Coevolutionary Neural Dynamics Considering Multiple Strategies for Nonconvex Optimization

In the field of practical applications, the solution of nonconvex optimization problems plays a crucial role. However, many practical applications often encounter perturbations that may affect solutions to relevant nonconvex problems. Such perturbations are typically unavoidable. Moreover, in the presence of perturbations, most algorithms for nonconvex optimization suffer from low solution accuracy and a tendency to become trapped in local optima. To address this limitation, this paper proposes a coevolutionary neural dynamics considering multiple strategies (CNDMS) model. Firstly, a modified neural dynamics model with a dual-gradient accumulation term is constructed as a local search operator, which effectively explores the local optimal value in the presence of noises. Secondly, a modified opposition-based learning method is employed to generate improved candidate solutions based on the current solution, thereby ensuring the population diversity throughout the search process. Additionally, a hybrid variation strategy is utilized to mutate the global optimal solution and reduce the probability of the proposed CNDMS model falling into the local optimum. The global convergence and robustness of the proposed CNDMS model is proven with theoretical analyses, and are further validated through numerical experiments and an engineering application.