Selective arc‐ng pricing for vehicle routing

Abstract

Column generation algorithms for solving vehicle routing problems often rely on a relaxed pricing subproblem where routes may be nonelementary and which is solved by a labeling algorithm. This pricing algorithm is said to be selective if it can discard nonelementary paths that may be Pareto‐optimal but guarantees finding at least one (not necessarily elementary) path of negative reduced cost when there exists at least one elementary path of negative reduced cost. In this paper, we propose a selective pricing mechanism for a recently introduced variant of the ng‐route relaxation, in which the neighborhoods are associated with arcs instead of nodes. We extend a state‐of‐the‐art set‐based dominance criterion for this problem and show, by means of an exhaustive computational campaign, that the resulting mechanism is effective at reducing the number of nondominated labels as compared to the original pricing algorithm for the same problem. As a result, typically shorter computing times are required to compute similar lower bounds when the proposed mechanism is embedded within a column generation solver.

Partial dominance in branch-price-and-cut algorithms for vehicle routing and scheduling problems with a single-segment tradeoff

“…Full dominance occurs when a label cannot be extended either due to the set of dominated extensions or due to ng-route restrictions. These ideas were further exploited by Costa et al (2021) where even stronger arc-ng-route dominance rules were proven in the context of selective pricing (Desaulniers et al 2019).…”