Comparing an ACO algorithm with other heuristics for the single machine scheduling problem with sequence-dependent setup times

We compare several heuristics for solving a single machine scheduling problem. In the operating situation modelled, setup times are sequence-dependent and the objective is to minimize total tardiness. We describe an Ant Colony Optimization (ACO) algorithm having a new feature using look-ahead information in the transition rule. This feature shows an improvement in performance. A comparison with a genetic algorithm, a simulated annealing approach, a local search method and a branch-and-bound algorithm indicates that the ACO that we describe is competitive and has a certain advantage for larger problems.

[1]  M Dorigo,et al.  Ant colonies for the travelling salesman problem. , 1997, Bio Systems.

[2]  Martin Middendorf,et al.  An ACO algorithm for the shortest common supersequence problem , 1999 .

[3]  Christos Koulamas,et al.  The Total Tardiness Problem: Review and Extensions , 1994, Oper. Res..

[4]  Hamilton Emmons,et al.  One-Machine Sequencing to Minimize Certain Functions of Job Tardiness , 1969, Oper. Res..

[5]  Keah Choon Tan,et al.  Minimizing Tardiness on a Single Processor with Sequence Dependent Setup Times: A Simulated Annealing Approach , 1997 .

[6]  Corso Elvezia,et al.  Ant colonies for the traveling salesman problem , 1997 .

[7]  Christos H. Papadimitriou,et al.  Local Search for the Asymmetric Traveling Salesman Problem , 1980, Oper. Res..

[8]  Richard F. Hartl,et al.  An ant colony optimization approach for the single machine total tardiness problem , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[9]  J. Deneubourg,et al.  Probabilistic behaviour in ants: A strategy of errors? , 1983 .

[10]  B. M. Khumawala,et al.  A Savings Index Heuristic Algorithm for Flowshop Scheduling with Sequence Dependent Set-up Times , 1995 .

[11]  Kenneth N. McKay,et al.  Unifying the theory and practice of production scheduling , 1999 .

[12]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[13]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[14]  Marco Dorigo,et al.  Distributed Optimization by Ant Colonies , 1992 .

[15]  R. Iman,et al.  Rank Transformations as a Bridge between Parametric and Nonparametric Statistics , 1981 .

[16]  Joseph Y.-T. Leung,et al.  Minimizing Total Tardiness on One Machine is NP-Hard , 1990, Math. Oper. Res..

[17]  Michael Pinedo,et al.  A heuristic to minimize the total weighted tardiness with sequence-dependent setups , 1997 .

[18]  E. Lawler.  A “Pseudopolynomial” Algorithm for Sequencing Jobs to Minimize Total Tardiness , 1977 .

[19]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[20]  Marc Gravel,et al.  Scheduling jobs in an Alcan aluminium foundry using a genetic algorithm , 2000 .

[21]  Jatinder N. D. Gupta,et al.  A review of scheduling research involving setup considerations , 1999 .

[22]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[23]  Jiyin Liu,et al.  Addressing the gap in scheduling research: a review of optimization and heuristic methods in production scheduling , 1993 .

[24]  Vittorio Maniezzo,et al.  Exact and Approximate Nondeterministic Tree-Search Procedures for the Quadratic Assignment Problem , 1999, INFORMS J. Comput..

[25]  Paul A. Rubin,et al.  A comparison of four methods for minimizing total tardiness on a single processor with sequence dependent setup times , 2000 .

[26]  Michel Gendreau,et al.  A tabu search heuristic for the multiprocessor scheduling problem with sequence dependent setup times , 1996 .

[27]  Wen-Hwa Yang,et al.  Survey of scheduling research involving setup times , 1999, Int. J. Syst. Sci..

[28]  Matthijs den Besten,et al.  Ant Colony Optimization for the Total Weighted Tardiness Problem , 2000, PPSN.

[29]  Luca Maria Gambardella,et al.  Ant Algorithms for Discrete Optimization , 1999, Artificial Life.

[30]  Marc Gravel,et al.  Scheduling continuous casting of aluminum using a multiple objective ant colony optimization metaheuristic , 2002, Eur. J. Oper. Res..

[31]  Paul A. Rubin,et al.  Scheduling in a sequence dependent setup environment with genetic search , 1995, Comput. Oper. Res..