Transforming arc routing into node routing problems
Computers and Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
The Capacitated Arc Routing Problem: Valid Inequalities and Facets
Computational Optimization and Applications
Discrete Mathematics
A Genetic Algorithm for the Capacitated Arc Routing Problem and Its Extensions
Proceedings of the EvoWorkshops on Applications of Evolutionary Computing
A cutting plane algorithm for the capacitated arc routing problem
Computers and Operations Research
A Tabu Search Heuristic for the Capacitated Arc Routing Problem
Operations Research
A new branch-and-cut algorithm for the capacitated vehicle routing problem
Mathematical Programming: Series A and B
Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem
Mathematical Programming: Series A and B
The Shortest-Path Problem with Resource Constraints and k-Cycle Elimination for k ≥ 3
INFORMS Journal on Computing
Selected Topics in Column Generation
Operations Research
Dual-Optimal Inequalities for Stabilized Column Generation
Operations Research
A deterministic tabu search algorithm for the capacitated arc routing problem
Computers and Operations Research
Odd Minimum Cut Sets and $b$-Matchings Revisited
SIAM Journal on Discrete Mathematics
Exploiting sparsity in pricing routines for the capacitated arc routing problem
Computers and Operations Research
Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows
Operations Research
Solving capacitated arc routing problems using a transformation to the CVRP
Computers and Operations Research
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This paper presents the first full-fledged branch-and-price bap algorithm for the capacitated arc-routing problem CARP. Prior exact solution techniques either rely on cutting planes or the transformation of the CARP into a node-routing problem. The drawbacks are either models with inherent symmetry, dense underlying networks, or a formulation where edge flows in a potential solution do not allow the reconstruction of unique CARP tours. The proposed algorithm circumvents all these drawbacks by taking the beneficial ingredients from existing CARP methods and combining them in a new way. The first step is the solution of the one-index formulation of the CARP in order to produce strong cuts and an excellent lower bound. It is known that this bound is typically stronger than relaxations of a pure set-partitioning CARP model. Such a set-partitioning master program results from a Dantzig-Wolfe decomposition. In the second phase, the master program is initialized with the strong cuts, CARP tours are iteratively generated by a pricing procedure, and branching is required to produce integer solutions. This is a cut-first bap-second algorithm and its main function is, in fact, the splitting of edge flows into unique CARP tours.