EDA-Based Multi-objective Optimization Using Preference Order Ranking and Multivariate Gaussian Copula

Estimation of distribution algorithms (EDAs) are a class of evolutionary optimization algorithms based on probability distribution model. This article extends the basic EDAs for tackling multi-objective optimization problems by incorporating multivariate Gaussian copulas for constructing probability distribution model, and using the concept of preference order. In the algorithm, the multivariate Gaussian copula is used to construct probability distribution model in EDAs. By estimating Kendall's τ and using the relationship of correlation matrix and Kendall's τ, correlation matrix R in Gaussian copula are firstly estimated from the current population, and then is used to generate offsprings. Preference order is used to identify the best individuals in order to guide the search process. The population with the current population and current offsprings population is sorted based on preference order, 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. The experimental results show that the algorithm is effective on the benchmark functions.