Genetic algorithm with adaptive and dynamic penalty functions for the selection of cleaner production measures: a constrained optimization problem

This paper presents a new approach of genetic algorithm (GA) to solve the constrained optimization problem. In a constrained optimization problem, feasible and infeasible regions occupy the search space. The infeasible regions consist of the solutions that violate the constraint. Oftentimes classical genetic operators generate infeasible or invalid chromosomes. This situation takes a turn for the worse when infeasible chromosomes alone occupy the whole population. To address this problem, dynamic and adaptive penalty functions are proposed for the GA search process. This is a novel strategy because it will attempt to transform the constrained problem into an unconstrained problem by penalizing the GA fitness function dynamically and adaptively. New equations describing these functions are presented and tested. The effects of the proposed functions developed have been investigated and tested using different GA parameters such as mutation and crossover. Comparisons of the performance of the proposed adaptive and dynamic penalty functions with traditional static penalty functions are presented. The result from the experiments show that the proposed functions developed are more accurate, efficient, robust and easy to implement. The algorithms developed in this research can be applied to evaluate environmental impacts from process operations.