On the usefulness of infeasible solutions in evolutionary search: A theoretical study

Evolutionary algorithms (EAs) have been widely used in optimization, where infeasible solutions are often encountered. Some EAs regard infeasible solutions as useless individuals while some utilize infeasible solutions based on heuristic ideas. It is not clear yet that whether infeasible solutions are helpful or not in the evolutionary search. This paper theoretically analyzes that under what conditions infeasible solutions are beneficial. A sufficient condition and a necessary condition are derived and discussed. Then, the paper theoretically shows that the use of infeasible solutions could change the hardness of the task. For example, an EA-hard problem can be transformed to EA-easy by exploiting infeasible solutions. While, the conditions derived in the paper can be used to judge whether to use infeasible solutions or not.