A self-adaptive arithmetic optimization algorithm with hybrid search modes for 0–1 knapsack problem

Arithmetic optimization algorithm (AOA) is a recently proposed algorithm inspired by mathematical operations. It has been used to solve a variety of optimization problems due to its simplicity of parameters and ease of implementation. However, it has been found that AOA encounters challenges such as poor exploration and premature convergence. To solve these issues, this paper proposes a self-adaptive AOA with hybrid search modes, named AOAHSM. In this algorithm, two hybrid search modes, i.e., the parallel search mode and the serial search mode, are established by combining AOA and differential evolution (DE) in different ways to enhance the exploration and exploitation abilities, respectively. In the parallel search mode, AOA and DE independently implement on their respective subpopulations to maintain a high distribution of the population. In the serial search mode, DE is embedded into AOA to provide more diversified solutions and thereby help the population jump out of local optima. Then, a self-adaptive conversion strategy is employed to dynamically switch between the two modes so as to achieve a better balance between exploration and exploitation. Additionally, a Levy flight strategy is used to perturb and update the best solution obtained in each iteration to further prevent premature convergence. Lastly, a binary version of AOAHSM is proposed to tackle the 0–1 knapsack problem. The proposed algorithms are evaluated on CEC2019, CEC2020 test functions, two typical engineering design problems and 45 instances of the 0–1 knapsack problem and compared with a number of state-of-the-art meta-heuristic algorithms. The obtained results demonstrate that AOAHSM and its binary version not only significantly outperform the original AOA but also achieve superior performance to the comparison algorithms in most cases.