CHIP: Constraint Handling with Individual Penalty approach using a hybrid evolutionary algorithm

Abstract

Constraint normalization ensures consistency in scaling for each constraint in an optimization problem. Most constraint handling studies only address the issue to deal with constraints and use problem information to scale the constraints. In this paper, we propose a hybrid evolutionary algorithm-Constraint Handling with Individual Penalty Approach (CHIP)-which scales all constraints adaptively without any problem specific information from the user. Penalty parameters for all constraints are estimated adaptively by considering overall constraint violation as a helper objective for minimization and as a result any number of constraints can be dealt without incurring proportional computational cost. The efficiency of the proposed method is demonstrated using 23 test problems and two problems from engineering optimization. The constrained optimum and function evaluations of CHIP method are inspected with five recently developed evolutionary-based constraint handling methods. The simulation results show that the proposed CHIP mechanism is very efficient, faster and comparable in the aspect of accuracy against other recently developed methods.