A Non-cooperative Game for Faster Convergence in Cooperative Coevolution for Multi-objective Optimization


Cooperative coevolution is an approach for evolving solutions from different populations which are evaluated based on how well they perform together. The advantage of cooperative coevolutionary algorithms is the decomposition of the problem which allows us to learn different parts of the problem instead of the whole problem at once. However, previous research within the field of global optimization has shown that cooperative coevolutionary algorithms are biased towards equilibrium states. Since studies concerning cooperative coevolutionary algorithms used for solving multi- objective optimization problems were initiated, no attention has been paid to this issue. In this paper, we show empirical evidence of the existence of these problems within the multi-objective optimization field and present a novel cooperative coevolution framework which, through the use of the concept of Nash equilibrium, alleviates some of those optimization-related pathologies present in cooperative coevolutionary algorithms. We compare our proposed algorithm with respect to two algorithms that make use of the cooperative coevolutionary model to multi-objective optimization, NSCCGA (that makes use of Potter's coevolutionary model) and GCEA (a game theory based coevolutionary algorithm). The computational effort required by each algorithm (measured in terms of the number of fitness function evaluations) is also analyzed. Our preliminary results indicate that the proposed framework clearly outperforms the results of the aforementioned algorithms when using the Deb-Thiele- Laumanns-Zitzler (DTLZ) and the Zitzler-Deb-Thiele (ZDT) test suites.