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Robust branchandcutandprice for the capacitated vehicle routing problem
 IN PROCEEDINGS OF THE INTERNATIONAL NETWORK OPTIMIZATION CONFERENCE
, 2003
"... During the eigthies and early nineties, the best exact algorithms for the Capacitated Vehicle Routing Problem (CVRP) utilized lower bounds obtained by Lagrangean relaxation or column generation. Next, the advances in the polyhedral description of the CVRP yielded branchandcut algorithms giving bett ..."
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Cited by 55 (14 self)
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During the eigthies and early nineties, the best exact algorithms for the Capacitated Vehicle Routing Problem (CVRP) utilized lower bounds obtained by Lagrangean relaxation or column generation. Next, the advances in the polyhedral description of the CVRP yielded branchandcut algorithms giving better results. However, several instances in the range of 50–80 vertices, some proposed more than 30 years ago, can not be solved with current known techniques. This paper presents an algorithm utilizing a lower bound obtained by minimizing over the intersection of the polytopes associated to a traditional Lagrangean relaxation over qroutes and the one defined by bounds, degree and the capacity constraints. This is equivalent to a linear program with an exponential number of both variables and constraints. Computational experiments show the new lower bound to be superior to the previous ones, specially when the number of vehicles is large. The resulting branchandcutandprice could solve to optimality almost all instances from the literature up to 100 vertices, nearly doubling the size of the instances that can be consistently solved. Further progress in this algorithm may be soon obtained by also using other known families of inequalities.
A New BranchandCut Algorithm for the Capacitated Vehicle Routing Problem
 Mathematical Programming
, 2003
"... We present a new branchandcut algorithm for the capacitated vehicle routing problem (CVRP). The algorithm uses a variety of cutting planes, including capacity, framed capacity, generalized capacity, strengthened comb, multistar, partial multistar, extended hypotour inequalities, and classical Gomo ..."
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Cited by 27 (4 self)
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We present a new branchandcut algorithm for the capacitated vehicle routing problem (CVRP). The algorithm uses a variety of cutting planes, including capacity, framed capacity, generalized capacity, strengthened comb, multistar, partial multistar, extended hypotour inequalities, and classical Gomory mixedinteger cuts. For each of these classes of inequalities we descrine our separation algorithms in detail......
Data gathering tours in sensor networks
 IN IPSN
, 2006
"... A basic task in sensor networks is to interactively gather data from a subset of the sensor nodes. When data needs to be gathered from a selected set of nodes in the network, existing communication schemes often behave poorly. In this paper, we study the algorithmic challenges in efficiently routing ..."
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Cited by 23 (6 self)
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A basic task in sensor networks is to interactively gather data from a subset of the sensor nodes. When data needs to be gathered from a selected set of nodes in the network, existing communication schemes often behave poorly. In this paper, we study the algorithmic challenges in efficiently routing a fixedsize packet through a small number of nodes in a sensor network, picking up data as the query is routed. We show that computing the optimal routing scheme to visit a specific set of nodes is NPcomplete, but we develop approximation algorithms that produce plans with costs within a constant factor of the optimum. We enhance the robustness of our initial approach to accommodate the practical issues of limitedsized packets as well as network link and node failures, and examine how different approaches behave with dynamic changes in the network topology. Our theoretical results are validated via an implementation of our algorithms on the TinyOS platform and a controlled simulation study using Matlab and TOSSIM.
Solving capacitated arc routing problems using a transformation to the CVRP
 Computers & Operations Research
, 2006
"... A well known transformation by Pearn, Assad and Golden reduces a Capacitated Arc Routing Problem (CARP) into an equivalent Capacitated Vehicle Routing Problem (CVRP). However, that transformation is regarded as unpractical, since an original instance with r required edges is turned into a CVRP over ..."
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Cited by 21 (3 self)
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A well known transformation by Pearn, Assad and Golden reduces a Capacitated Arc Routing Problem (CARP) into an equivalent Capacitated Vehicle Routing Problem (CVRP). However, that transformation is regarded as unpractical, since an original instance with r required edges is turned into a CVRP over a complete graph with 3r + 1 vertices. We propose a similar transformation that reduces this graph to 2r + 1 vertices, with the additional restriction that r edges are already fixed to 1. Using a recent branchandcutandprice algorithm for the CVRP, we observed that it yields an effective way of attacking the CARP, being significantly better than the exact methods created specifically for that problem. Computational experiments obtained improved lower bounds for almost all open instances from the literature. Several such instances could be solved to optimality.
Vehicle routing problem: Doing it the evolutionary way
 In GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference
, 2002
"... In this paper we describe three evolutionary approaches to the vehicle routing problem. In our first approach we use a standard genetic algorithm whilst in the second we use a coevolutionary model. The third approach concerns the extension of the previous ones through the inclusion of heuristics. We ..."
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Cited by 16 (4 self)
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In this paper we describe three evolutionary approaches to the vehicle routing problem. In our first approach we use a standard genetic algorithm whilst in the second we use a coevolutionary model. The third approach concerns the extension of the previous ones through the inclusion of heuristics. We present and compare the experimental results achieved by the algorithms. 1
A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty
, 2006
"... In this paper we introduce a robust optimization approach to solve the Vehicle Routing Problem (VRP) with demand uncertainty. This approach yields routes that minimize transportation costs while satisfying all demands in a given bounded uncertainty set. We show that for the MillerTuckerZemlin form ..."
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Cited by 14 (5 self)
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In this paper we introduce a robust optimization approach to solve the Vehicle Routing Problem (VRP) with demand uncertainty. This approach yields routes that minimize transportation costs while satisfying all demands in a given bounded uncertainty set. We show that for the MillerTuckerZemlin formulation of the VRP and specific uncertainty sets, solving for the robust solution is no more difficult than solving a single deterministic VRP. We present computational results that investigate the tradeoffs of a robust solution for the Augerat et al. suite of capacitated VRP problems and for families of clustered instances. Our computational results show that the robust solution can protect from unmet demand while incurring a small additional cost over deterministic optimal routes. This is most profound for clustered instances under moderate uncertainty, where remaining vehicle capacity is used to protect against variations within each cluster at a small additional cost. We observe that the robust solution amounts to a clever management of the remaining vehicle capacity.
An Improved Algorithm for Biobjective Integer Programs
, 2005
"... A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling ..."
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Cited by 9 (5 self)
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A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version that provides access to all Pareto outcomes. Extensive computational tests on instances of the biobjective knapsack problem and a capacitated network routing problem are presented.
Decomposition and dynamic cut generation in integer linear programming
, 2004
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Gonzàlez. The capacitated mring star problem
 Operations Research
"... The Capacitated mRingStar Problem (CmRSP) is the problem of designing a set of rings that pass through a central depot and through some transition points and/or customers, and then assigning each nonvisited customer to a visited point or customer. The number of customers visited and assigned to ..."
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Cited by 7 (0 self)
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The Capacitated mRingStar Problem (CmRSP) is the problem of designing a set of rings that pass through a central depot and through some transition points and/or customers, and then assigning each nonvisited customer to a visited point or customer. The number of customers visited and assigned to a ring is bounded by an upper limit: the capacity of the ring. The objective is to minimize the total routing cost plus assignment costs. The problem has practical applications in the design of urban optical telecommunication networks. This paper presents and discusses two integer programming formulations for the CmRSP. Valid inequalities are proposed to strengthen the linear programming relaxation, and are used as cutting planes in a branchandcut approach. The procedure is implemented and tested on a large family of instances, including realworld instances, and the good performance of the proposed approach is demonstrated. Subject classifications: Networks/graphs: optical network design. Programming, integer, cutting plane: Branchandcut algorithm.