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

Authors:
Antoniya Georgieva;Ivan Jordanov
Affiliations:
Nuffield Department of Obstetrics and Gynaecology, John Radcliffe Hospital, Oxford University, OX3 9DU, UK;School of Computing, University of Portsmouth, PO1 3HE, UK
Venue:
Computers and Operations Research
Year:
2010

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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 LP@tOptimisation(LP@tO) 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 LP@tO method. The combination of the two techniques (LP@tO and NM) provides a powerful hybrid optimisation technique, which we call LP@tNM. Its properties-applicability, convergence, consistency and stability are discussed here in detail. The LP@tNM is tested on a number of benchmark multimodal mathematical functions from 2 to 20 dimensions and compared with results from other stochastic heuristic methods.