Evolving MNK-landscapes with structural constraints

In this paper we propose a method for the generation of instances of the MNK-landscapes that maximize different measures used to characterize multi-objective problems. In contrast to previous approaches, the introduced algorithm works by modifying the neighborhood structure of the variables of the MNK-landscape while keeping fixed the local parameters of its functions. A variant of the algorithm is presented to deal with situations in which the exhaustive enumeration of search space is unfeasible. We show how the introduced method can be used to generate instances with an increased number of solutions in the Pareto front. Furthermore, we investigate whether direct optimization of the correlation between objectives can be used as an indirect method to increase the size of the Pareto fronts of the generated instances.

[1]  Bilel Derbel,et al.  Shake Them All! - Rethinking Selection and Replacement in MOEA/D , 2014, PPSN.

[2]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[3]  José Antonio Lozano Alonso,et al.  Using network mesures to test evolved NK-landscapes , 2012 .

[4]  Kiyoshi Tanaka,et al.  Working principles, behavior, and performance of MOEAs on MNK-landscapes , 2007, Eur. J. Oper. Res..

[5]  Sébastien Vérel,et al.  On the Impact of Multiobjective Scalarizing Functions , 2014, PPSN.

[6]  Carlos A. Coello Coello,et al.  Objective reduction using a feature selection technique , 2008, GECCO '08.

[7]  Martin Pelikan.  Analysis of estimation of distribution algorithms and genetic algorithms on NK landscapes , 2008, GECCO '08.

[8]  Peter J. Fleming,et al.  On the Evolutionary Optimization of Many Conflicting Objectives , 2007, IEEE Transactions on Evolutionary Computation.

[9]  Sébastien Vérel,et al.  Where are bottlenecks in NK fitness landscapes? , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[10]  Kiyoshi Tanaka,et al.  Genetic Algorithms on NK-Landscapes: Effects of Selection, Drift, Mutation, and Recombination , 2003, EvoWorkshops.

[11]  J. A. Lozano,et al.  Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms (Studies in Fuzziness and Soft Computing) , 2006 .

[12]  Bernard Manderick,et al.  The Genetic Algorithm and the Structure of the Fitness Landscape , 1991, ICGA.

[13]  Concha Bielza,et al.  Multi-objective Optimization with Joint Probabilistic Modeling of Objectives and Variables , 2011, EMO.

[14]  Sébastien Vérel,et al.  Local Optima Networks of NK Landscapes With Neutrality , 2011, IEEE Transactions on Evolutionary Computation.

[15]  Roberto Santana,et al.  Evolving NK-complexity for evolutionary solvers , 2012, GECCO '12.

[16]  Concha Bielza,et al.  Multiobjective Estimation of Distribution Algorithm Based on Joint Modeling of Objectives and Variables , 2014, IEEE Transactions on Evolutionary Computation.

[17]  Siddhartha Shakya,et al.  Markov Networks in Evolutionary Computation , 2012 .

[18]  David W. Corne,et al.  Instance Generators and Test Suites for the Multiobjective Quadratic Assignment Problem , 2003, EMO.

[19]  Concha Bielza,et al.  A review on probabilistic graphical models in evolutionary computation , 2012, J. Heuristics.

[20]  Sébastien Vérel,et al.  Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives , 2014, PPSN.

[21]  Joshua D. Knowles,et al.  A comparison of encodings and algorithms for multiobjective minimum spanning tree problems , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[22]  Arnaud Liefooghe,et al.  New Results - On the Structure of Multiobjective Combinatorial Search Space: Multiobjective NK-Landscapes with Correlated Objectives , 2011 .

[23]  Stuart A. Kauffman,et al.  ORIGINS OF ORDER , 2019, Origins of Order.

[24]  Kiyoshi Tanaka,et al.  Insights on properties of multiobjective MNK-landscapes , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[25]  Pedro Larrañaga,et al.  Towards a New Evolutionary Computation - Advances in the Estimation of Distribution Algorithms , 2006, Towards a New Evolutionary Computation.

[26]  Concha Bielza,et al.  Optimizing Brain Networks Topologies Using Multi-objective Evolutionary Computation , 2011, Neuroinformatics.

[27]  Peter J. Fleming,et al.  Conflict, Harmony, and Independence: Relationships in Evolutionary Multi-criterion Optimisation , 2003, EMO.