Backtracking Search Algorithm with three constraint handling methods for constrained optimization problems

Abstract

A new evolutionary algorithm, Backtracking Search Algorithm (BSA), is applied to solve constrained optimization problems. Three constraint handling methods are combined with BSA for constrained optimization problems; namely feasibility and dominance (FAD) rules, ε-constrained method with fixed control way of ε value and a proposed ε-constrained method with self-adaptive control way of ε value. The proposed method controls ε value according to the properties of current population. This kind of ε value enables algorithm to sufficiently search boundaries between infeasible regions and feasible regions. It can avoid low search efficiency and premature convergence which happens in fixed control method and FAD rules. The comparison of the above three algorithms demonstrates BSA combined ε-constrained method with self-adaptive control way of ε value (BSA-SAε) is the best one. The proposed BSA-SAε also outperforms other five classic and the latest constrained optimization algorithms. Then, BSA-SAε has been applied to four engineering optimization instances, and the comparison with other algorithms has proven its advantages. Finally, BSA-SAε is used to solve the car side impact design optimization problem, which illustrates the wide application prospects of the proposed BSA-SAε.