Hybrid PSO-α BB Global Optimisation for C² Box-Constrained Multimodal NLPs

$\alpha $ BB is an elegant deterministic branch and bound global optimisation that guarantees global optimum convergence with minimal parameter tuning. However, the method suffers from a slow convergence speed calling for computational improvements in several areas. The current paper proposes hybridising the branch and bound process with particle swarm optimisation to improve its global convergence speed when solving twice differentiable ( $C^{2}$ ) box-constrained multimodal functions. This hybridisation complemented with interval analysis leads to an early discovery of the global optimum, quicker pruning of suboptimal regions in the problem space, thus improving global convergence. Also, when used as a heuristic search algorithm, the hybrid algorithm yields superior solution accuracy owing to the combined search capabilities of PSO and the branch and bound framework. Computational experiments have been conducted on CEC 2017/2019 test sets and on n-dimensional classical test sets yielding improved convergence speed in the complete search configuration and superior solution accuracy in the heuristic search configuration.