Problem-Driven Scenario Clustering in Stochastic Optimization

TL;DR

This paper introduces a new, efficient scenario clustering method for stochastic optimization that minimizes implementation error, reducing complexity while maintaining solution accuracy, and outperforms existing approaches in complex problems.

Contribution

The paper presents a novel, problem-driven scenario clustering approach that effectively reduces scenarios based on implementation error, improving efficiency in stochastic optimization.

Findings

Outperforms alternative clustering methods and Monte Carlo sampling.

Reduces scenario set size while maintaining solution quality.

Demonstrates effectiveness on network design and facility location problems.

Abstract

In stochastic optimisation, the large number of scenarios required to faithfully represent the underlying uncertainty is often a barrier to finding efficient numerical solutions. This motivates the scenario reduction problem: by find a smaller subset of scenarios, reduce the numerical complexity while keeping the error at an acceptable level. In this paper we propose a novel and computationally efficient methodology to tackle the scenario reduction problem when the error to be minimised is the implementation error, i.e. the error incurred by implementing the solution of the reduced problem in the original problem. Specifically, we develop a problem-driven scenario clustering method that produces a partition of the scenario set. Each cluster contains a representative scenario that best reflects the conditional objective values in each cluster of the partition to be identified. We demonstrate the efficiency of our method by applying it to two challenging stochastic combinatorial optimization problems: the two-stage stochastic network design problem and the two-stage facility location problem. When compared to alternative clustering methods and Monte Carlo sampling, our method is shown to clearly outperform all other methods.