A hybrid meta-heuristic for global optimisation using low-discrepancy sequences of points

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.cor.2008.07.004 Byline: Antoniya Georgieva (a), Ivan Jordanov (b) Abstract: A hybrid novel meta-heuristic technique for bound-constrained global optimisation (GO) is proposed in this paper. We have developed an iterative algorithm called LPI Optimisation (LPIO) that uses low-discrepancy sequences of points and meta-heuristic knowledge to find regions of attraction when searching for a global minimum of an objective function. Subsequently, the well-known Nelder-Mead (NM) simplex local search is used to refine the solution found by the LPIO method. The combination of the two techniques (LPIO and NM) provides a powerful hybrid optimisation technique, which we call LPINM. Its properties -- applicability, convergence, consistency and stability are discussed here in detail. The LPINM is tested on a number of benchmark multimodal mathematical functions from 2 to 20 dimensions and compared with results from other stochastic heuristic methods. Author Affiliation: (a) Nuffield Department of Obstetrics and Gynaecology, John Radcliffe Hospital, Oxford University, OX3 9DU, UK (b) School of Computing, University of Portsmouth, PO1 3HE, UK