A Hybrid Bi-Objective Evolutionary-Penalty Approach for Computationally Fast and Accurate Constrained Optimization∗

Constrained optimization is a computationally difficult task, particularly if the constraint functions are non-linear and nonconvex. As a generic classical approach, the penalty function approach is a popular methodology which degrades the objective function value by adding a penalty proportional to the constraint violation. However, the penalty function approach has been criticized for its sensitivity to the associated penalty parameters. Since its inception, evolutionary algorithms (EAs) are modified in various ways to solve constrained optimization problems. Of them, the recent use of a bi-objective evolutionary algorithm in which the minimization of the constraint violation is included as an additional objective, has received a significant attention. In this paper, we propose a combination of a bi-objective evolutionary approach with the penalty function methodology in a manner complementary to each other. The bi-objective approach provides an appropriate estimate of the penalty parameter, while the solution of unconstrained penalized function by a classical method induces a convergence property to the overall hybrid algorithm. We demonstrate the working of the procedure on a number of standard numerical test problems from the EA literature. In most cases, our proposed hybrid methodology is observed to take one or more orders of magnitude lesser number of function evaluations to find the constrained minimum solution accurately than some of the best-reported existing methodologies.