Analysis of causality-driven changes of diffusion speed in non-Markovian temporal networks generated on the basis of differential evolution dynamics

Abstract Differential evolution (DE) is one popular meta-heuristic, which is used to solve difficult optimization problems. In the last years, a huge number of new variants of the differential evolution has been introduced to outperform previously presented algorithms. To provide solutions of higher quality or to speed-up the convergence principles as control parameters adaptation, novel mutation strategies, or combination of different mutation strategies are often used. In this work, five different variants of the differential evolution have been chosen with the goal to investigate their inner dynamics, especially spread of positive genomes within the population. To capture relationships between individuals, temporal networks, more precisely contact sequences, are used. Based on the empirical results, we have concluded that temporal networks generated on the basis of the DE algorithms dynamics are non-Markovian temporal networks. For this reason, to analyze the causality-driven changes of diffusion speed in these networks, analytical methods described by Scholtes et al. have been used.

[1]  Esteban Moro Egido,et al.  The dynamical strength of social ties in information spreading , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Alex S. Fukunaga,et al.  Reevaluating Exponential Crossover in Differential Evolution , 2014, PPSN.

[3]  Godfrey C. Onwubolu,et al.  Enhanced differential evolution hybrid scatter search for discrete optimization , 2007, 2007 IEEE Congress on Evolutionary Computation.

[4]  Andries Petrus Engelbrecht,et al.  Self-adaptive Differential Evolution , 2005, CIS.

[5]  Jason Teo,et al.  Exploring dynamic self-adaptive populations in differential evolution , 2006, Soft Comput..

[6]  Mehmet Fatih Tasgetiren,et al.  Differential evolution algorithm with ensemble of parameters and mutation strategies , 2011, Appl. Soft Comput..

[7]  Alessandro Vespignani,et al.  Evolution and Structure of the Internet: A Statistical Physics Approach , 2004 .

[8]  Rainer Storn,et al.  System design by constraint adaptation and differential evolution , 1999, IEEE Trans. Evol. Comput..

[9]  Jure Leskovec,et al.  Planetary-scale views on a large instant-messaging network , 2008, WWW.

[10]  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).

[11]  Michal Pluhacek,et al.  Capturing Inner Dynamics of Firefly Algorithm in Complex Network - Initial Study , 2015, AECIA.

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

[13]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[14]  Swagatam Das,et al.  Automatic Clustering Using an Improved Differential Evolution Algorithm , 2007 .

[15]  Mikko Sams,et al.  Inter-Subject Correlation of Brain Hemodynamic Responses During Watching a Movie: Localization in Space and Frequency , 2009, Front. Neuroinform..

[16]  Jean-Pierre Eckmann,et al.  Entropy of dialogues creates coherent structures in e-mail traffic. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Alfred O. Hero,et al.  Inferring Time-Varying Network Topologies from Gene Expression Data , 2007, EURASIP J. Bioinform. Syst. Biol..

[18]  Arthur C. Sanderson,et al.  JADE: Adaptive Differential Evolution With Optional External Archive , 2009, IEEE Transactions on Evolutionary Computation.

[19]  Vadlamani Ravi,et al.  Differential evolution trained wavelet neural networks: Application to bankruptcy prediction in banks , 2009, Expert Syst. Appl..

[20]  Zhi-Dan Zhao,et al.  Empirical Analysis on the Human Dynamics of a Large-Scale Short Message Communication System , 2011 .

[21]  M. Fiedler Algebraic connectivity of graphs , 1973 .

[22]  Claudia Pahl-Wostl,et al.  The Dynamic Nature of Ecosystems: Chaos and Order Entwined , 1995 .

[23]  Jari Saramäki,et al.  Temporal Networks , 2011, Encyclopedia of Social Network Analysis and Mining.

[24]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[25]  Jari Saramäki,et al.  Path lengths, correlations, and centrality in temporal networks , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Michal Pluhacek,et al.  Particle Swarm Optimizer with Diversity Measure Based on Swarm Representation in Complex Network , 2015, AECIA.

[27]  Robert E. Ulanowicz,et al.  Quantitative methods for ecological network analysi , 2004, Comput. Biol. Chem..

[28]  Jouni Lampinen,et al.  A Fuzzy Adaptive Differential Evolution Algorithm , 2005, Soft Comput..

[29]  H. Abbass,et al.  PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[30]  Liang Gao,et al.  A new differential evolution algorithm with a hybrid mutation operator and self-adapting control parameters for global optimization problems , 2014, Applied Intelligence.

[31]  Arthur C. Sanderson,et al.  Minimal representation multisensor fusion using differential evolution , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[32]  H. Abbass The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[33]  Alex S. Fukunaga,et al.  Success-history based parameter adaptation for Differential Evolution , 2013, 2013 IEEE Congress on Evolutionary Computation.

[34]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[35]  A. Barabasi,et al.  Impact of non-Poissonian activity patterns on spreading processes. , 2006, Physical review letters.

[36]  Wenyin Gong,et al.  Differential Evolution With Ranking-Based Mutation Operators , 2013, IEEE Transactions on Cybernetics.

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

[38]  Alex S. Fukunaga,et al.  Improving the search performance of SHADE using linear population size reduction , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[39]  Michael P. H. Stumpf,et al.  Statistical inference of the time-varying structure of gene-regulation networks , 2010, BMC Systems Biology.

[40]  A-L Barabási,et al.  Structure and tie strengths in mobile communication networks , 2006, Proceedings of the National Academy of Sciences.

[41]  D. Koller,et al.  Activity motifs reveal principles of timing in transcriptional control of the yeast metabolic network , 2008, Nature Biotechnology.

[42]  Michal Pluhacek,et al.  PSO as Complex Network - Capturing the Inner Dynamics - Initial Study , 2015, AECIA.

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

[44]  Michal Pluhacek,et al.  Complex Network Analysis of Evolutionary Algorithms Applied to Combinatorial Optimisation Problem , 2014, IBICA.

[45]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

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

[47]  Ponnuthurai N. Suganthan,et al.  Recent advances in differential evolution - An updated survey , 2016, Swarm Evol. Comput..

[48]  Lan V. Zhang,et al.  Evidence for dynamically organized modularity in the yeast protein–protein interaction network , 2004, Nature.