A Largest Empty Hypersphere Metaheuristic for Robust Optimisation with Implementation Uncertainty

TL;DR

This paper introduces a novel global search method using the largest empty hypersphere for robust optimisation under implementation uncertainty, effective even in high-dimensional problems without prior knowledge of the objective function.

Contribution

The paper proposes a new metaheuristic based on the largest empty hypersphere for robust optimisation, applicable to simulation-optimisation and high-dimensional problems.

Findings

Demonstrates strong performance compared to state-of-the-art methods

Effective in high-dimensional robust optimisation problems

Does not require knowledge of the objective function structure

Abstract

We consider box-constrained robust optimisation problems with implementation uncertainty. In this setting, the solution that a decision maker wants to implement may become perturbed. The aim is to find a solution that optimises the worst possible performance over all possible perturbances. Previously, only few generic search methods have been developed for this setting. We introduce a new approach for a global search, based on placing a largest empty hypersphere. We do not assume any knowledge on the structure of the original objective function, making this approach also viable for simulation-optimisation settings. In computational experiments we demonstrate a strong performance of our approach in comparison with state-of-the-art methods, which makes it possible to solve even high-dimensional problems.