Differential Evolution Enhanced by the Closeness Centrality: Initial Study

The closeness centrality can be considered as the natural distance metric between pairs of nodes in connected graphs. This paper is the initial study of the influence of the closeness centrality of the graph built on the basis of the differential evolution dynamics to the differential evolution convergence rate. Our algorithm is based on the principle that the differential evolution creates graph for each generation, where nodes represent the individuals and edges the relationships between them. For each individual the closeness centrality is computed and on the basis of its value the individuals are selected in the mutation step of the algorithm. The higher value of the closeness centrality means the higher probability to become the parent in the mutation step. This enhancement has been incorporated in the classical differential evolution and a set of 21 well-known benchmark functions has been used to test and evaluate the performance of the proposed enhancement of the differential evolution. The experimental results and statistical analysis indicate that the enhanced algorithm performs better or at least comparable to its original version.

[1]  Xin Yao,et al.  Making a Difference to Differential Evolution , 2008, Advances in Metaheuristics for Hard Optimization.

[2]  Roman Senkerik,et al.  Preliminary investigation on relations between complex networks and evolutionary algorithms dynamics , 2010, 2010 International Conference on Computer Information Systems and Industrial Management Applications (CISIM).

[3]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[4]  Thomas Wilhelm,et al.  What is a complex graph , 2008 .

[5]  Daniela Zaharie,et al.  Influence of crossover on the behavior of Differential Evolution Algorithms , 2009, Appl. Soft Comput..

[6]  Michal Pluhacek,et al.  Complex Network Analysis of Discrete Self-organising Migrating Algorithm , 2014 .

[7]  Ponnuthurai N. Suganthan,et al.  An Adaptive Differential Evolution Algorithm With Novel Mutation and Crossover Strategies for Global Numerical Optimization , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[8]  Qingfu Zhang,et al.  Differential Evolution With Composite Trial Vector Generation Strategies and Control Parameters , 2011, IEEE Transactions on Evolutionary Computation.

[9]  Liang Gao,et al.  A differential evolution algorithm with intersect mutation operator , 2013, Appl. Soft Comput..

[10]  A. Kai Qin,et al.  Self-adaptive differential evolution algorithm for numerical optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[11]  Carlos A. Coello Coello,et al.  A comparative study of differential evolution variants for global optimization , 2006, GECCO.

[12]  Nenad Mladenovic,et al.  DE-VNS: Self-adaptive Differential Evolution with crossover neighborhood search for continuous global optimization , 2013, Comput. Oper. Res..

[13]  Xin Yao,et al.  Self-adaptive differential evolution with neighborhood search , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[14]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[15]  Jouni Lampinen,et al.  GDE3: the third evolution step of generalized differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[16]  Saku Kukkonen,et al.  Real-parameter optimization with differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[17]  Tea Tusar,et al.  GP-DEMO: Differential Evolution for Multiobjective Optimization based on Gaussian Process models , 2015, Eur. J. Oper. Res..

[18]  Leandro dos Santos Coelho,et al.  A self-adaptive chaotic differential evolution algorithm using gamma distribution for unconstrained global optimization , 2014, Appl. Math. Comput..

[19]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[20]  Amit Konar,et al.  Differential Evolution Using a Neighborhood-Based Mutation Operator , 2009, IEEE Transactions on Evolutionary Computation.

[21]  Roman Senkerik,et al.  Do Evolutionary Algorithm Dynamics Create Complex Network Structures? , 2011, Complex Syst..

[22]  Shilpa Chakravartula,et al.  Complex Networks: Structure and Dynamics , 2014 .