Journal ArticleDOI
Some New Branching and Bounding Criteria for the Asymmetric Travelling Salesman Problem
Giorgio Carpaneto,Paolo Toth +1 more
TLDR
This paper presents a breadth-first branch and bound algorithm which differs from the method of Smith, Srinivasan and Thompson in the selection of the subtour to be split, in the ordering of the arcs in the selected subtour, and in the computation of different partial lower bounds and in different data structures to facilitate the updating of the cost matrix.Abstract:
Many algorithms have been developed for the optimal solution of the asymmetric travelling salesman problem: the most efficient ones are based on the subtour elimination approach. This paper presents a breadth-first branch and bound algorithm which differs from the method of Smith, Srinivasan and Thompson in the selection of the subtour to be split, in the ordering of the arcs in the selected subtour, in the computation of different partial lower bounds and in different data structures to facilitate the updating of the cost matrix. Extensive computational results considering random problems with up to 240 vertices are presented for various ranges of the coefficients of the cost matrix.read more
Citations
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Journal ArticleDOI
Models, relaxations and exact approaches for the capacitated vehicle routing problem
Paolo Toth,Daniele Vigo +1 more
TL;DR: This paper reviews the exact algorithms based on the branch and bound approach proposed in the last years for the solution of the basic version of the vehicle routing problem (VRP), where only the vehicle capacity constraints are considered, and concludes by examining possible future directions of research in this field.
Journal ArticleDOI
The General Pickup and Delivery Problem
TL;DR: Several characteristics that distinguish pickup and delivery problems from standard vehicle routing problems are discussed and a survey of the problem types and solution methods found in the literature is presented.
Journal ArticleDOI
The traveling salesman problem: An overview of exact and approximate algorithms
TL;DR: Some of the main known algorithms for the traveling salesman problem are surveyed and the definition and applications of these algorithms are explained.
Journal ArticleDOI
Fifty Years of Vehicle Routing
TL;DR: In this article, the authors provide a brief account of the development in the field of exact algorithms and heuristics for the VRP and present a metaheuristic for the problem.
References
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Book
An Algorithm for the Traveling Salesman Problem
TL;DR: A “branch and bound” algorithm is presented for solving the traveling salesman problem, where the set of all tours feasible solutions is broken up into increasingly small subsets by a procedure called branching.
Journal ArticleDOI
Pathology of Traveling-Salesman Subtour-Elimination Algorithms
M. Bellmore,John C. Malone +1 more
TL;DR: An underlying theory for the traveling-salesman problem is developed, pathological performance of some existing techniques are predicted, and two algorithms are presented, based upon the theory, with predictable polynomial growth in expected computation time and resistence to pathological problems.
Journal ArticleDOI
Algorithm 548: Solution of the Assignment Problem [H]
Giorgio Carpaneto,Paolo Toth +1 more
TL;DR: R H U first ( s ) nex t (s) last ( s) as the row ass igned to c o l u m n y ( j -1 ) as the label o f c o L R , = 0, row i is un labe led (i = 1 , . . . , n);
Journal ArticleDOI
An operator theory of parametric programming for the transportation problem‐II
V. Srinivasan,Gerald L. Thompson +1 more
TL;DR: In this article, the effect on the optimum solution of a (capacitated) transportation problem when the data of the problem (the rim conditions-i.e., the warehouse supplies and market demands-the per unit transportation costs and the upper bounds) are continuously varied as a (linear) function of a single parameter is investigated.
Book ChapterDOI
Computational Performance of Three Subtour Elimination Algorithms for Solving Asymmetric Traveling Salesman Problems.
TL;DR: Three implicit enumeration algorithms for solving the asymmetric traveling salesman problem with subtour elimination using the assignment problem relaxation similar to the previous approaches by Eastman, Shapiro and Bellmore and Malone are developed and computationally test.