An adaptive multiobjective estimation of distribution algorithm with a novel Gaussian sampling strategy

In most of existing multiobjective estimation of distribution algorithms (MEDAs), there exist drawbacks: incorrect treatment of population outliers; the loss of population diversity; and too much computational effort being spent on finding an optimal population model. To ease the drawbacks, this paper designs a novel clustering-based multivariate Gaussian sampling strategy and proposes an adaptive MEDA called AMEDA. A clustering analysis approach is utilized in AMEDA to discover the distribution structure of the population. Based on the distribution information, with a certain probability, a local or a global multivariate Gaussian model (MGM) is built for each solution to sample a new solution. A covariance sharing strategy is designed in AMEDA to reduce the complexity of building MGMs, and an adaptive update strategy of the probability that controls the contributions of the two types of MGMs is developed to dynamically balance exploration and exploitation. AMEDA is compared with four representative MOEAs on a number of test instances with complex Pareto fronts and variable linkages. Experimental results suggest that AMEDA outperforms the comparison algorithms on dealing with the test instances. The effectiveness of the clustering-based multivariate Gaussian sampling strategy and the adaptive probability update strategy is also experimentally verified.