Primal-Dual Interior Point Method Particle Swarm Optimization (pdipmPSO) Algorithm

Particle Swarm Optimization (PSO) is a metaheuristic optimization algorithm that have been used to solve complex optimization problems that the traditional techniques finds very
difficult to solve. The Interior-Point Methods (IPMs) are efficient tools for solving nonlinear optimization problems. The IPMs having constrains that are active at the current point, are now believed to be the most robust algorithms for solving large-scale nonlinear optimization problems. Though they are very efficient, but they are still plagued with several challenges such as how to handle of nonconvexity, the procedure for making the barrier constraint up to date is cumbersome despite the existence of nonlinearities, and the need to ensure progress toward the solution. In order to overcome some of the shortcomings of the standard PSO such as premature convergence
and particles been trapped at the local minimal, we proposed the Primal-Dual Interior Point Particle Swarm Optimization (pdipmPSO) to surmount the shortcomings of the original PSO. We applied the
Primal Dual to each particle in a finite number of iterations, and feed the PSO with the output of the Primal Dual. We compared the performance of our new algorithm (pdipmPSO) with IPM and PSO
using 13 different benchmark functions. Optimization results reveal that pdipmPSO performs better than PSO and IPM. Our proposed algorithm is shown to have great capacity to prevent premature convergence, and the curse of particles being trapped in the local minimal which have characterised many variants of PSO.