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

Nottingham University Business School, Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, United Kingdom
Department of Mathematics, University of Portsmouth, Portsmouth PO1 3HE, United Kingdom
Center for Industrial Management, Katholieke Universiteit Leuven, Celestijnenlaan 300A, B-3001 Heverlee, Belgium
Center for Industrial Management, Katholieke Universiteit Leuven, Celestijnenlaan 300A, B-3001 Heverlee, Belgium
luc.muyldermans{at}nottingham.ac.uk
patrick.beullens{at}port.ac.uk
dirk.cattrysse{at}cib.kuleuven.ac.be
dirk.vanoudheusden{at}cib.kuleuven.ac.be

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.

Subject classifications: transportation, vehicle routing: local search, 2-opt; networks/graphs, traveling salesman: arc routing, general routing problem, rural postman problem.
History: Received November 2001; revision received October 2002; revision received April 2004; accepted September 2004.