# Robust optimization for the pooling problem

## TL;DR

This paper explores robust optimization techniques for the non-linear, non-convex pooling problem, accounting for parametric uncertainty, and compares reformulation and cutting plane methods on multiple instances.

## Contribution

It introduces the application of robust optimization approaches to the pooling problem with uncertain parameters, a novel extension beyond traditional deterministic methods.

## Key findings

- Reformulation and cutting plane methods show different computational efficiencies.
- Accounting for uncertainty alters the optimal solutions.
- Robust optimization is feasible for non-convex, global optimization problems.

## Abstract

The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of parametric uncertainty. This paper applies two robust optimization approaches, reformulation and cutting planes, to the non-linear, non-convex pooling problem. Most applications of robust optimization have been either convex or mixed-integer linear problems. We explore the suitability of robust optimization in the context of global optimization problems which are concave in the uncertain parameters by considering the pooling problem with uncertain inlet concentrations. We compare the computational efficiency of reformulation and cutting plane approaches for three commonly-used uncertainty set geometries on 14 pooling problem instances and demonstrate how accounting for uncertainty changes the optimal solution.