An advanced Hybrid Algorithm for Engineering Design Optimization

Abstract

Among numerous meta-heuristic algorithms, Differential evolution (DE) and Particle Swarm Optimization (PSO) are found to be an efficient and powerful optimization algorithm. Similarly, it has been observed that their hybrid algorithms provide a reliable estimate to global optimum. Therefore, in this paper based on multi-swarm approach an advanced hybrid algorithm haDEPSO is suggested for engineering design optimization problems. Where, proposed advanced DE (aDE) and PSO (aPSO) are integrated with the suggested hybrid. In aDE, a novel mutation and crossover strategy along with the slightly changed selection scheme are introduced, to avoid premature convergence. And aPSO comprises of novel gradually varying parameters, to avoid stagnation. In haDEPSO, entire population (\n $$pop$$\n ) is sorted according to the fitness function value and divided into two sub-populations $$pop_{{{ }1}}$$\n and $$pop_{{{ }2}}$$\n . Since $$pop_{{{ }1}}$$\n and $$pop_{{{ }2}}$$\n contains best and rest half of the main population which implies global and local search capability respectively. In order to maintain local and global search capability, applying aDE (due to its good local search ability) and aPSO (because of its virtuous global search capability) on the respective sub-population. Evaluating both sub-population then better solution obtained in $$pop_{{{ }1}}$$\n and $$pop_{{{ }2}}$$\n are named as best and gbest separately. If best is less than gbest then $$pop_{{{ }2}}$$\n is merged with $$pop_{{{ }1}}$$\n thereafter merged population evaluated by aDE (as it mitigates the potential stagnation). Otherwise, $$pop_{{{ }1}}$$\n is merged with $$pop_{{{ }2}}$$\n afterward merged population evaluated by aPSO (as it established to guide better movements). The convergence characteristic of aDE and aPSO provides different approximation to the solution space, thus haDEPSO achieve better solutions. Performance of proposed hybrid haDEPSO and its integrating component aDE and aPSO have been verified on CEC 2006 constrained benchmark functions. Then they applied on five engineering design optimization problems. Results confirms the superiority of proposed approaches over many state-of-the-art algorithms.