Variable-Number Sample-Path Optimization

Authors:
Geng Deng;Michael C. Ferris
Affiliations:
University of Wisconsin, Department of Mathematics, 480 Lincoln Drive, 53706, Madison, WI, USA;University of Wisconsin, Computer Sciences Department, 1210 West Dayton Street, 53706, Madison, WI, USA
Venue:
Mathematical Programming: Series A and B
Year:
2008

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Abstract

The sample-path method is one of the most important tools in simulation-based optimization. The basic idea of the method is to approximate the expected simulation output by the average of sample observations with a common random number sequence. In this paper, we describe a new variant of Powell’s unconstrained optimization by quadratic approximation (UOBYQA) method, which integrates a Bayesian variable-number sample-path (VNSP) scheme to choose appropriate number of samples at each iteration. The statistically accurate scheme determines the number of simulation runs, and guarantees the global convergence of the algorithm. The VNSP scheme saves a significant amount of simulation operations compared to general purpose ‘fixed-number’ sample-path methods. We present numerical results based on the new algorithm.