Determination of the Effects of Penalty Coefficient on the Meta-Heuristic Optimization Process

In the case of unconstrained continuous value problems, a cost is minimized or a gain is maximized. While in the case of constrained optimization problems, the cost function is optimized and the conditions related to the constraints must be met. Moreover, the constraints are typically nonlinear. Constraints are often violated while attempting to improve the objective function. In this case the penalty procedure is applied. Penalties prevent violations of the constraints but often cause the optimum solution also to be missed. The most important reason why the optimal solution is missed is that the penalty coefficient is randomly determined by the researchers. In this process, researchers use very large number to prevent the solution candidates from violating the constraints. For all these reasons, unlike unconstrained continuous value optimization problems, exploring the global solution of constrained optimization problems is a challenge task. Besides, in the majority of the publications on which the meta-heuristic algorithms are introduced, the search performance of the algorithms is only tested on unconstrained continuous optimization problems. There are two problems for researchers in this case. The first of these is that there is no accepted solution for determining the penalty coefficient. Second, there is insufficient information about the search performance of meta-heuristic search algorithms for constrained optimization problems. One purpose of this study is to research the effect of penalty coefficients used for constraint violations through the optimization process. Another goal of the study is to measure the performance of the commonly used and modern meta-heuristic search algorithms on constrained optimization problems. Important information for researchers has been obtained from experimental studies.