A New Hybrid Improved Arithmetic Optimization Algorithm for Solving Global and Engineering Optimization Problems

The Arithmetic Optimization Algorithm (AOA) is a novel metaheuristic inspired by mathematical arithmetic operators. Due to its simple structure and flexible parameter adjustment, the AOA has been applied to solve various engineering problems. However, the AOA still faces challenges such as poor exploitation ability and a tendency to fall into local optima, especially in complex, high-dimensional problems. In this paper, we propose a Hybrid Improved Arithmetic Optimization Algorithm (HIAOA) to address the issues of susceptibility to local optima in AOAs. First, grey wolf optimization is incorporated into the AOAs, where the group hunting behavior of GWO allows multiple individuals to perform local searches at the same time, enabling the solution to be more finely tuned and avoiding over-concentration in a particular region, which can improve the exploitation capability of the AOA. Second, at the end of each AOA run, the follower mechanism and the Cauchy mutation operation of the Sparrow Search Algorithm are selected with the same probability and perturbed to enhance the ability of the AOA to escape from the local optimum. The overall performance of the improved algorithm is assessed by selecting 23 benchmark functions and using the Wilcoxon rank-sum test. The results of the HIAOA are compared with other intelligent optimization algorithms. Furthermore, the HIAOA can also solve three engineering design problems successfully, demonstrating its competitiveness. According to the experimental results, the HIAOA has better test results than the comparator.