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Branch-and-cut-and-price for the robust capacitated vehicle routing problem with knapsack uncertainty

Artur Pessoa(artur.a.pessoa***at***gmail.com)
Michael Poss(michael.poss***at***lirmm.fr)
Ruslan Sadykov(Ruslan.Sadykov***at***inria.fr)
François Vanderbeck(Francois.Vanderbeck***at***math.u-bordeaux.fr)

Abstract: We examine the robust counterpart of the classical Capacitated Vehicle Routing Problem (CVRP). We consider two types of uncertainty sets for the customer demands: the classical budget polytope introduced by Bertsimas and Sim (2003), and a partitioned budget polytope proposed by Gounaris et al. (2013). We show that using the set-partitioning formulation it is possible to reformulate our problem as a deterministic heterogeneous vehicle routing problem. Thus, many state-of-the-art techniques for exactly solving deterministic VRPs can be applied for the robust counterpart, and a modern branch-and-cut-and-price algorithm can be adapted to our setting by keeping the number of pricing subproblems strictly polynomial. More importantly, we introduce new techniques to significantly improve the efficiency of the algorithm. We present analytical conditions under which a pricing subproblem is infeasible. This result is general and can be applied to other combinatorial optimization problems with knapsack uncertainty. We also introduce robust capacity cuts which are provably stronger than the ones known in the literature. Finally, a fast iterated local search algorithm is proposed to obtain heuristic solutions for the problem. Using our branch-and-cut-and-price algorithm incorporating existing and new techniques, we are able to solve to optimality all but one open instances from the literature.

Keywords: branch-and-cut-and-price; robust optimization; capacity inequalities; local search

Category 1: Robust Optimization

Category 2: Combinatorial Optimization (Branch and Cut Algorithms )

Citation:

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Entry Submitted: 09/11/2018
Entry Accepted: 09/11/2018
Entry Last Modified: 09/11/2018

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