On the improved performances of the particle swarm optimization algorithms with adaptive parameters, cross-over operators and root mean square (RMS) variants for computing optimal control of a class of hybrid systems

This paper deals with the concept of including the popular genetic algorithm operator, cross-over and root mean square (RMS) variants into particle swarm optimization (PSO) algorithm to make the convergence faster. Two different PSO algorithms are considered in this paper: the first one is the conventional PSO (cPSO) and the second is the global-local best values based PSO (GLbest-PSO). The GLbest-PSO includes global-local best inertia weight (GLbestIW) with global-local best acceleration coefficient (GLbestAC), whereas the cPSO has a time varying inertia weight (TVIW) and either time varying acceleration coefficient (TVAC) or fixed AC (FAC). The effectiveness of the cross-over operator with both PSO algorithms is tested through a constrained optimal control problem of a class of hybrid systems. The experimental results illustrate the advantage of PSO with cross-over operator, which sharpens the convergence and tunes to the best solution. In order to compare and verify the validity and effectiveness of the new approaches for PSO, several statistical analyses are carried out. The results clearly demonstrate that the GLbest-PSO with the cross-over operator is a very promising optimization technique. Similar conclusions can be made for the GLbest-PSO with RMS variants also.