Exploring Variants of 2-Opt and 3-Opt for the General Routing Problem

The general routing problem (GRP) is the problem of finding a minimum length tour, visiting a number of specified vertices and edges in an undirected graph. In this paper, we describe how the well-known 2-opt and 3-opt local search procedures for node routing problems can be adapted to solve arc and...

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Bibliographic Details
Published in:Operations research Vol. 53; no. 6; pp. 982 - 995
Main Authors: Muyldermans, Luc, Beullens, Patrick, Cattrysse, Dirk, Van Oudheusden, Dirk
Format: Journal Article
Language:English
Published: Linthicum, MD INFORMS 01.11.2005
Institute for Operations Research and the Management Sciences
Subjects:
Algorithms
Applied sciences
Case studies
Dynamic programming
Exact sciences and technology
Flows in networks. Combinatorial problems
Graph theory
Heuristics
Itinerant sales
Local minimum
Management science
Mathematics
Neighborhoods
networks/graphs, traveling salesman: arc routing, general routing problem, rural postman problem
Operational research and scientific management
Operational research. Management science
Operations research
Optimal solutions
Preprocessing
Routing
Studies
transportation, vehicle routing: local search, 2-opt
Traveling salesman problem
Vehicles
Vertices
United Kingdom
general routing problem
Local search
rural postman problem
vehicle routing: local search
Vehicle routing problem
Travelling salesman problem
Marking
transportation
2-opt; networks/graphs
traveling salesman: arc routing
Dynamic programming
Postman problem
Tour
ISSN:0030-364X, 1526-5463
Online Access:Get full text
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Summary:The general routing problem (GRP) is the problem of finding a minimum length tour, visiting a number of specified vertices and edges in an undirected graph. In this paper, we describe how the well-known 2-opt and 3-opt local search procedures for node routing problems can be adapted to solve arc and general routing problems successfully. Two forms of the 2-opt and 3-opt approaches are applied to the GRP. The first version is similar to the conventional approach for the traveling salesman problem; the second version includes a dynamic programming procedure and explores a larger neighborhood at the expense of higher running times. Extensive computational tests, including ones on larger instances than previously reported in the arc routing literature, are performed with variants of both algorithms. In combination with the guided local search metaheuristic and the mechanisms of marking and neighbor lists, the procedures systematically detect optimal or high-quality solutions within limited computation time.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1040.0205