An Adaptive Gaussian Process-Based Search for Stochastically Constrained Optimization via Simulation

Abstract

Simulation optimization (SO) techniques show a strong ability to solve large-scale problems. In this article, we concentrate on stochastically constrained SO. There are some challenges to tackle the problem: 1) the objective and constraints have no analytical forms and need to be evaluated via simulation; 2) we should make a tradeoff between exploiting around the best solution and exploring more unknown regions; and 3) both the objective value and feasibility determine the quality of a solution. Motivated by these issues, we propose an adaptive Gaussian process-based search (AGPS) to address stochastically constrained discrete SO problems. AGPS fast constructs the Gaussian process for each performance and then builds a new sampling distribution to adaptively balance exploration and exploitation considering the objective function and stochastic constraints. We show that AGPS converges to the set of globally optimal solutions with probability one. Numerical experiments demonstrate the superiority of our method compared with other advanced approaches. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Simulation is widely used to model complex and large-scale systems, such as healthcare, transportation, and supply chain logistics. When optimizing these systems, practitioners always assess overall performance by multiple indicators. Inspired by this issue, this article focuses on a general problem that aims to optimize the system’s primary performance while keeping the secondary performance within limits. We propose an adaptive Gaussian process-based method called AGPS to search for a high-quality solution. The bright spot of AGPS is that it can intelligently determine the quality of a solution considering all the stochastic performance and adaptively search the solution space. The merit lightens the burden of practitioners to design specific parameters for different performance indicators. Numerical experiments demonstrate that AGPS can apply to the large-scale discrete optimization problems with smooth function values and shows higher efficiency than existing methods.