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