Deep Learning Surrogate-Assisted Particle Swarm Optimization in Partitioned Search Spaces with Adaptive Neighborhood Topology for Continuous Optimization (PSA-PSO)

In this paper, we propose Partitioned Surrogate Adaptive Particle Swarm Optimization (PSA-PSO), a hybrid optimization framework that integrates deeplearning–based surrogate modeling, search space partitioning, and adaptiveneighborhood topology to enhance performance in global continuous optimization. The proposed method first partitions the search space into multiple zonesaround the central search region. Within each zone, a deep neural network surrogate model is trained to approximate the objective function using sampled data.A gradient-based minimization procedure is then applied to the surrogate modelto estimate promising local minima within each partition. These estimated minima are subsequently used to initialize the particles of the main PSO swarm,providing a diverse and informed starting population. To further balance exploration and exploitation during the optimization process,PSA-PSO employs an adaptive ring topology in which the neighborhood sizegradually expands over iterations, enabling controlled information sharing amongparticles. The proposed framework is evaluated on a set of uni-modal and multi-modal continuous benchmark functions, including cases with coordinate rotation and shifttransformations. Experimental results demonstrate that PSA-PSO achieves competitive performance and improved robustness compared to conventional PSOvariants and several state-of-the-art continuous optimization algorithms