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 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.
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