A Scalable Parallel Algorithm for Global Optimization Based on Seed-Growth Techniques

Abstract

Global optimization requires huge computations for complex objective functions. Conventional global optimization based on stochastic and probability algorithms can not guarantee an actual global optimum with finite searching iteration. A numerical implementation of the scalable parallel Seed-Growth (SG) algorithm is introduced for global optimization of two-dimensional multi-extremal functions. The proposed parallel SG algorithm is characterized by a parallel phase that exploits the local optimum neighborhood features of the objective function assigned to each processor. The seeds are located at the optimum and inner neighborhood points. Seeds grow towards nearby grids and attach flags to them until reaching the boundary points in each dimension. When all grids in the subspace assigned to each CPU have been searched, the local optimum neighborhood boundaries are determined. As the definition domain is completely divided into different subdomains, the global optimal solution of each CPU is found. A coordination phase follows which, by a synchronous interaction scheme, optimizes the partial results obtained by the parallel phase. The actual global optimum in the total definition space can be determined. Numerical examples demonstrate the high efficiency, global searching ability, robustness and stability of this method.