An improved biogeography/complex algorithm based on decomposition for many-objective optimization

It is difficult to maintain the balance between convergence and diversity for many-objective optimization problems (MaOPs) in the algorithms of evolutionary multi-objective (EMO). EMO algorithms are useful technology to solve the multi-objective optimization problems (MOPs). However, with the larger of optimization objectives, enough Pareto selection pressure will be loosed, and results in the performance of the algorithms are significantly reduced. The decomposition-based EMO developed for MaOPs have been shown to be effective, and the BBO algorithm is a low-complexity algorithm. In this paper, a hybrid decomposition-based BBO/Complex algorithm (HDB/BBO) for MaOPs is proposed. First, a set of uniformly distributed weight vectors and K-means aggregate method is introduced for decomposing MaOPs into several subsystems. Then, inferior migrated islands will not be chosen unless they pass the Metropolis criterion twice during the within-subsystem migration and cross-subsystem migration. The penalty-based boundary intersection (PBI) distance to calculate neighbor islands distance for balancing the algorithm of convergence and diversity. Finally, after mutation and clear duplication, a uniform distribution Pareto set can be obtained. Experimental results on both DTLZ and WFG benchmarks problems demonstrate the superiority of the proposed algorithm in comparison with three state-of-the-art algorithms in terms of both convergence and diversity.