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Article Dans Une Revue Mathematical Programming Computation Année : 2017

Swap-vertex based neighborhood for Steiner tree problems

Résumé

Steiner tree problems (STPs) are very important in both theory and practice. In this paper, we introduce a powerful swap-vertex move operator which can be used as a basic element of any neighborhood search heuristic to solve many STP variants. Given the incumbent solution tree T, the swap-vertex move operator exchanges a vertex in T with another vertex out of T, and then attempts to construct a minimum spanning tree, leading to a neighboring solution (if feasible). We develop a series of dynamic data structures, which allow us to efficiently evaluate the feasibility of swap-vertex moves. Additionally, in order to discriminate different swap-vertex moves corresponding to the same objective value, we also develop an auxiliary evaluation function. We present a computational assessment based on a number of challenging problem instances (corresponding to three representative STP variants) which clearly shows the effectiveness of the techniques introduced in this paper. Particularly, as a key element of our KTS algorithm which participated in the 11th DIMACS implementation challenge, the swap-vertex operator as well as the auxiliary evaluation function contributed significantly to the excellent performance of our algorithm.

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Dates et versions

hal-01532908 , version 1 (04-06-2017)
hal-01532908 , version 2 (04-06-2017)

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Zhang-Hua Fu, Jin-Kao Hao. Swap-vertex based neighborhood for Steiner tree problems. Mathematical Programming Computation, 2017, 9(2) (212/311–2413123213310), pp.297-320. ⟨10.1007/s12532-016-0116-8⟩. ⟨hal-01532908v2⟩

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