Pruning by dominance in best-first search for the job shop Scheduling problem with total flow time
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Best-First search is a problem solving paradigm that allows to design exact or admissible algorithms. In this paper, we confront the Job Shop Scheduling problem with total flow time minimization by means of the A * algorithm. We devised a heuristic from a problem relaxation that relies on computing Jackson’s preemptive schedules. In order to reduce the effective search space, we formalized a method for pruning nodes based on dominance relations and established a rule to apply this method efficiently during the search. By means of experimental study, we show that the proposed method is more efficient than a genetic algorithm in solving instances with 10 jobs and 5 machines and that pruning by dominance allows A * to reach optimal schedules, while these instances are not solved by A * otherwise. These experiments have also made it clear that the Job Shop Scheduling problem with total flow time minimization is harder to solve than the same problem with makespan minimization.
KeywordsJob shop scheduling Total flow time minimization Best first search Admissible heuristics Pruning by dominance
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- Bierwirth C. (1995) A generalized permutation approach to jobshop scheduling with genetic algorithms. OR Spectrum 17: 87–92Google Scholar
- Blazewicz, J., Ecker, K.~H., Pesch, E., Schmidt, G., & Werglarz, J. (1996). Scheduling computer and manufacturing processes. Springer.Google Scholar
- Brucker, P. (2004). Scheduling algorithms (4th edn.). Springer.Google Scholar
- Brucker, P., & Knust, S. (2006). Complex scheduling. Springer.Google Scholar
- Mattfeld D.C. (1995). Evolutionary search and the job shop investigations on genetic algorithms for production scheduling. Springer-Verlag.Google Scholar
- Nilsson N. (1980) Principles of artificial intelligence. Tioga, Palo Alto, CAGoogle Scholar
- Pearl, J. (1984). Heuristics: Intelligent search strategies for computer problem solving. Addison-Wesley.Google Scholar
- Sierra, M., & Varela, R. (2005). Optimal scheduling with heuristic best first search. In Proceedings of AI*IA’2005, Lecture Notes in Computer Science, Vol. 3673, pp. 173–176.Google Scholar
- Sierra, M., & Varela, R. (2007). Pruning by dominance in best-first search. In Proceedings of CAEPIA’2007, Vol. 2, pp. 289–298.Google Scholar
- Yamada, T., & Nakano, R. (1996). Scheduling by genetic local search with multi-step crossover. In Proceedings of Fourth International Conference On Parallel Problem Solving from Nature (PPSN IV 1996), pp. 960–969.Google Scholar