Multi-objective Group Learning Algorithm with A Multi-objective Real-world Engineering Problem

Abstract

The concern of multi-objective optimization is to deal with optimization problems with more than one objective that should be optimized at the same time. In this paper, a new multi-objective optimization algorithm called multi-objective group learning algorithm is examined. The algorithm is based on the effect of group leaders on the group members and the effect that the group members have on each other. The algorithm is evaluated against the five Zitzler, Deb and Thiele (ZDT) benchmark functions, two standard functions of the DTLZ benchmarks, and a real-world engineering problem. To quantitatively examine the ability of the algorithm four metrics are utilized. Additionally, to statistically confirm the results, standard deviation and the average metrics are used. Moreover, the Wilcoxon rank sum test is used to examine the importance of the results statistically. Finally, the results of the algorithm are evaluated against multi-objective ant lion optimizer, multi-objective evolutionary algorithm based on decomposition, Pareto envelop-based selection algorithm-II, and multi-object moth swarm algorithm. The results of the benchmark functions showed that the proposed work produced better results in most of the metrics for three out of five ZDT benchmarks, and for the rest of the benchmarks it produced better results in at least one of the metrics compared to the participated algorithms. Moreover, the result of the real world engineering problem proved the ability of the proposed algorithm in producing acceptable and better Pareto front in almost all the metrics. For the proposed algorithm, the result of the generational distance for the speed reducer design problem is 0.8002, whereas it is 7.9375710, and 61.98134 for the multi-objective evolutionary algorithm based on decomposition, multi-objective ant lion optimizer, respectively. Additionally, the produced result for the spacing metric by the proposed algorithm was smaller than the result of the other algorithms for the same metric by at least 100 points. The result of the aforementioned metric proves the good distribution of the non-dominated solutions by the proposed algorithm.