E. Corchado et al. (Eds.): IDEAL 2014, LNCS 8669, pp. 449–456, 2014. © Springer International Publishing Switzerland 2014 Multivariate Cauchy EDA Optimisation Momodou L.Sanyang 1,2 and Ata Kaban 1 School of Computer Science, University of Birmingham ଴ ଵ , Edgbaston, UK, B15 2TT {M.L.Sanyang,A.Kaban}@cs.bham.ac.uk School of Information Technolgy and Communication, University of the Gambia ଴ ଶ Brikama Campus, P.O. Box 3530, Serekunda, The Gambia MLSanyang@utg.edu.gm Abstract. We consider Black-Box continuous optimization by Estimation of Distribution Algorithms (EDA). In continuous EDA, the multivariate Gaussian distribution is widely used as a search operator, and it has the well-known ad- vantage of modelling the correlation structure of the search variables, which univariate EDA lacks. However, the Gaussian distribution as a search operator is prone to premature convergence when the population is far from the optimum. Recent work suggests that replacing the univariate Gaussian with a univariate Cauchy distribution in EDA holds promise in alleviating this problem because it is able to make larger jumps in the search space due to the Cauchy distribution's heavy tails. In this paper, we propose the use of a multivariate Cauchy distribu- tion to blend together the advantages of multivariate modelling with the ability of escaping early convergence to efficiently explore the search space. Experi- ments on 16 benchmark functions demonstrate the superiority of multivariate Cauchy EDA against univariate Cauchy EDA, and its advantages against multi- variate Gaussian EDA when the population lies far from the optimum. Keywords: Multivariate Gaussian distribution, Multivariate Cauchy Distribu- tion, Estimation of Distribution Algorithm, Black-box Optimization. 1 Introduction Black-box global optimization is an important problem which has many applications in lots of disciplines. Optimization is at the core of many scientific and engineering problems. Mathematical optimization only deals with very specific problem types, while on the other hand the search heuristics like evolutionary computation work in a black box manner. They are not specialized on specific kinds of functions although they don’t have the guarantees that the mathematical optimizations do. This paper presents a method which is classified as a search heuristic, and it is an extension of a recent version called Estimation of Distribution Algorithm (EDA). EDA is a population based stochastic black-box optimization method that guides the search to the optimum by building and sampling explicit probability models of promising candidate solutions [2]. In EDA, the new population of individuals is gen- erated without using neither crossover nor mutation operations, which is in contrast to