Evaluate till you violate: A differential evolution algorithm based on partial evaluation of the constraint set

Abstract

Evolutionary algorithms are a popular choice for solving multi-disciplinary optimization problems as they are simple to use and are widely applicable. However, such algorithms require numerous function evaluations prior to its convergence. In the context of constrained optimization (i.e. a vast majority of real life problems), such algorithms use some sort of constraint violation (CV) measure to rank infeasible solutions in the population. Existing algorithms compute such constraint violation measure by evaluating all constraints of the problem. If the user is only interested in the final set of feasible solutions (i.e. Pareto solutions), such an approach can be questioned as “what is the worth of evaluating subsequent constraints when the solution has already violated at least once ?”. This question becomes even more relevant and important in the event if evaluation of such constraints is computationally expensive or the problem involves many constraints. Based on the above motivation, an algorithm is designed using the framework of differential evolution. The population is divided into multiple sub-populations and each sub-population is assigned a prescribed constraint sequence. In any sub-population, evaluation of a solution is aborted whenever it violates a constraint. Such a strategy allows the population to approach the feasible space from different directions, thereby offering a greater chance to reach the Pareto front. The benefits of such a sequencing approach are illustrated using an example before illustrating its performance across a number of engineering design optimization problems. The results of the proposed approach are compared with NSGA-II and the same differential evolution algorithm relying on constraint violation measure derived through evaluation of all its constraints. The results clearly indicate, that the approach is able to identify the first feasible solution earlier than other approaches and often has a greater diversity which in turn results in a better non-dominated set of solutions.