A fast and accurate solution of constrained optimization problems using a hybrid bi-objective and penalty function approach

Evolutionary algorithms are modified in various ways to solve constrained optimization problems. Of them, the 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. Classical penalty function approach is another common methodology which requires an appropriate knowledge of the associated penalty parameter. In this paper, we combine a bi-objective evolutionary approach with the penalty function methodology in a manner complementary to each other. The bi-objective optimization approach provides a good estimate of the penalty parameter, while the unconstrained penalty function approach using classical means provides the overall hybrid algorithm its convergence property. We demonstrate the working of the procedure on a two-variable problem and then solve a number of standard numerical test problems from the EA literature. In all cases, our proposed hybrid methodology is observed to take one or more orders of magnitude smaller number of function evaluations to find the constrained minimum solution accurately. To the best of our knowledge, no previous evolutionary constrained optimization algorithm has reported such a fast and accurate performance on the chosen problems.