Multiobjective Estimation of Distribution Algorithm Based on Joint Modeling of Objectives and Variables

This paper proposes a new multiobjective estimation of distribution algorithm (EDA) based on joint probabilistic modeling of objectives and variables. This EDA uses the multidimensional Bayesian network as its probabilistic model. In this way, it can capture the dependencies between objectives, variables and objectives, as well as the dependencies learned between variables in other Bayesian network-based EDAs. This model leads to a problem decomposition that helps the proposed algorithm find better tradeoff solutions to the multiobjective problem. In addition to Pareto set approximation, the algorithm is also able to estimate the structure of the multiobjective problem. To apply the algorithm to many-objective problems, the algorithm includes four different ranking methods proposed in the literature for this purpose. The algorithm is first applied to the set of walking fish group problems, and its optimization performance is compared with a standard multiobjective evolutionary algorithm and another competitive multiobjective EDA. The experimental results show that on several of these problems, and for different objective space dimensions, the proposed algorithm performs significantly better and on some others achieves comparable results when compared with the other two algorithms. The algorithm is then tested on the set of CEC09 problems, where the results show that multiobjective optimization based on joint model estimation is able to obtain considerably better fronts for some of the problems compared with the search based on conventional genetic operators in the state-of-the-art multiobjective evolutionary algorithms.