An Improved LSHADE-RSP Algorithm with the Cauchy Perturbation: iLSHADE-RSP

A new method for improving the optimization performance of a state-of-the-art differential evolution (DE) variant is proposed in this paper. The technique can increase the exploration by adopting the long-tailed property of the Cauchy distribution, which helps the algorithm to generate a trial vector with great diversity. Compared to the previous approaches, the proposed approach perturbs a target vector instead of a mutant vector based on a jumping rate. We applied the proposed approach to LSHADE-RSP ranked second place in the CEC 2018 competition on single objective real-valued optimization. A set of 30 different and difficult optimization problems is used to evaluate the optimization performance of the improved LSHADE-RSP. Our experimental results verify that the improved LSHADE-RSP significantly outperformed not only its predecessor LSHADE-RSP but also several cutting-edge DE variants in terms of convergence speed and solution accuracy.

[1]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[2]  Julian Togelius,et al.  Advanced Cauchy Mutation for Differential Evolution in Numerical Optimization , 2020, IEEE Access.

[3]  Ponnuthurai N. Suganthan,et al.  Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood for solving CEC2017 benchmark problems , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[4]  Millie Pant,et al.  Improving the performance of differential evolution algorithm using Cauchy mutation , 2011, Soft Comput..

[5]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[6]  David E. Goldberg,et al.  Finite Markov Chain Analysis of Genetic Algorithms , 1987, ICGA.

[7]  Dong Yue,et al.  Adaptive grid based multi-objective Cauchy differential evolution for stochastic dynamic economic emission dispatch with wind power uncertainty , 2017, PloS one.

[8]  Maoguo Gong,et al.  A memetic algorithm for computing and transforming structural balance in signed networks , 2015, Knowl. Based Syst..

[9]  Ponnuthurai Nagaratnam Suganthan,et al.  Problem Definitions and Evaluation Criteria for the CEC 2014 Special Session and Competition on Single Objective Real-Parameter Numerical Optimization , 2014 .

[10]  Karol R. Opara,et al.  Differential Evolution: A survey of theoretical analyses , 2019, Swarm Evol. Comput..

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

[12]  Martin Pelikan,et al.  An introduction and survey of estimation of distribution algorithms , 2011, Swarm Evol. Comput..

[13]  P. Levy,et al.  Sur les intégrales dont les éléments sont des variables aléatoires indépendantes , 1934 .

[14]  Anas A. Hadi,et al.  LSHADE with semi-parameter adaptation hybrid with CMA-ES for solving CEC 2017 benchmark problems , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[15]  Maoguo Gong,et al.  Cost-Aware Robust Control of Signed Networks by Using a Memetic Algorithm , 2020, IEEE Transactions on Cybernetics.

[16]  Hee Yong Youn,et al.  Adaptive Differential Evolution with Elite Opposition-Based Learning and its Application to Training Artificial Neural Networks , 2019, Fundam. Informaticae.

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

[18]  Robert G. Reynolds,et al.  An ensemble sinusoidal parameter adaptation incorporated with L-SHADE for solving CEC2014 benchmark problems , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[19]  L. Jiao,et al.  A Novel Clonal Selection Algorithm for Community Detection in Complex Networks , 2015, Comput. Intell..

[20]  A. E. Eiben,et al.  On Evolutionary Exploration and Exploitation , 1998, Fundam. Informaticae.

[21]  Eugene Semenkin,et al.  LSHADE Algorithm with Rank-Based Selective Pressure Strategy for Solving CEC 2017 Benchmark Problems , 2018, 2018 IEEE Congress on Evolutionary Computation (CEC).

[22]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Comparing Review , 2006, Towards a New Evolutionary Computation.

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

[24]  Tae Jong Choi,et al.  Asynchronous Differential Evolution with Strategy Adaptation for Global Numerical Optimization , 2018, HPCCT 2018.

[25]  Haifeng Li,et al.  Ensemble of differential evolution variants , 2018, Inf. Sci..

[26]  Robert G. Reynolds,et al.  A novel differential crossover strategy based on covariance matrix learning with Euclidean neighborhood for solving real-world problems , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[27]  Ning Xiong,et al.  Adapting Differential Evolution Algorithms For Continuous Optimization Via Greedy Adjustment Of Control Parameters , 2016, J. Artif. Intell. Soft Comput. Res..

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

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

[30]  Julian Togelius,et al.  ACM-DE: Adaptive p-best Cauchy Mutation with linear failure threshold reduction for Differential Evolution in numerical optimization , 2019, ArXiv.

[31]  Janez Brest,et al.  iL-SHADE: Improved L-SHADE algorithm for single objective real-parameter optimization , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[32]  Julian Togelius,et al.  A Fast and Efficient Stochastic Opposition-Based Learning for Differential Evolution in Numerical Optimization , 2019, Swarm Evol. Comput..

[33]  Tae Jong Choi,et al.  A Performance Comparison of Crossover Variations in Differential Evolution for Training Multi-layer Perceptron Neural Networks , 2018, BIC-TA.

[34]  Rafał Weron,et al.  Computationally intensive Value at Risk calculations , 2004 .

[35]  Tae Jong Choi,et al.  Asynchronous differential evolution with selfadaptive parameter control for global numerical optimization , 2018 .

[36]  Ponnuthurai N. Suganthan,et al.  Ensemble of parameters in a sinusoidal differential evolution with niching-based population reduction , 2017, Swarm Evol. Comput..

[37]  Janez Demsar,et al.  Statistical Comparisons of Classifiers over Multiple Data Sets , 2006, J. Mach. Learn. Res..

[38]  Guohua Wu,et al.  Differential evolution with multi-population based ensemble of mutation strategies , 2016, Inf. Sci..

[39]  Lei Liu,et al.  Particle swarm optimization algorithm: an overview , 2017, Soft Computing.

[40]  Tae Jong Choi,et al.  An Adaptive Population Resizing Scheme for Differential Evolution in Numerical Optimization , 2015 .

[41]  David E. Goldberg,et al.  A Survey of Optimization by Building and Using Probabilistic Models , 2002, Comput. Optim. Appl..

[42]  Rawaa Dawoud Al-Dabbagh,et al.  Algorithmic design issues in adaptive differential evolution schemes: Review and taxonomy , 2018, Swarm Evol. Comput..

[43]  Marjan Mernik,et al.  Exploration and exploitation in evolutionary algorithms: A survey , 2013, CSUR.

[44]  Tae Jong Choi,et al.  Adaptive Cauchy Differential Evolution with Strategy Adaptation and Its Application to Training Large-Scale Artificial Neural Networks , 2017, BIC-TA.

[45]  C. Mallows,et al.  A Method for Simulating Stable Random Variables , 1976 .

[46]  Francisco Herrera,et al.  Dynamically updated region based memetic algorithm for the 2013 CEC Special Session and Competition on Real Parameter Single Objective Optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[47]  Petr Bujok,et al.  Enhanced individual-dependent differential evolution with population size adaptation , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[48]  Kenneth Alan De Jong,et al.  An analysis of the behavior of a class of genetic adaptive systems. , 1975 .

[49]  Tae Jong Choi,et al.  An Adaptive Cauchy Differential Evolution Algorithm with Bias Strategy Adaptation Mechanism for Global Numerical Optimization , 2014, J. Comput..

[50]  Thomas Stützle,et al.  Benchmark results for a simple hybrid algorithm on the CEC 2013 benchmark set for real-parameter optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[51]  Zhijian Wu,et al.  Enhanced opposition-based differential evolution for solving high-dimensional continuous optimization problems , 2011, Soft Comput..

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

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

[54]  Tsung-Che Chiang,et al.  Modified L-SHADE for Single Objective Real-Parameter Optimization , 2019, 2019 IEEE Congress on Evolutionary Computation (CEC).

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

[56]  Ju-Jang Lee,et al.  Stochastic Opposition-Based Learning Using a Beta Distribution in Differential Evolution , 2016, IEEE Transactions on Cybernetics.

[57]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..

[58]  Jun Zhang,et al.  SDE: a stochastic coding differential evolution for global optimization , 2012, GECCO '12.

[59]  Maoguo Gong,et al.  Detecting composite communities in multiplex networks: A multilevel memetic algorithm , 2017, Swarm Evol. Comput..

[60]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[61]  Sushil J. Louis,et al.  Syntactic Analysis of Convergence in Genetic Algorithms , 1992, FOGA.

[62]  Tae Jong Choi,et al.  An Improved Differential Evolution Algorithm and Its Application to Large-Scale Artificial Neural Networks , 2017 .

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

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

[65]  Janez Brest,et al.  Single objective real-parameter optimization: Algorithm jSO , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[66]  Janez Brest,et al.  Population size reduction for the differential evolution algorithm , 2008, Applied Intelligence.

[67]  Hui Wang,et al.  Gaussian Bare-Bones Differential Evolution , 2013, IEEE Transactions on Cybernetics.

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

[69]  Ying Wang,et al.  Multi-objective differential evolution with adaptive Cauchy mutation for short-term multi-objective optimal hydro-thermal scheduling , 2010 .

[70]  P. Hall.  A Comedy of Errors: The Canonical Form for a Stable Characteristic Function , 1981 .

[71]  Tae Jong Choi,et al.  An Adaptive Cauchy Differential Evolution Algorithm with Population Size Reduction and Modified Multiple Mutation Strategies , 2015 .

[72]  Maoguo Gong,et al.  Influence maximization in social networks based on discrete particle swarm optimization , 2016, Inf. Sci..

[73]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[74]  Tae Jong Choi,et al.  Adaptive α-stable differential evolution in numerical optimization , 2017, Natural Computing.

[75]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[76]  R. Weron.  Correction to: "On the Chambers–Mallows–Stuck Method for Simulating Skewed Stable Random Variables" , 1996 .

[77]  M.M.A. Salama,et al.  Opposition-Based Differential Evolution , 2008, IEEE Transactions on Evolutionary Computation.

[78]  Jinung An,et al.  An Adaptive Cauchy Differential Evolution Algorithm for Global Numerical Optimization , 2013, TheScientificWorldJournal.

[79]  Tae Jong Choi,et al.  An Adaptive Differential Evolution Algorithm with Automatic Population Resizing for Global Numerical Optimization , 2014, BIC-TA.

[80]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[81]  David Naso,et al.  Compact Differential Evolution , 2011, IEEE Transactions on Evolutionary Computation.