Abstract
We describe an edge based ejection chain method to generate compound neighborhood structures for the Traveling Salesman Problem (TSP). These neighborhood structures enclose a special substructure which is not necessarily a Hamiltonian tour. Instead the neighborhood components are linked together to compose successive levels of an ejection chain, and coordinated by a suitable reference structure to generate compound moves with outstanding proprieties. More precisely, such a substructure can be viewed as a relaxed tour, which allows solution transformations to be obtained without preserving the Hamiltonian property at each step. Furthermore, in the ejection chain process, the generation of substructures produces a variety of alternating paths for the selection of subsequent ejection moves as well as for the choice of the corresponding trial moves. Finally, we propose two algorithmic variants — a Preliminary and a Full Subpath Ejection Chain Method (P-SEC and F-SEC) — based on this type of compound neighborhood design. Both variants are guided by a simple tabu search mechanism. Computational results on 67 TSPLIB problems show that both the Preliminary and the Full methods find optimal and near-optimal solutions very quickly, frequently outperforming the best heuristic procedures for the TSP. In addition, the Full method generally dominates the best alternative TSP procedures.
Published Version
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