Multivariate Cauchy EDA Optimisation

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 advantage 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 distribution to blend together the advantages of multivariate modelling with the ability of escaping early convergence to efficiently explore the search space. Experiments on 16 benchmark functions demonstrate the superiority of multivariate Cauchy EDA against univariate Cauchy EDA, and its advantages against multivariate Gaussian EDA when the population lies far from the optimum.