A Population-based Local Search Technique with Random Descent and Jump for the Steiner Tree Problem in Graphs

The Steiner tree problem in graphs (STPG) is a well known NP-hard combinatorial problem with various applications in transport, computational biology, network and VLSI design. Exact methods have been developed to solve this problem to proven optimality, however the exponential nature of these algorithms mean that they become intractable with large-scale instances of the problem. Because of this phenomenon, there has been considerable research into using metaheuristics to obtain good quality solutions in a reasonable time. This paper presents a hybrid local search technique which is an extension of techniques from the literature with an added random jump operator which prevents the algorithm from becoming stuck in local minima. It is compared against greedy local search, the hybrid local search technique it extends and two metaheuristic techniques from the current literature and is shown to outperform them in nearly all cases.

[1]  Celso C. Ribeiro,et al.  Preprocessing Steiner problems from VLSI layout , 2002, Networks.

[2]  Natalio Krasnogor,et al.  Nature-inspired cooperative strategies for optimization , 2009 .

[3]  Tobias Polzin,et al.  Algorithms for the Steiner problem in networks , 2003 .

[4]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[5]  Dario Landa Silva,et al.  Particle swarm optimization for the Steiner tree in graph and delay-constrained multicast routing problems , 2013, J. Heuristics.

[6]  Emile H. L. Aarts,et al.  Theoretical aspects of local search , 2006, Monographs in Theoretical Computer Science. An EATCS Series.

[7]  Gurdip Singh,et al.  Ant Colony Algorithms for Steiner Trees: An Application to Routing in Sensor Networks , 2005 .

[8]  Renato F. Werneck,et al.  Fast Local Search for Steiner Trees in Graphs , 2010, ALENEX.

[9]  Mauricio G. C. Resende,et al.  Greedy Randomized Adaptive Search Procedures , 1995, J. Glob. Optim..

[10]  Siavash Vahdati Daneshmand,et al.  Primal-dual approaches to the Steiner problem , 2000, APPROX.

[11]  Petra Mutzel,et al.  Combining a Memetic Algorithm with Integer Programming to Solve the Prize-Collecting Steiner Tree Problem , 2004, GECCO.

[12]  Celso C. Ribeiro,et al.  Greedy randomized adaptive search procedures for the Steiner problem in graphs. , 1997 .

[13]  Panos M. Pardalos,et al.  Steiner Tree Problems , 2009, Encyclopedia of Optimization.

[14]  Sergio Consoli,et al.  Discrete Particle Swarm Optimization for the minimum labelling Steiner tree problem , 2010, Natural Computing.

[15]  V. J. Rayward-Smith,et al.  Effective Local Search Techniques for the Steiner Tree Problem , 2000 .

[16]  Leandro Nunes de Castro,et al.  Recent Developments In Biologically Inspired Computing , 2004 .

[17]  Siavash Vahdati Daneshmand,et al.  Algorithmic approaches to the Steiner problem in networks , 2004 .

[18]  Phan-Thuan Do,et al.  An ant colony optimization algorithm for solving Group Steiner Problem , 2013, The 2013 RIVF International Conference on Computing & Communication Technologies - Research, Innovation, and Vision for Future (RIVF).

[19]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[20]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[21]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[22]  Jun-Dong Cho,et al.  Steiner Tree Problems in VLSI Layout Designs , 2001 .

[23]  R. Prim Shortest connection networks and some generalizations , 1957 .

[24]  Markus Leitner,et al.  A Partition-Based Heuristic for the Steiner Tree Problem in Large Graphs , 2014, Hybrid Metaheuristics.

[25]  Emile H. L. Aarts,et al.  Theoretical Aspects of Local Search (Monographs in Theoretical Computer Science. An EATCS Series) , 2007 .

[26]  T. Koch,et al.  SteinLib: An Updated Library on Steiner Tree Problems in Graphs , 2001 .

[27]  K. Dowsland HILL-CLIMBING, SIMULATED ANNEALING AND THE STEINER PROBLEM IN GRAPHS , 1991 .

[28]  Ronald L. Graham,et al.  On the history of the Euclidean Steiner tree problem , 2013, Archive for History of Exact Sciences.

[29]  C. W. Duin Preprocessing the Steiner problem in graph , 2000 .

[30]  Mladen Kos,et al.  A GRASP heuristic for the delay-constrained multicast routing problem , 2006, Telecommun. Syst..