Gaussian variable neighborhood search for continuous optimization

Variable Neighborhood Search (VNS) has shown to be a powerful tool for solving both discrete and box‐constrained continuous optimization problems. In this note we extend the methodology by allowing also to address unconstrained continuous optimization problems. Instead of perturbing the incumbent solution by randomly generating a trial point in a ball of a given metric, we propose to perturb the incumbent solution by adding some noise, following a Gaussian distribution. This way of generating new trial points allows one to give, in a simple and intuitive way, preference to some directions in the search space, or, contrarily, to treat uniformly all directions. Computational results show some advantages of this new approach.