# Heuristic solutions to robust variants of the minimum-cost integer flow problem

## TL;DR

This paper explores robust optimization for minimum-cost integer flow problems under cost uncertainty, demonstrating NP-hardness and proposing heuristics based on local search and evolutionary algorithms, validated through experiments.

## Contribution

It introduces and evaluates heuristics for two NP-hard robust variants of the minimum-cost integer flow problem with explicit cost scenarios.

## Key findings

- Heuristics effectively solve the NP-hard robust flow variants.
- Local search and evolutionary algorithms outperform baseline methods.
- Experimental results demonstrate the practical applicability of the proposed heuristics.

## Abstract

This paper deals with robust optimization applied to network flows. Two robust variants of the minimum-cost integer flow problem are considered. Thereby, uncertainty in problem formulation is limited to arc unit costs and expressed by a finite set of explicitly given scenarios. It is shown that both problem variants are NP-hard. To solve the considered variants, several heuristics based on local search or evolutionary computing are proposed. The heuristics are experimentally evaluated on appropriate problem instances.