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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

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Front. Mech. Eng.    2015, Vol. 10 Issue (4) : 392-404    https://doi.org/10.1007/s11465-015-0353-y
RESEARCH ARTICLE
Optimization of multi-objective integrated process planning and scheduling problem using a priority based optimization algorithm
Muhammad Farhan AUSAF(),Liang GAO,Xinyu LI
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
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Abstract

For increasing the overall performance of modern manufacturing systems, effective integration of process planning and scheduling functions has been an important area of consideration among researchers. Owing to the complexity of handling process planning and scheduling simultaneously, most of the research work has been limited to solving the integrated process planning and scheduling (IPPS) problem for a single objective function. As there are many conflicting objectives when dealing with process planning and scheduling, real world problems cannot be fully captured considering only a single objective for optimization. Therefore considering multi-objective IPPS (MOIPPS) problem is inevitable. Unfortunately, only a handful of research papers are available on solving MOIPPS problem. In this paper, an optimization algorithm for solving MOIPPS problem is presented. The proposed algorithm uses a set of dispatching rules coupled with priority assignment to optimize the IPPS problem for various objectives like makespan, total machine load, total tardiness, etc. A fixed sized external archive coupled with a crowding distance mechanism is used to store and maintain the non-dominated solutions. To compare the results with other algorithms, a C-matric based method has been used. Instances from four recent papers have been solved to demonstrate the effectiveness of the proposed algorithm. The experimental results show that the proposed method is an efficient approach for solving the MOIPPS problem.
Keywords integrated process planning and scheduling (IPPS)      dispatching rules      priority based optimization algorithm      multi-objective optimization     
Corresponding Author(s): Muhammad Farhan AUSAF   
Online First Date: 10 October 2015    Issue Date: 03 December 2015
 Cite this article:   
Muhammad Farhan AUSAF,Liang GAO,Xinyu LI. Optimization of multi-objective integrated process planning and scheduling problem using a priority based optimization algorithm[J]. Front. Mech. Eng., 2015, 10(4): 392-404.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-015-0353-y
https://academic.hep.com.cn/fme/EN/Y2015/V10/I4/392
Solution set MS MFT MML TML
1 427 319 203 1855
2 427 368 174 1837
3 427 339 166 1864
MS: Makespan; MFT: Flow time; MML: Maximal machine load; TML: Total machine load
Tab.1  Comparison between different solutions with same makespan
Fig.1  AND/OR graph for a job and possible process plans
Fig.2  Flow diagram for PBOA
Fig.3  Flow diagram for updating archive
Problem Optimal solutions set IGA [35] PBOA
MS MML TML MS MML TML
1 1 191 172 745 171 168 775
2 198 193 722 181 172 709
3 207 187 737 181 158 742
4 210 182 735 188 178 731
5 211 199 718 194 169 739
6 212 188 721 202 169 718
7 218 187 731 204 172 708
8 226 181 739 224 156 738
9 233 197 719 234 197 689
10 238 172 730 236 236 679
2 1 213 207 1149 174 166 1110
2 214 199 1163 175 158 1061
3 218 200 1159 187 155 1053
4 228 221 1139 190 148 1061
5 233 187 1153 201 178 1036
6 234 211 1146 205 168 1047
7 236 181 1164 226 158 1030
8 236 200 1142 260 236 999
9 236 203 1135 310 291 959
10 251 189 1137 396 258 988
3 1 708 708 2960 631 628 3037
2 747 747 2923 639 618 3035
3 784 784 2856 644 615 2977
4 806 806 2836 655 627 2922
5 871 871 2835 661 611 2969
6 883 883 2830 691 665 2888
7 738 710 2862
8 860 860 2768
9 908 889 2742
10 947 947 2712
Tab.2  Comparison of results between PBOA and IGA for Problem 1, Experiment 1
Fig.4  Gantt chart of best makespan obtained for Problem1, Experiment 1
Fig.5  Gantt chart of best makespan obtained for Problem 2, Experiment 1
Problem Job No. Operation sequence Machine sequence
1 1 O4, O3, O1, O2 M2, M2, M4, M1
2 O2, O1, O3, M2, M3, M5
3 O2, O4, O1, O3 M5, M5, M1, M3
4 O1, O2, O3, O4 M1, M1, M1, M2
5 O3, O4 M4, M3
2 1 O4, O5, O2, O3 M4, M2, M2, M5
2 O2, O1, O4 M6, M6, M7
3 O5, O3, O1, O4 M2, M5, M1, M8
4 O5, O3, O2, O4 M7, M5, M8, M3
5 O1, O4, O3 M8, M4, M2
6 O5, O4, O2, O3 M1, M4, M8, M5
7 O1, O2, O4 M3, M2, M5
8 O1, O5, O6 M3, M3, M6
Tab.3  Process plan for solution Set 1 of, Experiment 1
Problem C(PBOA,IGA) C(IGA,PBOA)
1 1.0 0
2 1.0 0
3 0.8 0
Tab.4  C-matric comparison between PBOA and IGA
Solutions set GTHA [26] PBOA
MS MML TML MS MML TML
1 122 106 751 131 117 744
2 122 102 784 146 99 761
3 123 107 750 153 100 754
4 176 122 736
5 217 217 730
Tab.5  Comparison between GBEA and PBOA for Problem 1 of Experiment 2
Fig.6  Gantt chart of best makespan obtained for Problem1, Experiment 2
Problem Objective GRASP [25] PBOA
Set 1 Set 1 Set 2 Set 3 Set 4 Set 5 Set 6 Set 7 Set 8 Set 9 Set 10
1 MS 242 177 181 186 191 192 195 196 208 209 216
MML 217 173 169 178 161 169 195 156 197 169 155
TML 750 749 735 706 735 704 749 744 703 724 741
TJT 365 281 268 344 336 353 254 300 362 289 308
TFT 895 811 798 874 866 883 784 830 892 819 838
2 MS 253 178 178 189 205 216 229 229 231 243 253
MML 237 157 178 156 175 178 165 158 153 151 176
TML 1189 1089 1075 1070 1094 1020 1023 1090 1096 1079 1010
TJT 908 534 452 520 504 587 413 482 615 584 755
TFT 1748 1334 1252 1320 1256 1387 1213 1281 1415 1384 1555
3 MS 421 349 350 362 366 378 400 401 404 405 414
MML 341 310 328 324 346 352 371 404 366 414
TML 1493 1472 1482 1470 1461 1468 1466 1474 1443 1441 1415
TJT 2025 1814 1809 1894 2019 1920 2004 1771 1942 1764 1980
TFT 3214 2874 2869 2954 3079 2980 3064 2831 3002 2824 3040
4 MS 924 651 670 674 681 682 707 712 715 720 814
MML 889 651 637 672 631 661 642 700 685 720 625
TML 2963 2950 2950 2914 2961 2939 2954 2921 2945 2932 2949
TJT 2919 1130 1745 1635 986 1489 1706 1551 1131 1163 1797
TFT 11585 10604 11541 11474 10498 11057 11023 11565 10949 10793 11116
Tab.6  Comparison between GRASP and PBOA for Experiment 3
Problem Objective SEA [15] PBOA
Set 1 Set 1 Set 2 Set 3 Set 4 Set 5 Set 6 Set 7 Set 8 Set 9 Set 10
1 MS 428 427 427 427 430 432 434 434 439 468 506
MFT 313 319 368 339 328 311 316 356 385 398 386
MML 203 174 166 193 187 176 149 193 145 223
TML 1855 1837 1864 1843 1846 1848 1854 1824 1875 1822
2 MS 343 343 343 346 347 349 352 359 371 380 384
MFT 281 319 308 282 317 281 328 304 311 311 367
MML 177 221 217 229 174 136 146 130 180 161
TML 1639 1639 1663 1635 1665 1683 1664 1690 1631 1640
6 MS 438 427 427 427 437 442 444 458 468 520 522
MFT 374 395 377 369 390 367 399 430 446 480 430
MML 213 182 224 196 253 198 162 208 166 224
TML 2155 2226 2183 2160 2176 2159 2195 2139 2175 2139
9 MS 428 427 427 427 432 437 437 439 446 456 506
MFT 293 353 299 291 374 327 312 360 288 362 425
MML 138 186 219 140 211 172 147 187 200 141
TML 1805 1733 1707 1750 1668 1713 1726 1713 1667 1719
Tab.7  Comparison between SEA and PBOA for Experiment 4
Fig.7  Gantt chart of best makespan obtained for Problem 1, Experiment 4
Fig.8  Gantt chart of best makespan obtained for Problem 6, Experiment 4
Experiment Result
1 Dominant solutions obtained for all three problems
2 Non-dominated solutions with better MML and TML obtained
3 Dominant solutions obtained for all four problems
4 New benchmark for MOIPPS with improved values for individual objectives
Tab.8  Summary of results for Experiments 1 to 4
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