Robust Branch-Cut-and-Price Algorithms for Vehicle Routing Problems

A Node-Flow Model for 1D Stock Cutting: Robust Branch-Cut-and-Price

Branch-and-Cut-and-Price (BCP) algorithms are branch-and-bound algorithms where both row generation (separation) and column generation (pricing) are performed. Following [12], we say that such an algorithm is robust when the separation and pricing subproblems are guaranteed to remain tractable during its execution. Robust BCP algorithms have been devised recently for a variety of problems, havi...

Integer Program Reformulation for Robust Branch-and-Cut-and-Price Algorithms

Since cut and column generation were established as two of the most important techniques in integer programming, researchers have looked for ways of combining them into a robust branch-and-cut-and-price algorithm. Here, “robust” means that neither branching nor the addition of cuts should change the structure of the pricing subproblems. In the last few years, several researchers independently n...

Computational Experience with Hypergraph-Based Methods for Automatic Decomposition in Discrete Optimization

Branch-and-price algorithms based on Dantzig-Wolfe decomposition have shown great success in solving mixed integer linear optimization problems (MILPs) with specific identifiable structure, such as vehicle routing and crew scheduling problems. For unstructured MILPs, the most frequently used methodology is branch-and-cut, which depends on generation of “generic” classes of valid inequalities to...

A Non-Robust Branch-And-Cut-And-Price Algorithm for the Vehicle Routing Problem with Time Windows

Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem

Abstract. The best exact algorithms for the Capacitated Vehicle Routing Problem (CVRP) have been based on either branch-and-cut or Lagrangean relaxation/column generation. This paper presents an algorithm that combines both approaches: it works over the intersection of two polytopes, one associated with a traditional Lagrangean relaxation over q-routes, the other defined by bound, degree and ca...