A modified Hooke and Jeeves algorithm with likelihood ratio performance extrapolation for simulation optimization

The Hooke and Jeeves algorithm (HJ) is a pattern search procedure widely used to optimize non-linear functions that are not necessarily continuous or differentiable. The algorithm performs repeatedly two types of search routines; an exploratory search and a pattern search. The HJ algorithm requires deterministic evaluation of the function being optimized. In this paper we consider situations where the objective function is stochastic and can be evaluated only through Monte Carlo simulation. To overcome the problem of expensive use of function evaluations for Monte Carlo simulation, a likelihood ratio performance extrapolation (LRPE) technique is used. We extrapolate the performance measure for different values of the decision parameters while simulating a single sample path from the underlying system. Our modified Hooke and Jeeves algorithm uses a likelihood ratio performance extrapolation for simulation optimization. Computational results are provided to demonstrate the performance of the proposed modified HJ algorithm.