Self-Adaptive Fitness Formulation: Theory and Application

A self-adaptive fitness formulation is presented for constrained evolutionary optimization. The method has been formulated to ensure that slightly infeasible solutions with a low objective function value remain fit. This is seen as a benefit in solving highly constrained problems that have solutions on one or more of the constraint bounds. In contrast, solutions furthest from the constraint bounds are seen as containing little genetic information that is of use and are therefore penalized. The dimensionality of the problem is reduced by representing the constraint violations by a single infeasibility measure. The infeasibility measure is used to form a two-stage penalty that is applied to the infeasible solutions. The performance of the method has been examined by its application to a set of eleven test cases from the specialized literature and also by its application to a water distribution network from literature. The results have been compared with previously published results from the literature. It is shown that the method is able to find the optimum solutions with less computational effort. The proposed method requires no parameter tuning and can be used as a fitness evaluator with any evolutionary algorithm. The approach is also robust in its handling of both linear and nonlinear equality and inequality constraint functions. Furthermore, the method does not require an initial feasible solution. Key-Words: Constraint handling, evolutionary algorithm, fitness, penalty, self-adaptive, real world problems