A Hybrid Particle Swarm Branch-and-Bound (HPB) Optimizer for Mixed Discrete Nonlinear Programming

This paper proposes a new algorithm for solving mixed discrete nonlinear programming (MDNLP) problems, designed to efficiently combine particle swarm optimization (PSO), which is a well-known global optimization technique, and branch-and-bound (BB), which is a widely used systematic deterministic algorithm for solving discrete problems. The proposed algorithm combines the global but slow search of PSO with the rapid but local search capabilities of BB, to simultaneously achieve an improved optimization accuracy and a reduced requirement for computational resources. It is capable of handling arbitrary continuous and discrete constraints without the use of a penalty function, which is frequently cumbersome to parameterize. At the same time, it maintains a simple, generic, and easy-to-implement architecture, and it is based on the sequential quadratic programming for solving the NLP subproblems in the BB tree. The performance of the new hybrid PSO-BB architecture algorithm is evaluated against real-world MDNLP benchmark problems, and it is found to be highly competitive compared with existing algorithms.