A genetic algorithm for robust schedules in a one-machine environment with ready times and due dates

Abstract.Computing a schedule for a single machine problem is often difficult, but when the data are uncertain, the problem is much more complicated. In this paper, we modify a genetic algorithm to compute robust schedules when release dates are subject to small variations. Two types of robustness are distinguished: quality robustness or robustness in the objective function space and solution robustness or robustness in the solution space. We show that the modified genetic algorithm can find solutions that are robust with respect to both types of robustness. Moreover, the risk associated with a specific solution can be easily evaluated. The modified genetic algorithm is applied to a just-in-time scheduling problem, a common problem in many industries.

[1]  Jürgen Branke,et al.  Creating Robust Solutions by Means of Evolutionary Algorithms , 1998, PPSN.

[2]  Shigeyoshi Tsutsui,et al.  Genetic algorithms with a robust solution searching scheme , 1997, IEEE Trans. Evol. Comput..

[3]  Philippe Baptiste,et al.  An O(n4) algorithm for preemptive scheduling of a single machine to minimize the number of late jobs , 1999, Oper. Res. Lett..

[4]  Stéphane Dauzère-Pérès,et al.  Minimizing late jobs in the general one machine scheduling problem , 1995 .

[5]  C. Reeves.  Modern heuristic techniques for combinatorial problems , 1993 .

[6]  J. Branke.  Reducing the sampling variance when searching for robust solutions , 2001 .

[7]  Peter Ross,et al.  An Immune System Approach to Scheduling in Changing Environments , 1999, GECCO.

[8]  Esko Ukkonen,et al.  Finding Approximate Patterns in Strings , 1985, J. Algorithms.

[9]  Willy Herroelen,et al.  Project scheduling under uncertainty: Survey and research potentials , 2005, Eur. J. Oper. Res..

[10]  Kenneth Sörensen,et al.  Tabu Searching for Robust Solutions , 2001 .

[11]  Stéphane Dauzère-Pérès,et al.  Genetic algorithms to minimize the weighted number of late jobs on a single machine , 2003, Eur. J. Oper. Res..

[12]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .

[13]  Michael J. Fischer,et al.  The String-to-String Correction Problem , 1974, JACM.

[14]  Shigeyoshi Tsutsui,et al.  A Robust Solution Searching Scheme in Genetic Search , 1996, PPSN.

[15]  Lakhmi C. Jain,et al.  Properties of robust solution searching in multi-dimensional space with genetic algorithms , 1998, 1998 Second International Conference. Knowledge-Based Intelligent Electronic Systems. Proceedings KES'98 (Cat. No.98EX111).

[16]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[17]  Vladimir I. Levenshtein,et al.  Binary codes capable of correcting deletions, insertions, and reversals , 1965 .

[18]  Mikkel T. Jensen,et al.  Robust and Flexible Scheduling with Evolutionary Computation , 2001 .

[19]  Shigeyoshi Tsutsui,et al.  A comparative study on the effects of adding perturbations to phenotypic parameters in genetic algorithms with a robust solution searching scheme , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[20]  Peter Ross,et al.  The evolution and analysis of potential antibody library for use in job-shop scheduling , 1999 .

[21]  Robert H. Storer,et al.  Robust Scheduling and Game-Theoretic Control for Short-Term Scheduling of Job-Shops , 1993 .

[22]  R. Storer,et al.  A game-theoretic control approach for job shops in the presence of disruptions , 1994 .

[23]  Robert H. Storer,et al.  Robustness Measures and Robust Scheduling for Job Shops , 1994 .

[24]  Philippe Baptiste,et al.  A branch and bound to minimize the number of late jobs on a single machine with release time constraints , 2003, Eur. J. Oper. Res..

[25]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[26]  Martin Christopher,et al.  Logistics and Supply Chain Management: Strategies for Reducing Cost and Improving Service (Second Edition) , 1999 .

[27]  Stéphane Dauzère-Pérès,et al.  An Exact Method to Minimize the Number of Tardy Jobs in Single Machine Scheduling , 2004, J. Sched..

[28]  Colin R. Reeves,et al.  Genetic Algorithms for the Operations Researcher , 1997, INFORMS J. Comput..

[29]  Stéphane Dauzère-Pérès,et al.  Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine , 2003 .