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An Efficient Mixed Integer Linear Programming Model for the Minimum Spanning Tree Problem

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  • Tamer F. Abdelmaguid

    (Department of Mechanical Engineering, School of Sciences and Engineering, American University in Cairo, AUC Avenue, P.O. Box 74, New Cairo 11835, Egypt
    Department of Mechanical Design and Production, Faculty of Engineering, Cairo University, Giza 12613, Egypt)

Abstract

Finding a minimum spanning tree in a given network is a famous combinatorial optimization problem that appears in different engineering applications. Even though this problem is solvable in polynomial time, having efficient mathematical programming models is important as they can provide insights for formulating larger models that integrate other decisions in more complex applications. In the literature, there are ten different integer and mixed integer linear programming (MILP) models for this problem. They are variants of set packing, cuts, network flow and node level formulations. In addition, this paper introduces an efficient node level MILP model. Comparisons for the eleven models are provided. First, the models are compared in terms of the number of decision variables and the number of constraints. Then, computational comparisons using a commercial MILP solver on sets of randomly generated instances of different sizes are conducted. Results provide evidence that the proposed MILP model is competitive in terms of the computational time needed for proving optimality of generated solutions for instances with up to 50 nodes. Meanwhile, the LP relaxation of a multi-commodity flow MILP model which has integer polyhedron provides stable computational times despite its larger size.

Suggested Citation

  • Tamer F. Abdelmaguid, 2018. "An Efficient Mixed Integer Linear Programming Model for the Minimum Spanning Tree Problem," Mathematics, MDPI, vol. 6(10), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:10:p:183-:d:172755
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    References listed on IDEAS

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    1. Zahreddine Hafsi & Sami Elaoud & Manoranjan Mishra & Mohsen Akrout, 2018. "Automated Framework for Water Looped Network Equilibrium," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(2), pages 641-657, January.
    2. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
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