Geometric Optimization of Radiant Enclosures Containing Specularly-Reflecting Surfaces through Quasi-Monte Carlo Simulation

Abstract

Monte Carlo (MC) ray-tracing simulation coupled with Kiefer–Wolfowitz stochastic programming is a standard tool for designing enclosures that contain specularly-reflecting surfaces. Unfortunately, the statistical uncertainty MC induces into the objective function combined with the error amplification inherent in finite-difference approximations of the gradient means that large numbers of bundles are often needed to obtain acceptable search directions. This article shows that quasi-Monte Carlo sampling reduces these uncertainties, allowing the required gradient estimations to be carried out using smaller sample sizes, in turn leading to a dramatic drop in optimization time.