Continuous variable neighbourhood search with modified Nelder-Mead for non-differentiable optimization

Several variants of variable neighbourhood search (VNS) for solving unconstrained and constrained continuous optimization problems have been proposed in the literature. In this paper, we suggest two new variants, one of which uses the recent modified Nelder-Mead (MNM) direct search method as a local search and the other an extension of the MNM method obtained by increasing the size of the simplex each time the search cannot be continued. For these new and some previous VNS variants, extensive computational experiments are performed on standard and large non-differentiable test instances. Some interesting observations regarding comparison of some VNS variants with NM based local search are made.