Mathematical Programming Computation

, Volume 9, Issue 2, pp 297–320 | Cite as

Swap-vertex based neighborhood for Steiner tree problems

Full Length Paper

Abstract

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.

Keywords

Network design Steiner tree problems Swap-vertex move Auxiliary evaluation function 11th DIMACS Implementation challenge 

Mathematics Subject Classification

90C27 Combinatorial optimization 90C59 Approximation methods and heuristics 

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Copyright information

© Springer-Verlag Berlin Heidelberg and The Mathematical Programming Society 2016

Authors and Affiliations

  1. 1.Institute of Robotics and Intelligent ManufacturingThe Chinese University of Hong Kong, ShenzhenShenzhenChina
  2. 2.LERIA, Université d’AngersAngers Cedex 01France
  3. 3.Institut Universitaire de FranceParisFrance

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