Abstract
The permutation flow-shop scheduling problem (PFSSP) is a typical combinational optimization problem, which is of wide engineering background and has been proved to be strongly NP-hard. In this paper, a hybrid algorithm based on differential evolution (DE), named HDE, is proposed for the single-objective PFSSPs. Firstly, to make DE suitable for solving PFSSPs, a largest-order-value (LOV) rule is presented to convert the continuous values of individuals in DE to job permutations. Secondly, after the DE-based exploration, a simple but efficient local search, which is designed according to the PFSSPs’ landscape, is applied to emphasize exploitation. Thus, not only does the HDE apply the parallel evolution mechanism of DE to perform effective exploration (global search), but it also adopts problem-dependent local search methodology to adequately perform exploitation (local search). Based on the theory of finite Markov chains, the convergence property of the HDE is analyzed. Then, the HDE is extended to a multi-objective HDE (MHDE) to solve the multi-objective PFSSPs. Simulations and comparisons based on benchmarks for both single-objective and multi-objective PFSSPs are carried out, which show the effectiveness, efficiency, and robustness of the proposed HDE and MHDE.
Similar content being viewed by others
References
Wang L (2003) Shop scheduling with genetic algorithms. Tsinghua University Press & Springer, Beijing, China
Stadtler H (2005) Supply chain management and advanced planning—basics, overview and challenges. Eur J Oper Res 163:575–588
Pinedo M (2002) Scheduling: theory, algorithms, and systems, 2nd edn. Prentice-Hall, New Jersey
Johnson SM (1954) Optimal two- and three- stage production schedules with setup times included. Nav Res Logist Q 1:61–68
Lageweg BJ, Lenstra JK, Rinnooy Kan AHG (1978) A general bounding scheme for the permutation flow-shop problem. Oper Res 26:53–67
Moscato P (1989) On evolution, search, optimization, genetic algorithms and martial arts: toward memetic algorithms. C3P Report 826, Caltech Concurrent Computation Program, California Institute of Technology, Pasadena, California
Palmer DS (1965) Sequencing jobs through a multi-stage process in the minimum total time—a quick method of obtaining a near optimum. Oper Res Q 16:101–107
Dannenbring D (1977) An evaluation of flow shop sequencing heuristics. Manage Sci 23:1174–1182
Campbell HG, Dudek RA, Smith ML (1970) A heuristic algorithm for the n job, m machine sequencing problem. Manage Sci 16(B):630–637
Nawaz M, Enscore E Jr, Ham I (1983) A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. OMEGA 11:91–95
Osman IH, Potts CN (1989) Simulated annealing for permutation flow-shop scheduling. OMEGA 17:551–557
Reeves CR (1995) A genetic algorithm for flowshop sequencing. Comput Oper Res 22:5–13
Reeves CR, Yamada T (1998) Genetic algorithms, path relinking and the flowshop sequencing problem. Evol Comput 6:45–60
Wang L, Zheng D-Z (2003) An effective hybrid heuristic for flow shop scheduling. Int J Adv Manuf Tech 21:38–44
Nowicki E, Smutnicki C (1996) A fast tabu search algorithm for the permutation flow-shop problem. Eur J Oper Res 91:160–175
Grabowski J, Wodecki M (2004) A very fast Tabu search algorithm for the permutation flow shop problem with makespan criterion. Comput Oper Res 31:1891–1909
Wang L, Zheng D-Z (2003) A modified evolutionary programming for flow shop scheduling. Int J Adv Manuf Tech 22:522–527
Hansen P, Mladenovic N (2001) Variable neighborhood search: principles and applications. Eur J Oper Res 130:449–467
Daniels RL, Chambers RJ (1990) Multiobjective flow-shop scheduling. Nav Res Log 37:981–995
Rajendran C (1992) Two-stage flowshop scheduling problem with bicriteria. J Oper Res Soc 43(9):871–884
Bagchi TP (1999) Multiobjective scheduling by genetic algorithms. Kluwer, Boston, Massachusetts
Srinivas N, Deb K (1995) Multiobjective optimization using nondominated sorting genetic algorithms. Evol Comput 2(3):221–248
T’kindt V, Monmarché N, Tercinet F, Laügt D (2002) An Ant Colony Optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem. Eur J Oper Res 142:250–257
Ponnambalam SG, Jagannathan H, Kataria M, Gadicheria A (2004) A TSP-GA multi-objective algorithm for flow-shop scheduling. Int J Adv Manuf Tech 23(11):909–915
Loukil T, Teghem J, Tuyttens D (2005) Solving multi-objective production scheduling problems using metaheuristics. Eur J Oper Res 161:42–61
Murata T, Ishibuchi H, Tanaka H (1996) Genetic algorithms for flowshop scheduling problems. Comput Ind Eng 30:1061–1071
Stutzle T (1998) An ant approach to the flow shop problem. In: Proceedings of the 6th European Congress on Intelligent Techniques and Soft Computing (EUFIT’98), Aachen, Germany, September 1998, pp 1560–1564
Nearchou AC (2004) A novel metaheuristic approach for the flow shop scheduling problem. Eng Appl of Artif Intel 17:289–300
Cheng RW, Gen M (1997) Parallel machine scheduling problems using memetic algorithms. Comput Ind Eng 33:761–764
Merz P (2000) Memetic algorithms for combinatorial optimization problems: fitness landscapes and effective search strategies. PhD dissertation, University of Siegen, Germany
Merz P, Freisleben B (2000) Fitness landscapes, memetic algorithms, and greedy operators for graph bipartitioning. Evol Comput 8:61–91
Burke EK, Smith AJ (2000) Hybrid evolutionary techniques for the maintenance scheduling problem. IEEE T Power Syst 15:122–128
Ong YS, Keane AJ (2004) Meta-Lamarckian learning in memetic algorithms. IEEE T Evol Comput 8:99–110
Merz P, Freisleben B (2000) Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE T Evol Comput 4:337–352
França PM, Mendes A, Moscato P (2001) A memetic algorithm for the total tardiness single machine scheduling problem. Eur J Oper Res 132:224–242
Quintero A, Pierre S (2003) Sequential and multi-population memetic algorithms for assigning cells to switches in mobile networks. Comput Netw 43:247–261
Pastorino M, Caorsi S, Massa A, Randazzo A (2004) Reconstruction algorithms for electromagnetic imaging. IEEE T Instrum Meas 3:692–699
Ishibuchi H, Yoshida T, Murata T (2003) Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE T Evol Comput 7:204–223
Hart WE, Krasnogor N, Smith JE (2004) Recent advances in memetic algorithms. Springer, Berlin Heidelberg New York
Ishibuchi H, Murata T (1998) A multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE T Syst Man Cy C 28(3):392–403
Arroyo JEC, Armentano VA (2005) Genetic local search for multi-objective flowshop scheduling problems. Eur J Oper Res 167:717–738
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Ilonen J, Kamarainen JK, Lampinen J (2003) Differential evolution training algorithm for feed-forward neural networks. Neural Process Lett 17(1):93–105
Chang FP, Hwang C (2004) Design of digital PID controllers for continuous-time plants with integral performance criteria. J Chin Inst Chem Eng 35(6):683–696
Chang YP, Wu CJ (2005) Optimal multiobjective planning of large-scale passive harmonic filters using hybrid differential evolution method considering parameter and loading uncertainty. IEEE T Power Deliver 20(1):408–416
Ali MM, Törn A (2004) Population set-based global optimization algorithms: some modifications and numerical studies. Comput Oper Res 31(10):1703–1725
Tasgetiren MF, Liang YC, Sevkli M, Gencyilmaz G (2004) Differential evolution algorithm for permutation flowshop sequencing problem with makespan criterion. In: Proceedings of the 4th International Symposium on Intelligent Manufacturing Systems (IMS 2004), Sakarya, Turkey, September 2004, pp 442–452
Onwubolu G, Davendra D (2006) Scheduling flow shops using differential evolution algorithm. Eur J Oper Res 171(2):674–692
Reeves CR (1999) Landscapes, operators and heuristic search. Ann Oper Res 86:473–490
Nowicki E, Smutnicki C (2006) Some aspects of scatter search in the flow-shop problem. Eur J Oper Res 169:654–666
Taillard ED (1990) Some efficient heuristic methods for the flow shop sequencing problem. Eur J Oper Res 47:65–74
Landa Silva JD, Burke EK, Petrovic S (2004) An introduction to multiobjective metaheuristics for scheduling and timetabling. Lect Notes Econ Math Syst 535:91–129
Price K, Storn R (2006) Differential evolution (DE) for continuous function optimization. Home page at http://www.icsi.berkeley.edu/%7Estorn/code.html
Bean JC (1994) Genetic algorithm and random keys for sequencing and optimization. ORSA J Comput 6(2):154–160
Krasnogor N (2002) Studies on the theory and design space of memetic algorithms. PhD dissertation, University of the West of England, Bristol, UK
Ong YS, Lim MH, Zhu N, Wong KW (2006) Classification of adaptive memetic algorithms: a comparative study. IEEE T Syst Man Cy B 36:141–152
Schiavinotto T, Stützle T (2007) A review of metrics on permutations for search landscape analysis. Comput Oper Res 34(10):3143–3153
Iosifescu M (1980) Finite Markov processes and their applications. Wiley, New York
Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, London, UK
Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. IEEE T Evol Comput 8(2):173–195
Carlier J (1978) Ordonnancements a contraintes disjonctives. R.A.I.R.O. Recherche Operationelle/Oper Res 12:333–351
Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE T Evol Comput 3(4):257–271
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE T Evol Comput 6(2):182–197
Knowles JK, Corne DW (2000) Approximating the nondominated front using the Pareto archived evolution strategy. Evol Comput 8(2):149–172
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Qian, B., Wang, L., Hu, R. et al. A hybrid differential evolution method for permutation flow-shop scheduling. Int J Adv Manuf Technol 38, 757–777 (2008). https://doi.org/10.1007/s00170-007-1115-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-007-1115-8