Solving the unsupervised graph partitioning problem with genetic algorithms: Classical and new encoding representations

Abstract The Graph Partitioning Problem (GPP) is one of the most ubiquitous models that operations research practitioners encounter. Therefore, several methods have been proposed to solve it. Among these methods, Genetic Algorithm (GA) appears to carry very promising performances. However, despite the huge number of papers being published with this approach, only few of them deal with the encoding representation and its role in the reported performances. In this paper, we present classical and new encoding representations for the unsupervised graph partitioning problem. That is, we suppose that the number of partition subsets (clusters) is not known apriori. Next, we conduct an empiric comparison to identify the most promising encodings.

[1]  Charles-Edmond Bichot,et al.  A metaheuristic based on fusion and fission for partitioning problems , 2006, Proceedings 20th IEEE International Parallel & Distributed Processing Symposium.

[2]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[3]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[4]  J. Hartmanis.  Computers and Intractability: A Guide to the Theory of NP-Completeness (Michael R. Garey and David S. Johnson) , 1982 .

[5]  Elin M. Wicks,et al.  Designing cellular manufacturing systems with dynamic part populations , 1999 .

[6]  Stefan Voß,et al.  A heuristic approach for dividing graphs into bi-connected components with a size constraint , 2016, J. Heuristics.

[7]  Shashi Shekhar,et al.  Multilevel hypergraph partitioning: applications in VLSI domain , 1999, IEEE Trans. Very Large Scale Integr. Syst..

[8]  S. L. Hakimi,et al.  Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[9]  Konstantin Andreev,et al.  Balanced graph partitioning , 2004, SPAA.

[10]  Luiz Antonio Nogueira Lorena,et al.  Constructive Genetic Algorithm for Clustering Problems , 2001, Evolutionary Computation.

[11]  T. Narendran,et al.  A genetic algorithm approach to the machine-component grouping problem with multiple objectives , 1992 .

[12]  S. Hakimi.  Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems , 1965 .

[13]  Thorsten Koch,et al.  Solving mixed integer linear and nonlinear problems using the SCIP Optimization Suite , 2012 .

[14]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[15]  Byung Ro Moon,et al.  Genetic Algorithm and Graph Partitioning , 1996, IEEE Trans. Computers.

[16]  Menouar Boulif,et al.  A new branch-&-bound-enhanced genetic algorithm for the manufacturing cell formation problem , 2006, Comput. Oper. Res..

[17]  Chris H. Q. Ding,et al.  A min-max cut algorithm for graph partitioning and data clustering , 2001, Proceedings 2001 IEEE International Conference on Data Mining.

[18]  Fabio Checconi,et al.  Scalable Community Detection with the Louvain Algorithm , 2015, 2015 IEEE International Parallel and Distributed Processing Symposium.

[19]  Peter Sanders,et al.  Recent Advances in Graph Partitioning , 2013, Algorithm Engineering.

[20]  Juan Li,et al.  Controlled Partitioning of a Power Network Considering Real and Reactive Power Balance , 2010, IEEE Transactions on Smart Grid.

[21]  Menouar Boulif,et al.  Constraint-driven exact algorithm for the manufacturing cell formation problem , 2016 .

[22]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[23]  Franz Rothlauf,et al.  Representations for genetic and evolutionary algorithms , 2002, Studies in Fuzziness and Soft Computing.

[24]  M. Friedman.  The Use of Ranks to Avoid the Assumption of Normality Implicit in the Analysis of Variance , 1937 .