A hybrid meta-heuristic for global optimisation 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 LPτLPτOptimisation  (LPτO)(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)(NM) simplex local search is used to refine the solution found by the LPτOLPτO method. The combination of the two techniques (LPτO(LPτO and NMNM) provides a powerful hybrid optimisation technique, which we call LPτNMLPτNM. Its properties—applicability, convergence, consistency and stability are discussed here in detail. The LPτNMLPτNM is tested on a number of benchmark multimodal mathematical functions from 2 to 20 dimensions and compared with results from other stochastic heuristic methods.