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A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling
In many countries, there is an energy pricing policy that varies according to the time-of-use. In this context, it is financially advantageous for the industries to plan their production considering this policy. This article introduces a new bi-objective unrelated parallel machine scheduling problem...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
PeerJ Inc.
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9044217/ https://www.ncbi.nlm.nih.gov/pubmed/35494814 http://dx.doi.org/10.7717/peerj-cs.844 |
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author | Rego, Marcelo F. Pinto, Júlio Cesar E.M. Cota, Luciano P. Souza, Marcone J.F. |
author_facet | Rego, Marcelo F. Pinto, Júlio Cesar E.M. Cota, Luciano P. Souza, Marcone J.F. |
author_sort | Rego, Marcelo F. |
collection | PubMed |
description | In many countries, there is an energy pricing policy that varies according to the time-of-use. In this context, it is financially advantageous for the industries to plan their production considering this policy. This article introduces a new bi-objective unrelated parallel machine scheduling problem with sequence-dependent setup times, in which the objectives are to minimize the makespan and the total energy cost. We propose a mixed-integer linear programming formulation based on the weighted sum method to obtain the Pareto front. We also developed an NSGA-II method to address large instances of the problem since the formulation cannot solve it in an acceptable computational time for decision-making. The results showed that the proposed NSGA-II is able to find a good approximation for the Pareto front when compared with the weighted sum method in small instances. Besides, in large instances, NSGA-II outperforms, with 95% confidence level, the MOGA and NSGA-I multi-objective techniques concerning the hypervolume and hierarchical cluster counting metrics. Thus, the proposed algorithm finds non-dominated solutions with good convergence, diversity, uniformity, and amplitude. |
format | Online Article Text |
id | pubmed-9044217 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | PeerJ Inc. |
record_format | MEDLINE/PubMed |
spelling | pubmed-90442172022-04-28 A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling Rego, Marcelo F. Pinto, Júlio Cesar E.M. Cota, Luciano P. Souza, Marcone J.F. PeerJ Comput Sci Artificial Intelligence In many countries, there is an energy pricing policy that varies according to the time-of-use. In this context, it is financially advantageous for the industries to plan their production considering this policy. This article introduces a new bi-objective unrelated parallel machine scheduling problem with sequence-dependent setup times, in which the objectives are to minimize the makespan and the total energy cost. We propose a mixed-integer linear programming formulation based on the weighted sum method to obtain the Pareto front. We also developed an NSGA-II method to address large instances of the problem since the formulation cannot solve it in an acceptable computational time for decision-making. The results showed that the proposed NSGA-II is able to find a good approximation for the Pareto front when compared with the weighted sum method in small instances. Besides, in large instances, NSGA-II outperforms, with 95% confidence level, the MOGA and NSGA-I multi-objective techniques concerning the hypervolume and hierarchical cluster counting metrics. Thus, the proposed algorithm finds non-dominated solutions with good convergence, diversity, uniformity, and amplitude. PeerJ Inc. 2022-02-03 /pmc/articles/PMC9044217/ /pubmed/35494814 http://dx.doi.org/10.7717/peerj-cs.844 Text en © 2022 Rego et al. https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Computer Science) and either DOI or URL of the article must be cited. |
spellingShingle | Artificial Intelligence Rego, Marcelo F. Pinto, Júlio Cesar E.M. Cota, Luciano P. Souza, Marcone J.F. A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling |
title | A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling |
title_full | A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling |
title_fullStr | A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling |
title_full_unstemmed | A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling |
title_short | A mathematical formulation and an NSGA-II algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling |
title_sort | mathematical formulation and an nsga-ii algorithm for minimizing the makespan and energy cost under time-of-use electricity price in an unrelated parallel machine scheduling |
topic | Artificial Intelligence |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9044217/ https://www.ncbi.nlm.nih.gov/pubmed/35494814 http://dx.doi.org/10.7717/peerj-cs.844 |
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