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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.
Rego, Marcelo F; Pinto, Júlio Cesar E M; Cota, Luciano P; Souza, Marcone J F.
Affiliation
  • Rego MF; Department of Computing, Universidade Federal dos Vales dos Jequitinhonha e Mucuri, Diamantina, Minas Gerais, Brazil.
  • Pinto JCEM; Department of Computing, Universidade Federal de Ouro Preto, Ouro Preto, Minas Gerais, Brazil.
  • Cota LP; Department of Computing, Universidade Federal de Ouro Preto, Ouro Preto, Minas Gerais, Brazil.
  • Souza MJF; Instituto Tecnológico Vale, Ouro Preto, Minas Gerais, Brazil.
PeerJ Comput Sci ; 8: e844, 2022.
Article in En | MEDLINE | ID: mdl-35494814
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.
Key words

Full text: 1 Collection: 01-internacional Database: MEDLINE Type of study: Health_economic_evaluation / Prognostic_studies Language: En Journal: PeerJ Comput Sci Year: 2022 Document type: Article Affiliation country: Brazil Country of publication: United States

Full text: 1 Collection: 01-internacional Database: MEDLINE Type of study: Health_economic_evaluation / Prognostic_studies Language: En Journal: PeerJ Comput Sci Year: 2022 Document type: Article Affiliation country: Brazil Country of publication: United States