Differential Evolution Algorithm for Permutation Flowshop Sequencing Problem with Makespan Criterion

This paper presents a differential evolution algorithm to solve the permutaion flowshop sequencing problem with makespan criterion. Differential evolution is one of the latest evolutionary optmization algorithm applied to continuous optimization problems where members of population use chromosomes based on floating-point numbers to represent candidate solutions. In this paper we also present a heuristic rule, called smallest parameter value first in the permutation, which enables the differential evolution algorithm to be applied to all classes of sequencing scheduling problems. The results for the well known benchmark suite in the literature is presented and compared to the well known approaches such as genetic algorithm and partical swarm optimization algorithm.

[1]  A. Kan.  Machine Scheduling Problems: Classification, Complexity and Computations , 1976 .

[2]  Chandrasekharan Rajendran,et al.  Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs , 2004, Eur. J. Oper. Res..

[3]  Colin R. Reeves,et al.  A genetic algorithm for flowshop sequencing , 1995, Comput. Oper. Res..

[4]  Jiyin Liu,et al.  Constructive and composite heuristic solutions to the P// Sigma Ci scheduling problem , 2001, Eur. J. Oper. Res..

[5]  C. Reeves,et al.  Genetic Algorithms, Path Relinking, the Flowshop Sequencing Problem and , 1998 .

[6]  Rainer Storn,et al.  System design by constraint adaptation and differential evolution , 1999, IEEE Trans. Evol. Comput..

[7]  Inyong Ham,et al.  A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem , 1983 .

[8]  David G. Dannenbring,et al.  An Evaluation of Flow Shop Sequencing Heuristics , 1977 .

[9]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[10]  Mehmet Fatih Tasgetiren,et al.  Particle swarm optimization algorithm for single machine total weighted tardiness problem , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[11]  Takeshi Yamada,et al.  Genetic Algorithms, Path Relinking, and the Flowshop Sequencing Problem , 1998, Evolutionary Computation.

[12]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[13]  Godfrey C. Onwubolu,et al.  New optimization techniques in engineering , 2004, Studies in Fuzziness and Soft Computing.

[14]  Thomas Sttzle,et al.  Applying iterated local search to the permutation ow shop problem , 1998 .

[15]  É. Taillard.  Some efficient heuristic methods for the flow shop sequencing problem , 1990 .

[16]  David K. Smith,et al.  The application of the simulated annealing algorithm to the solution of the n/m/Cmax flowshop problem , 1990, Comput. Oper. Res..

[17]  James C. Bean,et al.  Genetic Algorithms and Random Keys for Sequencing and Optimization , 1994, INFORMS J. Comput..

[18]  Thomas Stützle,et al.  An Ant Approach to the Flow Shop Problem , 1998 .

[19]  Mehmet Fatih Tasgetiren,et al.  Particle Swarm Optimization Algorithm for Permutation Flowshop Sequencing Problem , 2004, ANTS Workshop.

[20]  D. S. Palmer.  Sequencing Jobs Through a Multi-Stage Process in the Minimum Total Time—A Quick Method of Obtaining a Near Optimum , 1965 .

[21]  Jose M. Framiñan,et al.  Production , Manufacturing and Logistics Efficient heuristics for flowshop sequencing with the objectives of makespan and flowtime minimisation , 2002 .

[22]  D. Chaudhuri,et al.  An efficient heuristic approach to the scheduling of jobs in a flowshop , 1992 .

[23]  Colin R. Reeves,et al.  Improving the Efficiency of Tabu Search for Machine Sequencing Problems , 1993 .

[24]  E. Nowicki,et al.  A Fast Taboo Search Algorithm for the Job Shop Problem , 1996 .

[25]  I. Osman,et al.  Simulated annealing for permutation flow-shop scheduling , 1989 .

[26]  Éric D. Taillard,et al.  Benchmarks for basic scheduling problems , 1993 .

[27]  Mieczysław Wodecki,et al.  A very fast tabu search algorithm for the permutation flow shop problem with makespan criterion , 2004, Comput. Oper. Res..

[28]  L. Darrell Whitley,et al.  Contrasting Structured and Random Permutation Flow-Shop Scheduling Problems: Search-Space Topology and Algorithm Performance , 2002, INFORMS J. Comput..

[29]  J. Framiñan,et al.  An efficient constructive heuristic for flowtime minimisation in permutation flow shops , 2003 .

[30]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[31]  Ivan Zelinka,et al.  MIXED INTEGER-DISCRETE-CONTINUOUS OPTIMIZATION BY DIFFERENTIAL EVOLUTION Part 1: the optimization method , 2004 .