Journal ArticleDOI
Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees
TLDR
This work shows that the vehicle routing problem can be modeled as the problem of finding a minimum cost K-tree with two K edges incident on the depot and subject to some side constraints that impose vehicle capacity and the requirement that each customer be visited exactly once.Abstract:
We consider the problem of optimally scheduling a fleet of K vehicles to make deliveries to n customers subject to vehicle capacity constraints. Given a graph with n + 1 nodes, a K-tree is defined to be a set of n + K edges that span the graph. We show that the vehicle routing problem can be modeled as the problem of finding a minimum cost K-tree with two K edges incident on the depot and subject to some side constraints that impose vehicle capacity and the requirement that each customer be visited exactly once. The side constraints are dualized to obtain a Lagrangian problem that provides lower bounds in a branch-and-bound algorithm. This algorithm has produced proven optimal solutions for a number of difficult problems, including a well-known problem with 100 customers and several real problems with 25–71 customers.read more
Citations
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Book
Handbook of Constraint Programming
TL;DR: Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas.
Book ChapterDOI
Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems
TL;DR: In this paper, a local search method called Large Neighbourhood Search (LNS) is used to solve vehicle routing problems, analogous to the shuffling technique of job shop scheduling.
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
Probabilistic diversification and intensification in local search for vehicle routing
Yves Rochat,Éric D. Taillard +1 more
TL;DR: A probabilistic technique to diversify, intensify, and parallelize a local search adapted for solving vehicle routing problems and local searches is presented.
Book
MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows
TL;DR: It is shown that MACS-VRPTW is competitive with the best known existing methods both in terms of solution quality and computation time and improves some of the best solutions known for a number of problem instances in the literature.
References
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Journal ArticleDOI
An Effective Heuristic Algorithm for the Traveling-Salesman Problem
S. Lin,Brian W. Kernighan +1 more
TL;DR: This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem based on a general approach to heuristics that is believed to have wide applicability in combinatorial optimization problems.
Book
The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization
TL;DR: In this paper, Johnson and Papadimitriou proposed a performance guarantee for heuristics, based on the notion of well-solved special cases (P. Gilmore, et al.).
Journal ArticleDOI
A Dynamic Programming Approach to Sequencing Problems
Michael Held,Richard M. Karp +1 more
TL;DR: In this paper, a dynamic programming approach to the solution of three sequencing problems, namely, a scheduling problem involving arbitrary cost functions, the traveling-salesman problem, and an assembly line balancing problem, is presented.
Journal ArticleDOI
Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem
TL;DR: Approximate methods based on descent, hybrid simulated annealing/tabu search, and tabu search algorithms are developed and different search strategies are investigated and an estimate for the tabu list size is statistically derived.
Journal ArticleDOI
A generalized assignment heuristic for vehicle routing
TL;DR: This paper presents a heuristic for this problem in which an assignment of customers to vehicles is obtained by solving a generalized assignment problem with an objective function that approximates delivery cost and shows that it has outperformed the best existing heuristics on a sample of standard test problems.