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

PeerJ Computer Science

Marcone J.F. Souza¹  Júlio Cesar E.M. Pinto¹  Marcelo F. Rego²  Luciano P. Cota³ 

[1] Department of Computing, Universidade Federal de Ouro Preto, Ouro Preto, Minas Gerais, Brazil;Department of Computing, Universidade Federal dos Vales dos Jequitinhonha e Mucuri, Diamantina, Minas Gerais, Brazil;Instituto Tecnológico Vale, Ouro Preto, Minas Gerais, Brazil;

关键词: Unrelated parallel machine;    Total energy cost;    Makespan;    Mixed-integer linear programming;    NSGA-II;    Multi-objective optimization;   

DOI  :  10.7717/peerj-cs.844

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown