234 1946 203 [8] 234 1951 200 [8] 235 1885 218 [8] 235 1892 215 [8] 235 1898 214 [8] 235 1907 209 [8] 235 1922 205 [8] 235 1949 201 [8] 236 1876 230 [8] 236 1877 220 [8] 236 1883 215 [8] 236 1895 212 [8] 236 1898 210 [8] 236 1920 205 [8] 236 1926 204 [8] 237 1875 220 [8] 237 1881 218 [8] 237 1891 212 [8] 237 1896 210 [8] 237 1905 209 [8] 237 1937 203 [8] 238 1871 225 [8] 238 1878 218 [8] 238 1880 216 [8] 238 1903 209 [8] 239 1890 214 [8] 239 1894 210 [8] 239 1902 209 [8] 239 1936 203 [8] 239 1964 199 [8] 240 1872 220 [8] 240 1889 214 [8] 240 1900 209 [8] 240 1916 205 [8] 240 1923 204 [8] 240 1939 200 [8] 240 1953 199 [8] 241 1867 227 [8] 241 1869 225 [8] 241 1885 214 [8] 241 1890 212 [8] 241 1909 208 [8] 241 1937 201 [8] 242 1871 220 [8] 242 1875 218 [8] 242 1882 215 [8] 242 1913 206 [8] 242 1930 201 [8] 243 1877 216 [8] 243 1879 215 [8] 243 1886 212 [8] 243 1912 205 [8] 243 1918 204 [8] 243 1960 197 [8] 244 1864 235 [8] 244 1865 234 [8] 244 1866 225 [8] 244 1869 220 [8] 244 1926 201 [8] 245 1863 235 [8] 245 1864 227 [8] 246 1861 230 [8] 247 1860 240 [8] 248 1858 240 [8] 248 1859 236 [8] 248 1860 235 [8] 248 1861 227 [8] 248 1863 226 [8] 248 1917 204 [8] 248 1937 200 [8] 249 1863 225 [8] 249 1866 224 [8] 249 1950 199 [8] 250 1858 230 [8] 250 1885 212 [8] 250 1897 209 [8] 250 1908 208 [8] 251 1857 240 [8] 252 1855 240 [8] 252 1856 236 [8] 252 1891 210 [8] 252 1951 197 [8] 252 1986 196 [8] 253 1854 250 [8] 253 1909 205 [8] 253 1985 196 [8] 254 1889 210 [8] 255 1906 208 [8] 256 1957 196 [8] 258 1948 197 [8] 260 1853 260 [8] 260 1858 228 [8] 260 1908 205 [8] 261 1854 240 [8] 261 1855 230 [8] 261 1932 200 [8] 263 1850 260 [8] 263 1851 250 [8] 263 1852 240 [8] 263 1942 199 [8] 264 1853 236 [8] 270 1849 270 [8] 280 1848 280 [8] 290 1847 290 [8]