Document Open Access Logo

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

Authors Caleb Eardley , Dalton Gomez , Ryan Dupuis , Michael Papadopoulos , Sean Yaw

PDF

File

Thumbnail PDF
PDF
OASIcs.ATMOS.2025.10.pdf
  • Filesize: 2.06 MB
  • 14 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Computing methodologies → Planning and scheduling
  • Theory of computation → Network flows
Keywords
  • Fixed-Charge Network Flow
  • Genetic Algorithm
  • Matheuristic
  • Infrastructure Design

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

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 utility is demonstrated with an evaluation using real-world CO₂ capture, transportation, and storage infrastructure design data. The evaluation results highlight the genetic algorithm’s potential for solving large-scale network design problems.

Cite As Get BibTex

Caleb Eardley, Dalton Gomez, Ryan Dupuis, Michael Papadopoulos, and Sean Yaw. A Genetic Algorithm for Multi-Capacity Fixed-Charge Flow Network Design. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.ATMOS.2025.10

Author Details

Caleb Eardley
  • School of Computing, Montana State University, Bozeman, MT, USA
Dalton Gomez
  • School of Computing, Montana State University, Bozeman, MT, USA
Ryan Dupuis
  • School of Computing, Montana State University, Bozeman, MT, USA
Michael Papadopoulos
  • Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, USA
Sean Yaw
  • School of Computing, Montana State University, Bozeman, MT, USA

Funding

This research was funded by the U.S. Department of Energy’s Fossil Energy Office through the Carbon Utilization and Storage Partnership (CUSP) for the Western USA (Award No. DE-FE0031837) as well as by the U.S. National Science Foundation through the Research Experience for Undergraduates program (Award No. 2243010).

References

  1. Ashwin Arulselvan, Mohsen Rezapour, and Wolfgang A. Welz. Exact Approaches for Designing Multifacility Buy-at-Bulk Networks. INFORMS Journal on Computing, 29(4):597-611, November 2017. URL: https://doi.org/10.1287/IJOC.2017.0752.
  2. Huynh Thi Thanh Binh and Son Hong Ngo. Survivable flows routing in large scale network design using genetic algorithm. In Advances in Computer Science and its Applications: CSA 2013, pages 345-351, 2014. Google Scholar
  3. Carbon Solutions, LLC. https://www.carbonsolutionsllc.com/, 2024.
  4. Deeparnab Chakrabarty, Alina Ene, Ravishankar Krishnaswamy, and Debmalya Panigrahi. Online Buy-at-Bulk Network Design. SIAM J. Comput., 47(4):1505-1528, January 2018. URL: https://doi.org/10.1137/16M1117317.
  5. Clean Air Task Force. More for less: Strengthening epa’s proposed carbon pollution standards can achieve greater emissions reductions at a lower cost, 2023. URL: https://www.regulations.gov/comment/EPA-HQ-OAR-2023-0072-0893.
  6. Ovidiu Cosma, Petrica C Pop, and Cosmin Sabo. An efficient hybrid genetic algorithm for solving a particular two-stage fixed-charge transportation problem. In Hybrid Artificial Intelligent Systems: 14th International Conference, HAIS 2019, León, Spain, September 4-6, 2019, Proceedings 14, pages 157-167. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-29859-3_14.
  7. Teodor Gabriel Crainic, Bernard Gendron, and Geneviève Hernu. A Slope Scaling/Lagrangean Perturbation Heuristic with Long-Term Memory for Multicommodity Capacitated Fixed-Charge Network Design. Journal of Heuristics, 10(5):525-545, September 2004. URL: https://doi.org/10.1023/B:HEUR.0000045323.83583.BD.
  8. Moustapha Diaby. Successive Linear Approximation Procedure for Generalized Fixed-Charge Transportation Problems. Journal of the Operational Research Society, 42(11):991-1001, November 1991. Google Scholar
  9. Samira Doostie, Tetsuhei Nakashima-Paniagua, and John Doucette. A novel genetic algorithm-based methodology for large-scale fixed charge plus routing network design problem with efficient operators. IEEE Access, 9:114836-114853, 2021. URL: https://doi.org/10.1109/ACCESS.2021.3104794.
  10. Burak Ekşioğlu, Sandra Duni Ekşioğlu, and Panos M. Pardalos. Solving Large Scale Fixed Charge Network Flow Problems. In Equilibrium Problems and Variational Models, Nonconvex Optimization and Its Applications, pages 163-183. Springer US, Boston, MA, 2003. Google Scholar
  11. Martina Fischetti and Matteo Fischetti. Matheuristics. In Handbook of Heuristics, pages 121-153. Springer International Publishing, Cham, 2018. URL: https://doi.org/10.1007/978-3-319-07124-4_14.
  12. Dalila B.M.M. Fontes and José Fernando Gonçalves. Heuristic solutions for general concave minimum cost network flow problems. Networks, 50:67-76, April 2007. URL: https://doi.org/10.1002/NET.20167.
  13. Zachary Friggstad, Mohsen Rezapour, Mohammad R. Salavatipour, and Jose A. Soto. LP-Based Approximation Algorithms for Facility Location in Buy-at-Bulk Network Design. Algorithmica, 81(3):1075-1095, March 2019. URL: https://doi.org/10.1007/S00453-018-0458-X.
  14. Bernard Gendron, Saïd Hanafi, and Raca Todosijević. Matheuristics based on iterative linear programming and slope scaling for multicommodity capacitated fixed charge network design. European Journal of Operational Research, 268(1):70-81, July 2018. URL: https://doi.org/10.1016/J.EJOR.2018.01.022.
  15. Bernard Gendron and Mathieu Larose. Branch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design. EURO Journal on Computational Optimization, 2(1-2):55-75, 2014. URL: https://doi.org/10.1007/S13675-014-0020-9.
  16. Fred Glover. Parametric ghost image processes for fixed-charge problems: A study of transportation networks. Journal of Heuristics, 11:307-336, 2005. URL: https://doi.org/10.1007/S10732-005-2135-X.
  17. Jung-Bok Jo, Yinzhen Li, and Mitsuo Gen. Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering, 53(2):290-298, September 2007. URL: https://doi.org/10.1016/J.CIE.2007.06.022.
  18. Erick C Jones Jr, Sean Yaw, Jeffrey A Bennett, Jonathan D Ogland-Hand, Cooper Strahan, and Richard S Middleton. Designing multi-phased CO₂ capture and storage infrastructure deployments. Renewable and Sustainable Energy Transition, 2:100023, 2022. Google Scholar
  19. Sam Kwong, Tak-Ming Chan, Kim-Fung Man, and HW Chong. The use of multiple objective genetic algorithm in self-healing network. Applied Soft Computing, 2(2):104-128, 2002. URL: https://doi.org/10.1016/S1568-4946(02)00033-9.
  20. Richard S Middleton, Sean P Yaw, Brendan A Hoover, and Kevin M Ellett. SimCCS: An open-source tool for optimizing CO₂ capture, transport, and storage infrastructure. Environmental Modelling & Software, 124:104560, 2020. Google Scholar
  21. Artyom Nahapetyan and Panos Pardalos. Adaptive dynamic cost updating procedure for solving fixed charge network flow problems. Computational Optimization and Applications, 39(1):37-50, January 2008. URL: https://doi.org/10.1007/S10589-007-9060-X.
  22. National Energy Technology Laboratory. FE/NETL CO₂ transport cost model, 2018. URL: https://www.netl.doe.gov/research/energy-analysis/searchpublications/vuedetails?id=543.
  23. Jonathan Ogland-Hand, Kyle J Cox, Benjamin M Adams, Jeffrey A Bennett, Peter J Johnson, Erin J Middleton, Carl J Talsma, and Richard S Middleton. How to net-zero america: Nationwide cost and capacity estimates for geologic CO₂ storage, 2023. Google Scholar
  24. Daniel Olson, Caleb Eardley, and Sean Yaw. Planning for edge failure in fixed-charge flow networks, 2024. URL: https://doi.org/10.48550/arXiv.2407.20036.
  25. Diane Prisca Onguetou and Wayne D Grover. Solution of a 200-node p-cycle network design problem with ga-based pre-selection of candidate structures. In 2009 IEEE International Conference on Communications, pages 1-5, 2009. URL: https://doi.org/10.1109/ICC.2009.5199466.
  26. Hossain Poorzahedy and Omid Rouhani. Hybrid meta-heuristic algorithms for solving network design problem. European Journal of Operational Research, 182:578-596, 2007. URL: https://doi.org/10.1016/J.EJOR.2006.07.038.
  27. Caleb Whitman, Sean Yaw, Brendan Hoover, and Richard Middleton. Scalable algorithms for designing CO₂ capture and storage infrastructure. Optimization and Engineering, 23(2):1057-1083, June 2022. Google Scholar
  28. Fanrong Xie and Renan Jia. Nonlinear fixed charge transportation problem by minimum cost flow-based genetic algorithm. Computers & Industrial Engineering, 63:763-778, 2012. URL: https://doi.org/10.1016/J.CIE.2012.04.016.
  29. Yufeng Xin, George N Rouskas, and Harry G Perros. On the physical and logical topology design of large-scale optical networks. Journal of lightwave technology, 21(4):904, 2003. Google Scholar
  30. Shangyao Yan, Der shin Juang, Chien rong Chen, and Wei shen Lai. Global and local search algorithms for concave cost transshipment problems. Journal of Global Optimization, 33:123-156, 2005. URL: https://doi.org/10.1007/S10898-004-3133-5.
  31. Sean Yaw, Richard S Middleton, and Brendan Hoover. Graph simplification for infrastructure network design. In International Conference on Combinatorial Optimization and Applications, pages 576-589. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-36412-0_47.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact