A Coevolutionary Algorithm for Many-Objective Optimization Problems with Independent and Harmonious Objectives

Evolutionary algorithm is an effective strategy for solving many-objective optimization problems. At present, most evolutionary many-objective algorithms are designed for solving many-objective optimization problems where the objectives conflict with each other. In some cases, however, the objectives are not always in conflict. It consists of multiple independent objective subsets and the relationship between objectives is unknown in advance. The classical evolutionary many-objective algorithms may not be able to effectively solve such problems. Accordingly, we propose an objective set decomposition strategy based on the partial set covering model. It decomposes the objectives into a collection of objective subsets to preserve the nondominance relationship as much as possible. An optimization subproblem is defined on each objective subset. A coevolutionary algorithm is presented to optimize all subproblems simultaneously, in which a nondominance ranking is presented to interact information among these sub-populations. The proposed algorithm is compared with five popular many-objective evolutionary algorithms and four objective set decomposition based evolutionary algorithms on a series of test problems. Numerical experiments demonstrate that the proposed algorithm can achieve promising results for the many-objective optimization problems with independent and harmonious objectives.