Multiobjective Estimation of Distribution Algorithms Using Multivariate Archimedean Copulas and Average Ranking

Abstract

Estimation of distribution algorithms (EDAs) are a class of evolutionary optimization algorithms based on probability distribution model. This chapter extends the basic EDAs for tackling multiobjective optimization problems by incorporating multivariate Archimedean copulas for constructing probability distribution model, and using the concept of average ranking. In the algorithm, Archimedean copula is used to construct probability distribution model in EDA. By estimating Kendall’s τ and using the relationship of parameter of Archimedean copula generator and Kendall’s τ, the parameter of generator in Archimedean copula are first estimated from the current population. Then Archimedean copula sampling algorithm is used to generate offsprings. Average ranking is used to identify the best individuals in order to guide search process. Population with the current population and current offsprings population is sorted based on average ranking, and the best individuals are selected to form the next population. The algorithm is tested to compare with NSGA-II, GDE, MOEP, and MOPSO based on convergence metric and diversity metric using a set of benchmark functions. Experimental results show that the algorithm is effective on the benchmark functions.