A Multistrategy Improved Archimedes Optimization Algorithm for Solving Engineering Problems

Given the shortcomings of the Archimedes optimization algorithm (AOA), the traditional AOA exhibits the following limitations: the initialization phase employs a uniform 0-1 random number distribution to generate sequences, resulting in limited diversity of initial solutions. The original density factor gradually approaches zero with iterations, leading to susceptibility to local optima. Moreover, the algorithm’s heavy reliance on transfer function (TF) operators for decision-making during development or exploration processes often results in suboptimal convergence accuracy. This paper proposes a multistrategy improvement of AOA, named SSAOA, which incorporates the Sobol sequence and sigmoid function. First, the Sobol sequence is employed to generate the initial population, providing superior starting solutions for subsequent optimization. Second, the sigmoid function is used to reconstruct the density factor, enhancing the update intensity of population positions. Finally, the lens imaging reverse learning technique perturbs new individual positions to help escape local optima. SSAOA’s performance was evaluated through simulations on 16 benchmark test functions and eight CEC2022 test functions with diverse characteristics. Wilcoxon’s rank sum test confirmed that SSAOA significantly outperforms the comparison algorithms. Among the 16 benchmark functions, compared with AOA, AOA1, AOA2, and AOA3, the average, optimal, and worst values of SSAOA in 10 functions all achieved the best results 0, indicating the effectiveness of the improved strategy. Furthermore, SSAOA was applied to four engineering cases and the Traveling Salesman Problem with Pickup and Delivery, further validating its applicability and efficacy.