# Efficient Simulation Budget Allocation for Subset Selection Using Regression Metamodels

## TL;DR

This paper introduces a regression metamodel-based approach for efficient simulation budget allocation in subset selection problems, improving the probability of correctly identifying top designs under budget constraints.

## Contribution

It proposes a novel partitioned quadratic regression metamodel and an approximately optimal budget allocation rule for better simulation efficiency in subset selection.

## Key findings

- Significant improvement in simulation efficiency demonstrated through numerical experiments.
- Partitioned quadratic regression models effectively fit the domain within each partition.
- The proposed allocation rule outperforms existing methods in accuracy and efficiency.

## Abstract

This research considers the ranking and selection (R&S) problem of selecting the optimal subset from a finite set of alternative designs. Given the total simulation budget constraint, we aim to maximize the probability of correctly selecting the top-m designs. In order to improve the selection efficiency, we incorporate the information from across the domain into regression metamodels. In this research, we assume that the mean performance of each design is approximately quadratic. To achieve a better fit of this model, we divide the solution space into adjacent partitions such that the quadratic assumption can be satisfied within each partition. Using the large deviation theory, we propose an approximately optimal simulation budget allocation rule in the presence of partitioned domains. Numerical experiments demonstrate that our approach can enhance the simulation efficiency significantly.