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Soft Computing

, Volume 22, Issue 12, pp 4133–4151 | Cite as

A self-adaptive and stagnation-aware breakout local search algorithm on the grid for the Steiner tree problem with revenue, budget and hop constraints

  • Tansel Dokeroglu
  • Erhan Mengusoglu
Methodologies and Application
  • 122 Downloads

Abstract

The Steiner tree problem (STP) is a challenging NP-Hard combinatorial optimization problem. The STP with revenue, budget and hop constraints (STPRBH) determines a subtree of a given undirected graph with the defined constraints. In this study, we propose a novel self-adaptive and stagnation-aware breakout local search (BLS) algorithm (Grid-BLS) for the solution of the STPRBH. The proposed Grid-BLS is a parallel algorithm and keeps the parameters of the BLS heuristic in a population at the master node and tunes/updates them with the best performing parameters sent by the slave nodes. The parameter tuning of the BLS heuristic is considered as another optimization job and processed by a genetic algorithm that runs on the master node. The slave nodes perform BLS search and use a multistarting technique that prevents them to get stuck in a local optima by restarting the search processes. A master and slave communication topology is used for communicating with the slave processors. In order to evaluate the performance of the Grid-BLS algorithm, experiments are carried out on 240 benchmark problem instances. The solutions for 226 of these problems are reported to be optimal or the best solutions. The Grid-BLS achieves 21 new best solutions (graphs) that have never been found by any heuristic algorithm so far and performs better than the state-of-the-art heuristic algorithms Greedy, Destroy&Repair, Tabu Search, and Dynamic Memetic.

Keywords

Steiner tree problem Breakout local search Parallel processing Multistart Stagnation 

Notes

Compliance with ethical standards

Conflict of interest

There is no conflict of interest between authors.

Human and animal rights

This article does not contain any studies with human participants performed by any of the authors. This article does not contain any studies with animals performed by any of the authors. This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

There is no individual participant included in the study.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Computer Engineering DepartmentTurkish Aeronautical Association UniversityAnkaraTurkey
  2. 2.Computer Engineering DepartmentHacettepe UniversityAnkaraTurkey

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