A localized decomposition evolutionary algorithm for imbalanced multi-objective optimization

Multi-objective evolutionary algorithms based on decomposition (MOEA/Ds) convert a multi-objective optimization problem (MOP) into a set of scalar subproblems, which are then optimized in a collaborative manner. However, when tackling imbalanced MOPs, the performance of most MOEA/Ds will evidently deteriorate, as a few solutions will replace most of the others in the evolutionary process, resulting in a significant loss of diversity. To address this issue, this paper suggests a localized decomposition evolutionary algorithm (LDEA) for imbalanced MOPs. A localized decomposition method is proposed to assign a local region for each subproblem, where the inside solutions are associated and the solution update is restricted inside (i.e., solutions are only replaced by offspring within the same local region). Once off-spring are generated within an originally empty region, the best one is reserved for this subproblem to extend diversity. Meanwhile, the subproblem with the largest number of associated solutions will be found and one of its associated solutions with the worst aggregated value will be removed. Moreover, to speed up convergence for each subproblem while balancing the population's diversity, LDEA only evolves the best-associated solution in each subproblem and correspondingly tailors two decomposition methods in the environmental selection. When compared to nine competitive MOEAs, LDEA has shown the advantages in tackling two benchmark sets of imbalanced MOPs, one benchmark set of balanced yet complicated MOPs, and one real-world MOP.