An opposition learning and spiral modelling based arithmetic optimization algorithm for global continuous optimization problems

In engineering applications, many real-world optimization problems are nonlinear with multiple local optimums. Traditional algorithms that require gradients are not suitable for these problems. Meta-heuristic algorithms are popularly employed to deal with these problems because they can promisingly jump out of local optima and do not need any gradient information. The arithmetic optimization algorithm (AOA), a recently developed meta-heuristic algorithm, uses arithmetic operators (multiplication, division, subtraction, and addition) to solve optimization problems including nonlinear ones. However, the exploration and exploitation of AOA are not effective to handle some complex optimization problems. In this paper, an opposition learning and spiral modelling based AOA, namely OSAOA, is proposed for enhancing the optimization performance. It improves AOA from two perspectives. In the first perspective, the opposition-based learning (OBL) is committed to taking both candidate solutions and their opposite solutions into consideration for improving the global search with a high probability of jumping out of local minima. Then, the spiral modelling is introduced as the second perspective, which is particularly useful in getting the solutions gathering faster and accelerating the convergence speed in the later stage. In addition, OSAOA is compared with other existing advanced meta-heuristic algorithms based on 23 benchmark functions and four engineering problems: the three-bar truss design, the cantilever beam design, the pressure vessel design, and the tubular column design. From our simulations and engineering applications, the proposed OSAOA can provide better optimization results in dealing with these real-world optimization problems.