### Abstract

Simulation response optimization has wide applications for management of systems that are so complicated that the performance can only be evaluated by using simulation. This paper modifies the quasi-Newton method used in deterministic optimization to suit the stochastic environment in simulation response optimization. The basic idea is to use the estimated subgradient calculated from different replications and a metric matrix updated from the Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula to yield a quasi-Newton search direction. To avoid misjudging the minimal point, in both the line search and the quasi-Newton iterations, due to the stochastic nature, a t-test instead of a simple comparison of the mean responses is performed. It is proved that the resulting stochastic quasi-Newton algorithm is able to generate a sequence that converges to the optimal point, under certain conditions. Empirical results from a four-station queueing problem and an (s, S) inventory problem indicate that this method is able to find the optimal solutions in a statistical sense. Moreover, this method is robust with respect to the number of replications conducted at each trial point.

Original language | English |
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Pages (from-to) | 30-46 |

Number of pages | 17 |

Journal | European Journal of Operational Research |

Volume | 173 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2006 Aug 16 |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Modelling and Simulation
- Management Science and Operations Research
- Information Systems and Management

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## Cite this

*European Journal of Operational Research*,

*173*(1), 30-46. https://doi.org/10.1016/j.ejor.2004.12.011