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

Tipaluck Krityakierne,Taimoor Akhtar,Christine A Shoemaker

doi:10.1007/s10898-016-0407-7

Tipaluck Krityakierne, Taimoor Akhtar + Show 1 more

Open Access

https://doi.org/10.1007/s10898-016-0407-7

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Abstract

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 of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.

Highlights

Real-world applications in various fields, such as physics, engineering, or economics, often have a simulation model which is multimodal, computationally expensive, and blackbox
The mean of the best objective function value is plotted on the vertical axis and the wall-clock time is plotted on the horizontal axis
Parallel computation has the potential to greatly reduce the wall-clock time to solve a global optimization problem for a computationally expensive objective function, but that potential can only be realized if the parallel algorithm is able to effectively select the work to be computed in parallel

Summary

Introduction

Real-world applications in various fields, such as physics, engineering, or economics, often have a simulation model which is multimodal, computationally expensive, and blackbox. “Blackbox” implies that many mathematical characteristics are not known, including derivatives or number of local minima. Many existing optimization methods for black-box functions such as genetic algorithm, simulated annealing, or particle swarm are not suitable for this type of problem due to the large number of objective function evaluations that these methods generally require. One approach for dealing with this type of problem is to use a surrogate model (alternatively called metamodel or response surface) to approximate the objective function. Response surface based optimization methods start by building a (computationally inexpensive) surrogate surface, which is used to iteratively select new points for the expensive function evaluation. The surrogate surface is updated in each iteration

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