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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| Veröffentlicht in: | Operations research Jg. 53; H. 6; S. 982 - 995 |
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Linthicum, MD
INFORMS
01.11.2005
Institute for Operations Research and the Management Sciences |
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| Abstract | 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. |
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| AbstractList | 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. 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. [PUBLICATION ABSTRACT] |
| Audience | Trade |
| Author | Van Oudheusden, Dirk Muyldermans, Luc Cattrysse, Dirk Beullens, Patrick |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Exploring Variants of 2-Opt and 3-Opt for the General Routing Problem |
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