SOP: parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases the efficiency Electronic supplementary material The online version of this article (doi:10.1007/s10898-016-0407-7) contains supplementary material, which is available to authorized users. B Tipaluck Krityakierne [email protected] Taimoor Akhtar [email protected] Christine A. Shoemaker [email protected] 1 Institute of Mathematical Statistics and Actuarial Science, University of Bern, Bern, Switzerland 2 School of Civil and Environmental Engineering, Cornell University, Ithaca, NY, USA 3 Department of CEE, National University of Singapore, Singapore, Singapore 4 Department of ISE, National University of Singapore, Singapore, Singapore