An epsilon-constraint method for integer-ordered bi-objective simulation optimization. Cooper, K., Hunter, S. R., & Nagaraj, K. In Chan, W. K. V., D'Ambrogio, A., Zacharewicz, G., Mustafee, N., Wainer, G., & Page, E., editors, Proceedings of the 2017 Winter Simulation Conference, pages 2303–2314, Piscataway, NJ, 2017. Institute of Electrical and Electronics Engineers, Inc..
An epsilon-constraint method for integer-ordered bi-objective simulation optimization [pdf]Paper  doi  abstract   bibtex   
Consider the context of integer-ordered bi-objective simulation optimization, in which the feasible region is a finite subset of the integer lattice. We propose a retrospective approximation (RA) framework to identify a local Pareto set that involves solving a sequence of sample-path bi-objective optimization problems at increasing sample sizes. We apply the epsilon-constraint method to each sample-path bi-objective optimization problem, thus solving a sequence of constrained single-objective problems in each RA iteration. We solve each constrained single-objective optimization problem using the SPLINE algorithm, thus exploiting gradient-based information. In early RA iterations, when sample sizes are small and standard errors are relatively large, we provide only a rough characterization of the Pareto set by making the number of epsilon-constraint problems a function of the standard error. As the RA algorithm progresses, the granularity of the characterization increases until we solve as many epsilon-constraint problems as there are points in the (finite) image of the local Pareto set. Our algorithm displays promising numerical performance.

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