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A parallel memetic algorithm with explicit management of diversity for the job shop scheduling problem

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Abstract

The job shop scheduling problem (JSSP) is a very popular NP-hard optimization problem that involves assigning jobs to resources. Recent advances in the field of memetic algorithms show that explicitly managing the diversity of the population by taking into account the stopping criterion with the aim of dynamically adapting the balance between exploration and exploitation is key to their success. This is especially the case in long-term executions. However, this design principle has not yet been applied to the JSSP. This paper proposes a novel memetic algorithm that integrates some of the most advanced components devised in the literature for the JSSP with a replacement strategy that explicitly manages the diversity by considering a novel dissimilarity measure. To properly address large instances, a parallel master-worker model is used. Experimental validation shows the important advances attained by our proposal when compared to two state-of-the-art optimizers. The advantages are clear in both sequential and parallel cases, with more impressive achievements appearing in the parallel case. The parallel proposal has yielded new best-known solutions in 30 well-known JSSP instances, matching the lower bound in two of them, meaning that at least two new optimal solutions have been discovered.

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Notes

  1. https://codingcompetitions.withgoogle.com/hashcode/

  2. Source code is available at https://github.com/carlossegurag/MAEMD-JSSP

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Acknowledgements

Authors acknowledge the financial support from CONACyT through the “Ciencia Básica” project no. 285599 and the support from “Laboratorio de Supercómputo del Bajio” through the project 300832 from CONACyT.

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Authors and Affiliations

  1. Centro de Investigación en Matemáticas, Guanajuato, México

    Oscar Hernández Constantino & Carlos Segura

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  1. Oscar Hernández Constantino
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  2. Carlos Segura
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Correspondence to Carlos Segura.

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Appendix: New best-known solutions

Appendix: New best-known solutions

Several additional new best-known solutions were generated by carrying out additional parallel executions with up to 100 cores for several instances of the most popular benchmark sets. For each of these instances, Table 4 shows the old and new best-known solutions. The cases in which the lower bound was matched are shown in bold face. This happened in two cases, meaning that at least two new optimal solutions were discovered in this paper. The new upper bounds were generated by PMAEMD in 29 instances, whereas in the remaining case, PHEA generated the new best-known solution. The new solutions were uploaded to the job shop scheduling site [20].

Table 4 New best-known solutions generated with our novel proposals
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Constantino, O.H., Segura, C. A parallel memetic algorithm with explicit management of diversity for the job shop scheduling problem. Appl Intell 52, 141–153 (2022). https://doi.org/10.1007/s10489-021-02406-2

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