Topology-informed Derivative-Free Metaheuristic Optimization Method

Abstract

In this study, we propose a novel topology-informed search strategy for derivative-free metaheuristic optimization, enhancing both Simulated Annealing (SA) and Particle Swarm Optimization (PSO) through Topology Data Analysis (TDA). The proposed methods utilize persistence diagram and Gaussian kernel density estimation to guide search processes effectively. For SA, TDA evaluates neighboring points to generate persistence diagrams, guiding the search towards regions with significant topological features. This approach balances exploration and exploitation, reducing the risk of converging to suboptimal solutions. In PSO, dynamic adjustment of social and cognitive coefficients based on feature density in persistence diagrams ensures robust convergence. This strategy guides particles toward the best positions, promoting early exploration and later convergence. Lastly, nine continuous non-linear numerical problems and a cost optimization problem in pharmaceutical manufacturing illustrate the feasibility of the proposed methods. The study highlights the potential of TDA-informed metaheuristic strategies to improve derivative-free optimization methods, offering an advancement in navigating complex optimization landscapes.