DE-VNS: Self-adaptive Differential Evolution with crossover neighborhood search for continuous global optimization

Abstract

In this paper, we suggest DE-VNS heuristic for solving continuous (unconstrained) nonlinear optimization problems. It combines two well-known metaheuristic approaches: Differential Evolution (DE) and Variable Neighborhood Search (VNS), which have, in the last decade, attracted considerable attention in both academic circles and among practitioners. The basic idea of our hybrid heuristic is the use of the neighborhood change mechanism in order to estimate the crossover parameter of DE. Moreover, we introduce a new family of adaptive distributions to control the distances among solutions in the search space as well as experimental evidence of finding the best probability distribution function for VNS parameter supported by its statistical estimation. This hybrid heuristic has shown excellent characteristics and it turns out that it is more favorable than the state-of-the-art DE approaches when tested on standard instances from the literature.