Multiobjective hBOA, Clustering, and Scalability

This paper describes a scalable algorithm for solving multiobjective decomposable problems by combining the hierarchical Bayesian optimization algorithm (hBOA) with the nondominated sorting genetic algorithm (NSGA-II) and clustering in the objective space. It is first argued that for good scalability, clustering or some other form of niching in the objective space is necessary and the size of each niche should be approximately equal. Multiobjective hBOA (mohBOA) is then described that combines hBOA, NSGA-II and clustering in the objective space. The algorithm mohBOA differs from the multiobjective variants of BOA and hBOA proposed in the past by including clustering in the objective space and allocating an approximately equally sized portion of the population to each cluster. The algorithm mohBOA is shown to scale up well on a number of problems on which standard multiobjective evolutionary algorithms perform poorly.