A new EDA by a gradient-driven density

Abstract

This paper introduces the Gradient-driven Density Function (∇dD) approach, and its application to Estimation of Distribution Algorithms (EDAs). In order to compute the ∇dD, we also introduce the Expected Gradient Estimate (EGE), which is an estimation of the gradient, based on information from other individuals. Whilst EGE delivers an estimation of the gradient vector at the position of any individual, the ∇dD delivers a statistical model (e.g. the normal distribution) that allows the sampling of new individuals around the direction of the estimated gradient. Hence, in the proposed EDA, the gradient information is inherited to the new population. The computation of the EGE vector does not need additional function evaluations. It is worth noting that this paper focuses in black-box optimization. The proposed EDA is tested with a benchmark of 10 problems. The statistical tests show a competitive performance of the proposal.