Improved arithmetic optimization algorithm and its application to discrete structural optimization

Abstract

The arithmetic optimization algorithm (AOA) is a newly developed metaheuristic search technique that simulates the distribution characteristics of the basic arithmetic operations of addition, subtraction, multiplication, and division, and has been employed to solve some real-world optimization problems. However, it has been found that the AOA suffers from poor exploration and prematurely converges to non-optimal solutions, especially when applied to multi-dimensional optimization problems. In this paper, to overcome the shortcomings of the standard AOA, an improved variant of the AOA, called improved arithmetic optimization algorithm (IAOA), is proposed and then employed for optimization of skeletal structures with discrete design variables. Compared to the standard AOA, two major improvements are made in the proposed IAOA: (1) The original formulation of the AOA is modified to enhance the exploration and exploitation capabilities; (2) The proposed IAOA requires fewer algorithm-specific parameters compared with the standard AOA, making it easy to be implemented. To examine the efficiency and robustness of the proposed IAOA, three benchmark structural optimization problems with discrete design variables are investigated and the results are compared to those of the standard AOA and other methods available in the literature. To the best of our knowledge, this is the first attempt to apply AOA to structural optimization. The IAOA not only promotes the exploration capability of the search space but also overcomes the shortcoming of the premature convergence of the standard AOA. Experimental results indicate that IAOA significantly surpasses the standard AOA and achieves results comparable or superior to other state-of-the-art metaheuristics.