Abstract

Co-evolutionary algorithms involve two co-evolving populations, each having its own set of objectives and constraints, that interact with each other during function evaluation. Co-evolutionary algorithms are of great interest in cooperative and competing games and search tasks in which multiple agents having different interests are in play. Despite a number of single-objective co-evolutionary studies, there has been limited interest in multi-objective co-evolutionary algorithms. A recent study has revealed that in addition to the challenges associated with the development of an efficient algorithm, a proper understanding of the conflicting objectives within a single population and their interaction among objectives of the second population becomes extremely difficult to comprehend. In this paper, we extend the previous proof-of-principle multi-objective co-evolutionary (MOCoEv) study in three important directions. First, we enhance MOCoEv’s ability to handle mixed cooperating and conflicting scenarios among different players. Second, we propose an iterative multi-criterion decision-making (MCDM) approach to demonstrate how, in an arms-race type scenario, the most appropriate solution can be selected from the obtained Pareto-optimal solution set iteratively. Third, we extend the previous MOCoEv algorithm with a many-objective evolutionary algorithm (NSGA-III) to make them applicable to three or more objectives for each player. These three developments reveal better insights about the intricate issues related to multiple objectives and decision-making for co-evolutionary optimization and take MOCoEv a step closer to solving more complex multi-player problems.