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Several novel mixed-integer linear and bilinear formulations are proposed forthe optimum communication spanning tree problem. They implement thedistance-based approach: graph distances are directly modeled by continuous,integral, or binary variables, and interconnection between distance variablesis established using the recursive Bellman-type conditions or using matrixequations from algebraic graph theory. These non-linear relations are usedeither directly giving rise to the bilinear formulations, or, through the big-Mreformulation, resulting in the linear programs. A branch-and-bound frameworkof Gurobi 9.0 optimization software is employed to compare performance of thenovel formulations on the example of an optimum requirement spanning treeproblem with additional vertex degree constraints. Several real-worldrequirements matrices from transportation industry are used to generate anumber of examples of different size, and computational experiments show thesuperiority of the two novel linear distance-based formulations over the thetraditional multicommodity flow model.

Mixed-Integer Approaches to Constrained Optimum Communication Spanning Tree Problem