An Online Non-Stationary Simulation Optimization Approach Based on Regime Switching

TL;DR

This paper introduces an online simulation optimization method for non-stationary environments with regime-switching dynamics, using Bayesian and nonparametric models to improve decision-making under uncertainty.

Contribution

It develops a Bayesian framework with Markov Switching Models and a metamodel-based algorithm for online optimization in non-stationary, regime-switching settings, including unknown regimes.

Findings

Algorithm outperforms existing methods in numerical experiments.

Robustness demonstrated across various non-stationary scenarios.

Effective handling of unknown regimes with Bayesian nonparametrics.

Abstract

Dynamic and evolving operational and economic environments present significant challenges for decision-making. We explore a simulation optimization problem characterized by non-stationary input distributions with regime-switching dynamics across sequential decision stages. This problem encompasses both prediction uncertainty, arising from the regime-switching behavior of input distributions, and input uncertainty, resulting from parameter estimation for these distributions and their dynamics using finite data streams. To address these uncertainties, we develop a Bayesian framework that approximates the true objective function using a Markov Switching Model (MSM). We rigorously validate this approximation by establishing the consistency and asymptotic normality of the objective functions and optimal solutions. To solve the problem in an online fashion, we propose a metamodel-based algorithm that leverages simulation results from previous stages to enhance decision-making. Furthermore, we tackle scenarios with an unknown number of regimes through a Bayesian nonparametric method. Numerical experiments demonstrate that our algorithm achieves superior performance and robust adaptability.