Multi-objective Cooperative Coevolutionary Algorithm with Dynamic Species-Size Strategy

Although numbers of heuristic algorithms are successfully developed for solving portfolio optimization problems, this is not for all cases of the large-scale ones. A large-scale portfolio optimization involves dealing with the large search space and dense variance-covariance matrix associated with the problem. This paper proposed a new multi-objective algorithm for solving a large-scale optimization problem based upon the notion of cooperative coevolutionary algorithms (CCA). The new problem decomposition scheme was designed by allowing the species-size to be dynamically adjusted as the runs progress. This scheme enhances capability of traditional CCA in dealing with non-separable optimization problem. The collaborator selection method was modified to allow the proposed CCA to perform in a multi-objective (MO) optimization framework. Additionally, the proposed algorithm, named as “DMOCCA”, was implemented for solving large-scale portfolio optimization problem with cardinality constraint using the real-world data set having scale up to 2196 dimensions. Moreover, its performances were benchmarked with those of the SPEA-II and MOPSO.