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Pruning by dominance in best-first search for the job shop Scheduling problem with total flow time

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Abstract

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.

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Authors and Affiliations

  1. Department of Computer Science, University of Oviedo, Campus de Viesques, 1.2.11, Gijon, 33271, Spain

    María R. Sierra & Ramiro Varela

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  1. María R. Sierra
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  2. Ramiro Varela
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Correspondence to Ramiro Varela.

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Sierra, M.R., Varela, R. Pruning by dominance in best-first search for the job shop Scheduling problem with total flow time. J Intell Manuf 21, 111–119 (2010). https://doi.org/10.1007/s10845-008-0167-4

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  • DOI: https://doi.org/10.1007/s10845-008-0167-4

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