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arXiv · 2411.05798

A Genetic Algorithm for Multi-Capacity Fixed-Charge Flow Network Design

Caleb Eardley·Dalton Gomez·Ryan Dupuis·Michael Papadopoulos·Sean Yaw
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Abstract

The Multi-Capacity Fixed-Charge Network Flow (MC-FCNF) problem, a generalization of the Fixed-Charge Network Flow problem, aims to assign capacities to edges in a flow network such that a target amount of flow can be hosted at minimum cost. The cost model for both problems dictates that the fixed cost of an edge is incurred for any non-zero amount of flow hosted by that edge. This problem naturally arises in many areas including infrastructure design, transportation, telecommunications, and supply chain management. The MC-FCNF problem is NP-Hard, so solving large instances using exact techniques is impractical. This paper presents a genetic algorithm designed to quickly find high-quality flow solutions to the MC-FCNF problem. The genetic algorithm uses a novel solution representation scheme that eliminates the need to repair invalid flow solutions, which is an issue common to many other genetic algorithms for the MC-FCNF problem. The genetic algorithm's efficiency is displayed with an evaluation using real-world CO2 capture and storage infrastructure design data. The evaluation results highlight the genetic algorithm's potential for solving large-scale network design problems.

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Caleb Eardley, Dalton Gomez, Ryan Dupuis, Michael Papadopoulos, Sean Yaw. 2024-10-26. A Genetic Algorithm for Multi-Capacity Fixed-Charge Flow Network Design. https://arxiv.org/abs/2411.05798

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