The Benefit of Uncertainty Coupling in Robust and Adaptive Robust Optimization

TL;DR

This paper investigates how coupling uncertainty sets in robust optimization reduces conservatism, providing theoretical bounds and computational evidence that coupling improves objective values and adaptability.

Contribution

It introduces the concept of coupled uncertainty sets, derives bounds on objective improvements, and links uncertainty coupling with adaptability in robust optimization.

Findings

Coupling uncertainty sets alleviates conservatism in RO and ARO.

Theoretical bounds quantify the benefit of coupling.

Computational results confirm practical advantages of coupling.

Abstract

Despite the modeling power for problems under uncertainty, robust optimization (RO) and adaptive robust optimization (ARO) can exhibit too conservative solutions in terms of objective value degradation compared to the nominal case. One of the main reasons behind this conservatism is that, in many practical applications, uncertain constraints are directly designed as constraint-wise without taking into account couplings over multiple constraints. In this paper, we define a coupled uncertainty set as the intersection between a constraint-wise uncertainty set and a coupling set. We study the benefit of coupling in alleviating conservatism in RO and ARO. We provide theoretical tight and computable upper and lower bounds on the objective value improvement of RO and ARO problems under coupled uncertainty over constraint-wise uncertainty. In addition, we relate the power of adaptability over static solutions with the coupling of uncertainty set. Computational results demonstrate the benefit of coupling in applications.