Two ant-colony algorithms for minimizing total flowtime in permutation flowshops

doi:10.1016/j.cie.2004.12.009

Computers & Industrial Engineering

Volume 48, Issue 4, June 2005, Pages 789-797

https://doi.org/10.1016/j.cie.2004.12.009 Get rights and content

Abstract

The problem of scheduling in flowshops with the objective of minimizing total flowtime is studied. For solving the problem two ant-colony algorithms are proposed and analyzed. The first algorithm refers to some extent to ideas by Stuetzle [Stuetzle, T. (1998). An ant approach for the flow shop problem. In: Proceedings of the sixth European Congress on intelligent techniques and soft computing (EUFIT '98) (Vol. 3) (pp. 1560–1564). Aachen: Verlag Mainz] and Merkle and Middendorf [Merkle, D., & Middendorf, M. (2000). An ant algorithm with a new pheromone evaluation rule for total tardiness problems. In: Proceedings of the EvoWorkshops 2000, lecture notes in computer science 1803 (pp. 287–296). Berlin: Springer]. The second algorithm is newly developed. The proposed ant-colony algorithms have been applied to 90 benchmark problems taken from Taillard [Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64, 278–285]. A comparison of the solutions yielded by the ant-colony algorithms with the best heuristic solutions known for the benchmark problems up to now, as published in extensive studies by Liu and Reeves [Liu, J., & Reeves, C.R. (2001). Constructive and composite heuristic solutions to the P//ΣC_i scheduling problem. European Journal of Operational Research, 132, 439–452, and Rajendran and Ziegler [Rajendran, C., & Ziegler, H. (2004). Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs. European Journal of Operational Research, 155, 426–438], shows that the presented ant-colony algorithms are better, on an average, than the heuristics analyzed by Liu and Reeves and Rajendran and Ziegler.

Introduction

For solving flowshop scheduling problems with different objectives many exact algorithms and problem-specific traditional heuristics have been proposed (e.g. Campbell et al., 1970, Gelders and Sambandam, 1978, Ho, 1995, Ignall and Schrage, 1965, Johnson, 1954, Liu and Reeves, 2001, Miyazaki and Nishiyama, 1980, Miyazaki et al., 1978, Nawaz et al., 1983, Rajendran, 1993, Rajendran, 1995, Rajendran and Ziegler, 1997, Woo and Yim, 1998). In addition, metaheuristics such as genetic algorithms, simulated annealing and tabu search have been developed (e.g. Ben-Daya and Al-Fawzan, 1998, Ishibuchi et al., 1995, Nowicki and Smutnicki, 1996, Widmer and Hertz, 1989). In recent times, attempts are being made to solve combinatorial optimization problems by making use of ant-colony-optimization algorithms (ACO algorithms). For solving scheduling problems ACO algorithms have been proposed only recently (e.g. MMAS by Stuetzle (1998), and PACO by Rajendran and Ziegler (2004) for minimizing the makespan/total flowtime in flowshops, and Merkle and Middendorf (2000) for minimizing total weighted tardiness for the single machine problem).

In this paper, the problem of scheduling in flowshops with the objective of minimizing total flowtime by using ant-colony algorithms is investigated. The first algorithm presented relates to ideas of Stuetzle, 1998, Merkle and Middendorf, 2000, and the second one is based on new ideas. We evaluate the ACO algorithms in a comparison with the best heuristic solutions reported by Liu and Reeves (2001), and Rajendran and Ziegler (2004) for 90 benchmark flowshop scheduling problems taken from Taillard (1993).

Section snippets

The permutation flowshop scheduling problem

The flowshop scheduling problem consists in scheduling n jobs with given processing times on m machines, where the sequence of processing a job on all machines is identical for each job. Without loss of generality the route of the jobs is equal to 1, 2,…, m. It is assumed that each job can be processed on only one machine at a time and that each machine can process only one job at a time. Furthermore, the operations are not preemptable, the jobs are available for processing at time 0 and the

General structure of the algorithms

The main idea in ant-colony algorithms is to mimic the pheromone trail used by real ants searching for feed as a medium for communication and feedback. The pioneering work has been done by Dorigo (1992), an introduction to the ACO algorithms has been dealt with in Dorigo, Maniezzo, and Colorni (1996). Basically, ACO algorithms are population-based, cooperative search procedures. They make use of simple agents called ants that iteratively construct solutions to the problem considered. The

Performance analysis of the algorithms

Liu and Reeves (2001) developed a couple of new heuristics and compared these with a number of existing heuristics (e.g. the heuristics by Ho, 1995, Rajendran and Ziegler, 1997, Woo and Yim, 1998). They considered the benchmark problems of Taillard (1993) and reported the best heuristic solutions with respect to total flowtime objective. It is to be noted that no single heuristic has emerged to be the best for all benchmark problems. Rajendran and Ziegler (2004) proposed an ant-colony

Summary

Of late, attempts are being made to solve combinatorial optimization problems by making use of ant-colony-optimization algorithms. Compared to other metaheuristics such as genetic algorithms, simulated annealing and tabu search, relatively few attempts have been made to solve scheduling problems using ant-colony algorithms. In this paper, the problem of scheduling in flowshops with the objective of minimizing total flowtime has been investigated. Two ant-colony algorithms have been proposed and

Acknowledgements

The first author gratefully acknowledges the Research Fellowship of Alexander-von-Humboldt Foundation for carrying out this work. The authors are thankful to the reviewers and the Editor for their suggestions to improve the earlier versions of the paper.

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Two ant-colony algorithms for minimizing total flowtime in permutation flowshops

Abstract

Introduction

Section snippets

The permutation flowshop scheduling problem

General structure of the algorithms

Performance analysis of the algorithms

Summary

Acknowledgements

European Journal of Operational Research

European Journal of Operational Research

European Journal of Operational Research

European Journal of Operational Research

OMEGA

European Journal of Operational Research

International Journal of Production Economics

European Journal of Operational Research

European Journal of Operational Research

European Journal of Operational Research

European Journal of Operational Research