A Note on the Stochastic Ruler Method for Discrete Simulation Optimization

TL;DR

This paper introduces a relaxed version of the stochastic ruler method for discrete simulation optimization, reducing computational overhead and accelerating convergence while maintaining asymptotic optimality.

Contribution

The authors propose a modified stochastic ruler algorithm that relaxes the test passing requirement, leading to faster convergence and lower computational costs.

Findings

The modified method converges faster in numerical experiments.

It incurs less computational overhead compared to the original.

Theoretical proof of asymptotic convergence is provided.

Abstract

In this paper, we propose a relaxation to the stochastic ruler method originally described by Yan and Mukai in 1992 for asymptotically determining the global optima of discrete simulation optimization problems. The `original' version of the stochastic ruler and its variants require that a candidate for the next estimate of the optimal solution pass a certain number of tests with respect to the stochastic ruler to be selected as the next estimate of the optimal solution. This requirement - that all tests need to be passed - can lead to promising candidate solutions being rejected and can slow down the convergence of the algorithm. Our proposed modification to the stochastic ruler algorithm relaxes this requirement, and we show analytically that our proposed variant of the stochastic ruler method incurs lesser computational overhead when a new solution in the neighborhood of the current solution is a `successful' candidate for the next estimate of the current solution. We then show numerically that this can yield accelerated convergence to the optimal solution via multiple numerical examples. We also provide the theoretical grounding for the asymptotic convergence in probability of the variant to the global optimal solution under the same set of assumptions as those underlying the original stochastic ruler method.