  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.
