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Mixed-integer linear programming formulations and column generation algorithms for the Minimum Normalized Cuts problem on networks

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  • Ponce, Diego
  • Puerto, Justo
  • Temprano, Francisco

Abstract

This paper deals with the k-way normalized cut problem in complex networks. It presents a methodology that uses mathematical optimization to provide mixed-integer linear programming formulations for the problem. The paper also develops a branch-and-price algorithm for the above-mentioned problem which scales better than the compact formulations. Additionally, a heuristic algorithm which is able to approximate large-scale image problems in those cases where the exact methods are not applicable is presented. Extensive computational experiments assess the usefulness of these methods to solve the k-way normalized cut problem. Finally, we have applied the minimum normalized cut objective function to the segmentation of actual images, showing the applicability of the introduced methodology.

Suggested Citation

  • Ponce, Diego & Puerto, Justo & Temprano, Francisco, 2024. "Mixed-integer linear programming formulations and column generation algorithms for the Minimum Normalized Cuts problem on networks," European Journal of Operational Research, Elsevier, vol. 316(2), pages 519-538.
    • Handle: RePEc:eee:ejores:v:316:y:2024:i:2:p:519-538
    DOI: 10.1016/j.ejor.2024.02.033
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