Quantile-Based Simulation Optimization With Inequality Constraints: Methodology and Applications.

Many automation or manufacturing systems are too complex to be modeled by analytical approaches and can only resort to fast-running simulation. Stochastic Nelder–Mead simplex method (SNM) is a newly developed methodology for simulation optimization with expected-value-based objective functions. Quantile, as an important alternative to the usual expected value, provides additional information about the distribution of system performance. In particular, it is useful in describing the tail behavior of the distribution. In this paper, we exploit the structure of SNM and extend it to solve simulation optimization problems with quantile-based objective functions and inequality constraints. The proposed method, called SNM-QC, utilizes the same search strategy as SNM but further incorporates effective quantile estimation techniques and penalty function approaches to solve the problem. We prove that SNM-QC has the desirable global convergence guarantee, i.e., the algorithm is guaranteed to converge to the true optima with probability one. One advantage of SNM-QC is that it is a direct search method that determines the moving direction simply by comparing a set of solutions rather than estimating gradient, thus it can handle many practical problems where gradient does not exist or is difficult to estimate. An extensive numerical study shows that the performance of SNM-QC is promising compared to the existing heuristics. Two illustrative applications are provided in the end to demonstrate the viability of SNM-QC in practical settings. [ABSTRACT FROM AUTHOR]