Abstract
Simultaneous optimization of several competing objectives requires increasing the capability of optimization algorithms. This paper proposes the multi-objective moth swarm algorithm, for the first time, to solve various multi-objective problems. In the proposed algorithm, a new definition for pathfinder moths and moonlight was proposed to enhance the synchronization capability as well as to maintain a good spread of non-dominated solutions. In addition, the crowding-distance mechanism was employed to select the most efficient solutions within the population. This mechanism indicates the distribution of non-dominated solutions around a particular non-dominated solution. Accordingly, a set of non-dominated solutions obtained by the proposed multi-objective algorithm is kept in an archive to be used later for improving its exploratory capability. The capability of the proposed MOMSA was investigated by a set of multi-objective benchmark problems having 7 to 30 dimensions. The results were compared with three well-known meta-heuristics of multi-objective evolutionary algorithm based on decomposition (MOEA/D), Pareto envelope-based selection algorithm II (PESA-II), and multi-objective ant lion optimizer (MOALO). Four metrics of generational distance (GD), spacing (S), spread (Δ), and maximum spread (MS) were employed for comparison purposes. The qualitative and quantitative results indicated the superior performance and the higher capability of the proposed MOMSA algorithm over the other algorithms. The MOMSA algorithm with the average values of CPU time = 2771 s, GD = 0.138, S = 0.063, Δ = 1.053, and MS = 0.878 proved to be a robust and reliable model for multi-objective optimization.
Highlights
Simultaneous optimization of several competing objectives requires increasing the capability of optimization algorithms
In order to evaluate the performance of the developed multi-objective moth swarm algorithm (MOMSA) algorithm, four evaluation metrics of generational distance (GD), S, Δ, and maximum spread (MS) were used
The results of MOMSA were compared with three well-known algorithms of multi-objective evolutionary algorithm based on decomposition (MOEA/D), Pareto envelope-based selection algorithm II (PESA-II) and multi-objective ant lion optimizer (MOALO)
Summary
Simultaneous optimization of several competing objectives requires increasing the capability of optimization algorithms. This paper proposes the multi-objective moth swarm algorithm, for the first time, to solve various multi-objective problems. Most of the engineering problems require dealing with multiple conflicting objectives instead of a singleobjective For such problems, the multi-objective optimization (MOO) is an efficient technique for finding a set of solutions that define the best tradeoff between competing objectives while satisfying several criteria. In 1997, Wolpert and Macready, by proposing the No Free Lunch-NFL theorem, claimed that there is no optimization technique capable to solve all optimization problems[13] According to this theorem, the superior performance of an optimization method in a category of problems cannot guarantee its’ superiority on another category of problems. This paper proposes the multi-objective moth swarm algorithm (MOMSA), for the first time, in order to optimize the problems with multiple objectives. The proposed algorithm was tested on 7 multi-objective benchmark problems having 7 to 30 dimensions and the results were compared with three well-known meta-heuristics of MOEA/D, PESA-II and MOALO
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