research-article

Shaping communities of local optima by perturbation strength

Authors:

Sebastian Herrmann,

Matthias Herrmann,

Gabriela Ochoa, and

Franz RothlaufAuthors Info & Claims

GECCO '17: Proceedings of the Genetic and Evolutionary Computation Conference

July 2017

Pages 266 - 273

https://doi.org/10.1145/3071178.3071243

Published: 01 July 2017 Publication History

Abstract

Recent work discovered that fitness landscapes induced by Iterated Local Search (ILS) may consist of multiple clusters, denoted as funnels or communities of local optima. Such studies exist only for perturbation operators (kicks) with low strength. We examine how different strengths of the ILS perturbation operator affect the number and size of clusters. We present an empirical study based on local optima networks from NK fitness landscapes. Our results show that a properly selected perturbation strength can help overcome the effect of ILS getting trapped in clusters of local optima. This has implications for designing effective ILS approaches in practice, where traditionally only small perturbations or complete restarts are applied, with the middle ground of intermediate perturbation strengths largely unexplored.

References

[1]

Réka Albert and Albert-László Barabási. 2002. Statistical mechanics of complex networks. Reviews of Modern Physics 74, 1 (jan 2002), 47--97.

[2]

David Applegate, William Cook, and Andre Rohe. 2003. Chained Lin-Kernighan for Large Traveling Salesman Problems. INFORMS Journal on Computing 15, 1 (2003), 82--92.

Digital Library

[3]

Mathieu Bastian, Sebastien Heymann, and Mathieu Jacomy. 2009. Gephi: An Open Source Software for Exploring and Manipulating Networks. In Third International AAAI Conference on Weblogs and Social Media. 361--362.

[4]

Stefano Boccaletti, Vito Latora, Yamir Moreno, Martín Chávez Hoffmeister, and Dong-Uk Hwang. 2006. Complex networks: Structure and dynamics. Physics Reports 424, 4--5 (feb 2006), 175--308.

[5]

Kenneth D. Boese, Andrew B. Kahng, and Sudhakar Muddu. 1994. A new adaptive multi-start technique for combinatorial global optimizations. Operations Research Letters 16, 2 (1994), 101--113.

Digital Library

[6]

Stephen P. Borgatti. 2005. Centrality and network flow. Social Networks 27, 1 (jan 2005), 55--71.

[7]

Francisco Chicano, Fabio Daolio, Gabriela Ochoa, Sébastien Verel, Marco Tomassini, and Enrique Alba. 2012. Local Optima Networks, Landscape Autocorrelation and Heuristic Search Performance. In Parallel Problem Solving from Nature - PPSN XII: 12th International Conference, Carlos A. Coello Coello, Vincenzo Cutello, Kalyanmoy Deb, Stephanie Forrest, Giuseppe Nicosia, and Mario Pavone (Eds.), Vol. 7492 LNCS. Springer, Berlin and Heidelberg, 337--347. arXiv:arXiv:1210.4021v1

Digital Library

[8]

Fabio Daolio, Marco Tomassini, Sébastien Verel, and Gabriela Ochoa. 2011. Communities of minima in local optima networks of combinatorial spaces. Physica A: Statistical Mechanics and its Applications 390, 9 (may 2011), 1684--1694.

[9]

Fabio Daolio, Sébastien Verel, Gabriela Ochoa, and Marco Tomassini. 2012. Local optima networks and the performance of iterated local search. In Proceedings of the fourteenth international conference on Genetic and evolutionary computation conference - GECCO '12, Terence Soule (Ed.). ACM Press, Philadelphia, Pennsylvania, USA, 369. arXiv:arXiv:1210.3946v1

Digital Library

[10]

Santo Fortunato. 2010. Community detection in graphs. Physics Reports 486, 3--5 (feb 2010), 75--174. arXiv:0906.0612

[11]

Fred Glover. 1986. Future paths for integer programming and links to artificial intelligence. Computers & Operations Research 13, 5 (jan 1986), 533--549.

Digital Library

[12]

Doug R. Hains, Darrel L. Whitley, and Adele E. Howe. 2011. Revisiting the big valley search space structure in the TSP. Journal of the Operational Research Society 62, 2 (feb 2011), 305--312.

[13]

Sebastian Herrmann. 2016. Determining the Difficulty of Landscapes by PageRank Centrality in Local Optima Networks. In European Conference on Evolutionary Computation in Combinatorial Optimization (EvoCOP 2016). Porto, 74--87.

[14]

Sebastian Herrmann, Gabriela Ochoa, and Franz Rothlauf. 2016. Communities of Local Optima As Funnels in Fitness Landscapes. In Proceedings of the Genetic and Evolutionary Computation Conference 2016 (GECCO '16). ACM, New York, NY, USA, 325--331.

Digital Library

[15]

Sebastian Herrmann, Gabriela Ochoa, and Franz Rothlauf. 2016. Communities of Local Optima as Funnels in Fitness Landscapes. In Proceedings of the 2016 Genetic and Evolutionary Computation Conference - GECCO '16. ACM Press.

Digital Library

[16]

Sebastian Herrmann and Franz Rothlauf. 2015. Predicting Heuristic Search Performance with PageRank Centrality in Local Optima Networks. In Proceedings of the 2015 Genetic and Evolutionary Computation Conference - GECCO '15, Sara Silva (Ed.). ACM Press, Madrid, Spain, 401--408.

Digital Library

[17]

Stuart A. Kauffman. 1993. The origins of order. Oxford University Press.

[18]

Stuart A. Kauffman and Simon Levin. 1987. Towards a General Theory of Adaptive Walks on Rugged Landscapes. Journal of Theoretical Biology 128, 1 (1987), 11--45. http://www.sciencedirect.com/science/article/pii/S0022519387800292

[19]

Stuart A. Kauffman and Edward D. Weinberger. 1989. The NK model of rugged fitness landscapes and its application to maturation of the immune response. Journal of Theoretical Biology 141, 2 (1989), 211--245.

[20]

Pascal Kerschke, Mike Preuss, Simon Wessing, and Heike Trautmann. 2015. Detecting Funnel Structures by Means of Exploratory Landscape Analysis. In Proceedings of the 2015 Genetic and Evolutionary Computation Conference - GECCO '15, Sara Silva (Ed.). ACM Press, Madrid, Spain, 265--272.

Digital Library

[21]

S. Lin and B. W. Kernighan. 1973. An Effective Heuristic Algorithm for the Traveling-Salesman Problem. Operations Research 21, 2 (apr 1973), 498--516.

Digital Library

[22]

M. Locatelli. 2005. On the Multilevel Structure of Global optimization problems. Computational Optimization and Applications 30, 1 (2005), 5--22.

Digital Library

[23]

Helena R. Lourenço, Olivier C. Martin, and Thomas Stützle. 2003. Iterated Local Search. In Handbook of Metaheuristics. Kluwer Academic Publishers, Boston, 320--353.

[24]

Monte Lunacek and Darrell Whitley. 2006. The dispersion metric and the CMA evolution strategy. In Proceedings of the 8th annual conference on Genetic and evolutionary computation - GECCO '06. ACM Press, New York, New York, USA, 477.

Digital Library

[25]

Katherine M. Malan and Andries P. Engelbrecht. 2014. Fitness Landscape Analysis for Metaheuristic Performance Prediction. In Recent Advances in the Theory and Application of Fitness Landscapes, Hendrik Richter and Andries Engelbrecht (Eds.). Springer, Berlin and Heidelberg, 103--129.

[26]

B. Naudts and L. Kallel. 2000. A comparison of predictive measures of problem difficulty in evolutionary algorithms. IEEE Transactions on Evolutionary Computation 4, 1 (apr 2000), 1--15.

Digital Library

[27]

Gabriela Ochoa, Marco Tomassini, Sébastien Verel, and Christian Darabos. 2008. A study of NK landscapes' basins and local optima networks. In Proceedings of the 10th annual conference on Genetic and evolutionary computation - GECCO '08, Maarten Keijzer (Ed.). ACM Press, Atlanta, GA, USA, 555--562.

Digital Library

[28]

Gabriela Ochoa and Nadarajen Veerapen. 2016. Deconstructing the Big Valley Search Space Hypothesis. In Evolutionary Computation in Combinatorial Optimization: 16th European Conference, EvoCOP 2016, Porto, Portugal, March 30 -- April 1, 2016, Proceedings, Francisco Chicano, Bin Hu, and Pablo Garcia-Sanchez (Eds.). Springer, Porto, 58--73.

[29]

Gabriela Ochoa, Nadarajen Veerapen, Darrell Whitley, and Edmund K. Burke. 2016. The Multi-Funnel Structure of TSP Fitness Landscapes: A Visual Exploration. In Artificial Evolution: 12th International Conference, Evolution Artificielle, EA 2015. Springer International Publishing, Lyon, 1--13.

Digital Library

[30]

Travis E. Oliphant. 2007. Python for scientific computing. Computing in Science and Engineering 9, 3 (2007), 10--20.

Digital Library

[31]

Mason a. Porter, Jukka-Pekka Onnela, and Peter J. Mucha. 2009. Communities in Networks. Notices of the AMS 486, 3--5 (2009), 1082--1097. arXiv:0902.3788

[32]

R Development Core Team. 2009. R: A Language and Environment for Statistical Computing.

[33]

Christian M. Reidys and Peter F. Stadler. 2002. Combinatorial Landscapes. SIAM Rev. 44, 1 (jan 2002), 3--54.

Digital Library

[34]

Franz Rothlauf. 2011. Design of modern heuristics: Principles and application. Springer, Berlin and Heidelberg.

Digital Library

[35]

Venu Satuluri, Srinivasan Parthasarathy, and Duygu Ucar. 2010. Markov clustering of protein interaction networks with improved balance and scalability. In Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology - BCB '10. ACM Press, New York, USA, 247.

Digital Library

[36]

Peter F. Stadler. 1996. Landscapes and their correlation functions. Journal of Mathematical Chemistry 20, 1 (1996), 1--45.

[37]

E.G. Talbi and P. Bessière. 1991. A parallel genetic algorithm for the graph partitioning problem. In Proceedings of the 5th international conference on Supercomputing - ICS '91. ACM Press, New York, USA, 312--320.

Digital Library

[38]

Thomas W. Valente. 1996. Network models of the diffusion of innovations. Computational and Mathematical Organization Theory 2, 2 (1996), 134.

[39]

Stijn van Dongen. 2001. Graph clustering by flow simulation. Ph.D. Dissertation. Utrecht University.

[40]

Sébastien Verel, Fabio Daolio, Gabriela Ochoa, and Marco Tomassini. 2012. Local optima networks with escape edges. In Artificial Evolution. Springer, Angers, France, 49--60.

Digital Library

[41]

Edward D. Weinberger. 1990. Correlated and uncorrelated fitness landscapes and how to tell the difference. Biological cybernetics 336 (1990), 325--336. http://link.springer.com/article/10.1007/BF00202749

Digital Library

[42]

Sewall Wright. 1932. The roles of mutation, inbreeding, crossbreeding, and selection in evolution. In Proceedings of the 6th International Congress of Genetics, Donald F. Jones (Ed.). Morgan Kaufmann Publishers Inc., Ithaca, New York, 356--366. http://www.esp.org/books/6th-congress/facsimile/contents/6th-cong-p356-wright.pdf

Cited By

Ochoa GMalan KAuger AStützle T(2019)Recent advances in fitness landscape analysisProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3319619.3323383(1077-1094)Online publication date: 13-Jul-2019
https://dl.acm.org/doi/10.1145/3319619.3323383
Ochoa GVeerapen NTakadama K(2018)Search-mapsProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3205651.3207884(504-517)Online publication date: 6-Jul-2018
https://dl.acm.org/doi/10.1145/3205651.3207884
Ochoa GHerrmann S(2018)Perturbation Strength and the Global Structure of QAP Fitness LandscapesParallel Problem Solving from Nature – PPSN XV10.1007/978-3-319-99259-4_20(245-256)Online publication date: 21-Aug-2018
https://doi.org/10.1007/978-3-319-99259-4_20
Show More Cited By

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Shaping communities of local optima by perturbation strength
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cover image ACM Conferences

GECCO '17: Proceedings of the Genetic and Evolutionary Computation Conference

July 2017

1427 pages

ISBN:9781450349208

DOI:10.1145/3071178

General Chair:
Peter A. N. Bosman
Centrum Wiskunde & Informatica (CWI)

Copyright © 2017 ACM.

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Published: 01 July 2017

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Leverhulme Trust

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GECCO '17

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GECCO '17: Genetic and Evolutionary Computation Conference

July 15 - 19, 2017

Berlin, Germany

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GECCO '17 Paper Acceptance Rate 178 of 462 submissions, 39%;

Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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Cited By

Ochoa GMalan KAuger AStützle T(2019)Recent advances in fitness landscape analysisProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3319619.3323383(1077-1094)Online publication date: 13-Jul-2019
https://dl.acm.org/doi/10.1145/3319619.3323383
Ochoa GVeerapen NTakadama K(2018)Search-mapsProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3205651.3207884(504-517)Online publication date: 6-Jul-2018
https://dl.acm.org/doi/10.1145/3205651.3207884
Ochoa GHerrmann S(2018)Perturbation Strength and the Global Structure of QAP Fitness LandscapesParallel Problem Solving from Nature – PPSN XV10.1007/978-3-319-99259-4_20(245-256)Online publication date: 21-Aug-2018
https://doi.org/10.1007/978-3-319-99259-4_20
McMenemy PVeerapen NOchoa G(2018)How Perturbation Strength Shapes the Global Structure of TSP Fitness LandscapesEvolutionary Computation in Combinatorial Optimization10.1007/978-3-319-77449-7_3(34-49)Online publication date: 3-Mar-2018
https://doi.org/10.1007/978-3-319-77449-7_3

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