Simulation response optimization via direct conjugate direction method

Abstract

This paper modifies Powell's conjugate direction method for unconstrained, continuous, local optimization problems to adapt to the stochastic environment in simulation response optimization. The main idea underlying the proposed method is to conduct several replications at each trial point to obtain reliable estimate of the theoretical response. To avoid misjudging the real difference between two points due to the stochastic nature, a t-test of the statistical hypothesis is employed to replace the simple comparison of the mean responses. In an experimental comparison, the proposed method outperforms the Nelder–Mead simlex method, a quasi-Newton method, and several other methods in solving a stochastic Watson function with nine variables, a queueing problem with two variables, and an inventory problem with two variables. Scope and purpose In decision making there are many situations that the problem is so complicated that the conventional optimization methods are unable to apply. In this case, embedding the simulation technique with certain optimization method has been demonstrated to be very promising in solving the problem. There exist many optimization methods, of which Powell's conjugate direction method has been valued for its sound theoretical properties and the derivative-free nature in practice. The purpose of this paper is to embed Powell's method to the simulation technique to solve the unconstrained, continuous, local optimization problems in a stochastic sense.