Coevolutionary Neural Dynamics Considering Multiple Strategies for Nonconvex Optimization

Abstract In practical applications, solving 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. This paper proposes a coevolutionary neural dynamics considering multiple strategies (CNDMS) model to address this limitation. Firstly, a modified neural dynamics model with a dual-gradient accumulation term is constructed as a local search operator, effectively exploring the local optimal value in noise. Secondly, a modified opposition-based learning method is employed to generate improved candidate solutions based on the current solution, thereby ensuring 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 local optima. The global convergence and robustness of the proposed CNDMS model are proven by theoretical analyses and further validated through numerical experiments and an engineering application.