Adaptive Partitioning Strategy for High-Dimensional Discrete Simulation-based Optimization Problems

TL;DR

The paper tackles the computational challenges of high-dimensional discrete simulation-based optimization by introducing an adaptive partitioning strategy embedded in the ESB&B framework. It presents two partitioning families—parallel and hyperplane cuts—driven by data from already-sampled solutions and problem-specific structure, and formalizes an adaptive ESB&B algorithm that controls partition depth and sample allocation. Empirical results on the Griewank function and a real-world car-sharing fleet assignment demonstrate improved finite-time performance and higher likelihood of reaching the global optimum compared to the baseline ESB&B with generic partitioning. The approach offers a general-purpose tool for discrete simulation-based optimization with practical impact on operations research problems where evaluations are costly and high dimensionality is common.

Abstract

In this paper, we introduce a technique to enhance the computational efficiency of solution algorithms for high-dimensional discrete simulation-based optimization problems. The technique is based on innovative adaptive partitioning strategies that partition the feasible region using solutions that has already been simulated as well as prior knowledge of the problem of interesting. We integrate the proposed strategies with the Empirical Stochastic Branch-and-Bound framework proposed by Xu and Nelson (2013). This combination leads to a general-purpose discrete simulation-based optimization algorithm that is both globally convergent and has good small sample (finite-time) performance. The proposed general-purpose discrete simulation-based optimization algorithm is validated on a synthetic discrete simulation-based optimization problem and is then used to address a real-world car-sharing fleet assignment problem. Experiment results show that the proposed strategy can increase the algorithm efficiency significantly.

Figures (29)

• Figure 1: The ground truth values of $f(x_1,x_2)$ in the current best subregion.
• Figure 2: The sampled solutions of $f(x_1,x_2)$ in the current best subregion.
• Figure 3: A naive partition of the current best subregion.
• Figure 4: A better partition of the current best subregion.
• Figure 6: The contour plot of two-dimensional Griewank function on $[-5,5]\times[-5,5]$.