An empirical analysis of constraint handling on evolutionary multi-objective algorithms for the Environmental/Economic Load Dispatch problem

Abstract This paper analyses different multi-objective evolutionary algorithms to deal with the Environmental/Economic Load Dispatch (EELD). EELD is formulated as a multi-objective optimization problem in which two competing objectives (fuel cost and pollutants emission) should be optimized simultaneously while fulfilling constraints. Due to the typical process of an evolutionary algorithm (EA), the use of operators applied to individuals of the population might violate constraint rules of the problem. The way in which EAs deal with such constraint rules is an important point and it is directly related to the quality of the generated solutions. One of the contributions of this paper is the analysis of the impact of a repair procedure in four multi-objective EAs. The analyzed approaches are evaluated in eight known instances (with 3, 6, 10, 20 and 40 generators) of the multi-objective EELD. Furthermore, two new instances (with 80 and 120 generators) are proposed and evaluated in this work. Experiments were applied using Dominance Ranking, hypervolume and unary-epsilon indicators, empirical attainment functions and statistical tests, in order to evaluate the algorithms performances. The results point to the consistency of the NSGA-II with repair procedure compared to the literature algorithms, and it outperforms other approaches in most of the considered instances.

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