Genetic programming for a class of constrained optimization problems

Abstract

In recent years a host of constrained optimization problems have been studied using genetic algorithms or evolutionary programming. For genetic search we initially need to create a variety of solutions to the given problem, and reach a near-optimum solution through selection, crossover and mutation operations. For constrained optimization problems, the above four steps pose varied levels of difficulty depending on the problem constraints, if there is the restriction of keeping the set of population always valid. On the other hand, if invalid solutions are allowed, the genetic operations may be simple but the search space becomes enormous and finding a valid solution becomes impossible for large problems. We show that for a class of constrained optimization problems, it is more efficient to reach better solutions when we restrict the population only to valid solutions and define crossover and mutation operators so that they remain valid. In our experiments the genetic operators are aimed to improve individual solutions and not for random combination of them. Thus the genetic operations have specific result oriented direction, such as greedy algorithms in heuristic search. The difference between our algorithm and simple greedy algorithms is that we simultaneously carry out operations on a number of solutions in parallel and then probabilistically select good ones. Though the defined genetic operators facilitate only restricted search, they are found to be very efficient, could handle very large problems and yield results better or as good as existing soft-computing/heuristic approaches.