Hybrid the Arithmetic Optimization Algorithm for Constrained Optimization Problems

Abstract

Since many real-world problems can be designed as optimization problems, heuristic algorithms are increasingly preferred by researchers. The Arithmetic Optimization Algorithm (AOA) is a newly developed heuristic algorithm. It uses four arithmetic operations in its structure. The addition and subtraction operators enhanced the AOA's local search capability, while the multiplication and division operators enhanced the AOA's global search capability. It has been hybridized with the Tree Seed Algorithm (TSA) to increase the success of AOA. Thus, hybrid AOA-TSA (HAOA) has been proposed. The seed production mechanism of TSA is placed in the random walking stage of AOA. New candidate solutions (seeds) have been produced with the arithmetic operators involved in AOA and the candidate solutions have been compared with the existing solutions. Thus, the performance of AOA has increased. In this study, the success of AOA and HAOA was tested in thirteen constrained optimization problems. The success of AOA and HAOA has been tested for their performance in six different population sizes. The Wilcoxon Signed-Rank test was applied to the obtained results and its success has been proved statistically. The results proved the superiority of HAOA. HAOA has been compared with other heuristic methods in the literature and the success of HAOA has been shown. Additionally, AOA and HAOA have also been tested on three different engineering design problems. The results are discussed and evaluated.