(184a) An Algorithm for Bound-Constrained Problems in Simulation Optimization

The field of simulation optimization (SO), which deals with optimizing over simulations or experiments, is faced with challenges at every turn. Its use is of import in several engineering and business applications, including inventory management, urban traffic control, manufacturing plant design, and call center operations.

Apart from the lack of an explicit functional form for the objective function, and the steep cost of evaluating the objective at a point--the stumbling blocks in derivative-free optimization--SO also involves underlying simulations that are inherently stochastic in nature. Furthermore, the fundamental questions regarding the choice of an appropriate objective to include variability in function value and the characterization of optimal points add to its complexity.

We pose the problem as the local minimization of a statistic of a continuous black-box function, assuming that bounds are available on the control variables. Though the setup of the problem prohibits the direct use of traditional optimization, we draw heavily both from math programming and machine learning techniques to support our algorithmic framework. We present a deterministic algorithm that simultaneously looks for minima and performs relatively few function evaluations. The method does this by applying modern regression techniques while trading off performing simulations at new points against performing repeated simulations, and then embedding this in an iterative trust-region scheme.

A sketch of the fundamental ideas, a method for characterizing and comparing algorithms, and an evaluation of performance on test cases will be presented.