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A Benders decomposition based framework for solving cable trench problems. (English) Zbl 1391.90505
Summary: In this work, we present an algorithmic framework based on Benders decomposition for the capacitated \(p\)-cable trench problem with covering. We show that our approach can be applied to most variants of the cable trench problem (CTP) that have been considered in the literature. The proposed algorithm is augmented with a stabilization procedure to accelerate the convergence of the cut loop and with a primal heuristic to derive high-quality primal solutions. Three different variants of the CTP are considered in a computational study which compares the Benders approach with two compact integer linear programming formulations that are solved with CPLEX. The obtained results show that the proposed algorithm significantly outperforms the two compact models and that it can be used to tackle significantly larger instances than previously considered algorithms based on Lagrangean relaxation.

MSC:
90C27 Combinatorial optimization
90C35 Programming involving graphs or networks
90C11 Mixed integer programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
90B10 Deterministic network models in operations research
90B80 Discrete location and assignment
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