Multiobjective Ranking and Selection Using Stochastic Kriging

We consider multiobjective simulation optimization problems, where several conflicting objectives are optimized simultaneously, and can only be observed via stochastic simulation. The goal is to find or approximate a (discrete) set of Pareto-optimal solutions that reveal the essential trade-offs between the objectives, where optimality means that no objective can be improved without deteriorating the quality of any other objective. The noise in the observed performance may lead to two possible misclassification errors: solutions that are truly Pareto-optimal can be wrongly considered dominated, and solutions that are truly dominated can be wrongly considered Pareto-optimal. We propose a Bayesian multiobjective ranking and selection method to reduce the number of errors when identifying the solutions with the true best expected performance. We use stochastic kriging metamodels to build reliable predictive distributions of the objectives, and exploit this information in two efficient screening procedures and two novel sampling criteria. We use these in a sequential sampling algorithm to decide how to allocate samples. Experimental results show that the proposed method only requires a small fraction of samples compared to the standard allocation method, and it's competitive against the state-of-the-art, with the exploitation of the correlation structure being the dominant contributor to the improvement.