Hybrid metaheuristics for global optimization using low-discrepancy sequences of points

A hybrid novel meta-heuristic technique for bound-constrained global optimisation (GO) is proposed in this paper. We have developed an iterative algorithm called LPτ Optimisation (LPτO) 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 LPτO method. The combination of the two techniques (LPτO and NM) provides a powerful hybrid optimisation technique, which we call LPτNM. Its properties - applicability, convergence, consistency and stability are discussed here in detail. The LPτNM is tested on a number of benchmark multimodal mathematical functions from 2 to 20 dimensions and compared with results from other stochastic heuristic methods. Keywords: Global optimisation; Meta-heuristics; Hybrid methods; Local minima problem; Low-discrepancy sequences.