A Cluster-Based Differential Evolution Algorithm With External Archive for Optimization in Dynamic Environments

This paper presents a Cluster-based Dynamic Differential Evolution with external Ar chive (CDDE_Ar) for global optimization in dynamic fitness landscape. The algorithm uses a multipopulation method where the entire population is partitioned into several clusters according to the spatial locations of the trial solutions. The clusters are evolved separately using a standard differential evolution algorithm. The number of clusters is an adaptive parameter, and its value is updated after a certain number of iterations. Accordingly, the total population is redistributed into a new number of clusters. In this way, a certain sharing of information occurs periodically during the optimization process. The performance of CDDE_Ar is compared with six state-of-the-art dynamic optimizers over the moving peaks benchmark problems and dynamic optimization problem (DOP) benchmarks generated with the generalized-dynamic-benchmark-generator system for the competition and special session on dynamic optimization held under the 2009 IEEE Congress on Evolutionary Computation. Experimental results indicate that CDDE_Ar can enjoy a statistically superior performance on a wide range of DOPs in comparison to some of the best known dynamic evolutionary optimizers.

[1]  Ivan Zelinka,et al.  ON STAGNATION OF THE DIFFERENTIAL EVOLUTION ALGORITHM , 2000 .

[2]  John J. Grefenstette,et al.  Case-Based Initialization of Genetic Algorithms , 1993, ICGA.

[3]  David W. Pearson,et al.  An Immune System-Based Genetic Algorithm to Deal with Dynamic Environments : Diversity and Memory , 2004 .

[4]  Gerry Dozier,et al.  Adapting Particle Swarm Optimizationto Dynamic Environments , 2001 .

[5]  Shengxiang Yang,et al.  Genetic Algorithms with Memory- and Elitism-Based Immigrants in Dynamic Environments , 2008, Evolutionary Computation.

[6]  Jouni Lampinen,et al.  A Trigonometric Mutation Operation to Differential Evolution , 2003, J. Glob. Optim..

[7]  Ville Tirronen,et al.  An Enhanced Memetic Differential Evolution in Filter Design for Defect Detection in Paper Production , 2008, Evolutionary Computation.

[8]  Andries Petrus Engelbrecht,et al.  Improved differential evolution for dynamic optimization problems , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[9]  Changhe Li,et al.  A Clustering Particle Swarm Optimizer for Locating and Tracking Multiple Optima in Dynamic Environments , 2010, IEEE Transactions on Evolutionary Computation.

[10]  Shengxiang Yang,et al.  Particle Swarm Optimization With Composite Particles in Dynamic Environments , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Mohammad Reza Meybodi,et al.  CellularDE: A Cellular Based Differential Evolution for Dynamic Optimization Problems , 2011, ICANNGA.

[12]  John J. Grefenstette,et al.  Genetic Algorithms for Changing Environments , 1992, PPSN.

[13]  L.N. de Castro,et al.  An artificial immune network for multimodal function optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[14]  Jürgen Branke,et al.  Memory enhanced evolutionary algorithms for changing optimization problems , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[15]  Xiaodong Li,et al.  Comparing particle swarms for tracking extrema in dynamic environments , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[16]  S. Louis,et al.  Genetic Algorithms for Open Shop Scheduling and Re-scheduling , 1996 .

[17]  Terence C. Fogarty,et al.  Adaptive Combustion Balancing in Multiple Burner Boiler Using a Genetic Algorithm with Variable Range of Local Search , 1997, ICGA.

[18]  W. Cedeno,et al.  On the use of niching for dynamic landscapes , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[19]  Jürgen Branke,et al.  Evolutionary optimization in uncertain environments-a survey , 2005, IEEE Transactions on Evolutionary Computation.

[20]  J. Kennedy Stereotyping: improving particle swarm performance with cluster analysis , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[21]  Xin Yao,et al.  Benchmark Generator for CEC'2009 Competition on Dynamic Optimization , 2008 .

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

[23]  Jing Hu,et al.  A Diversity-Guided Particle Swarm Optimizer for Dynamic Environments , 2007, LSMS.

[24]  Peter Korošec,et al.  Applications of the Differential Ant-Stigmergy Algorithm on Real-World Continuous Optimization Problems , 2009 .

[25]  Shengxiang Yang,et al.  Evolutionary dynamic optimization: A survey of the state of the art , 2012, Swarm Evol. Comput..

[26]  Tom Lenaerts,et al.  Dynamic optimization using evolutionary algorithms with a case-based memory , 2002 .

[27]  Stefano Nolfi,et al.  Two is better than one: A diploid genotype for neural networks , 1996, Neural Processing Letters.

[28]  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).

[29]  R.W. Morrison,et al.  Triggered hypermutation revisited , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[30]  Xiaodong Li,et al.  This article has been accepted for inclusion in a future issue. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 1 Locating and Tracking Multiple Dynamic Optima by a Particle Swarm Model Using Speciation , 2022 .

[31]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[32]  Arvind S. Mohais,et al.  DynDE: a differential evolution for dynamic optimization problems , 2005, 2005 IEEE Congress on Evolutionary Computation.

[33]  Emma Hart,et al.  A Comparison of Dominance Mechanisms and Simple Mutation on Non-stationary Problems , 1998, PPSN.

[34]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

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

[36]  Janez Brest,et al.  Differential evolution and differential ant-stigmergy on dynamic optimisation problems , 2013, Int. J. Syst. Sci..

[37]  Jurij Silc,et al.  The Differential Ant-Stigmergy Algorithm applied to dynamic optimization problems , 2009, 2009 IEEE Congress on Evolutionary Computation.

[38]  Janez Brest,et al.  Dynamic optimization using Self-Adaptive Differential Evolution , 2009, 2009 IEEE Congress on Evolutionary Computation.

[39]  Kok Cheong Wong,et al.  A New Diploid Scheme and Dominance Change Mechanism for Non-Stationary Function Optimization , 1995, ICGA.

[40]  Jürgen Branke,et al.  Evolutionary Optimization in Dynamic Environments , 2001, Genetic Algorithms and Evolutionary Computation.

[41]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.

[42]  Changhe Li,et al.  A Generalized Approach to Construct Benchmark Problems for Dynamic Optimization , 2008, SEAL.

[43]  Shengxiang Yang,et al.  A comparative study of immune system based genetic algorithms in dynamic environments , 2006, GECCO '06.

[44]  F. Wilcoxon Individual Comparisons by Ranking Methods , 1945 .

[45]  Peter J. Bentley,et al.  Dynamic Search With Charged Swarms , 2002, GECCO.

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

[47]  Mark Wineberg,et al.  Enhancing the GA's Ability to Cope with Dynamic Environments , 2000, GECCO.

[48]  Shengxiang Yang,et al.  Associative Memory Scheme for Genetic Algorithms in Dynamic Environments , 2006, EvoWorkshops.

[49]  Russell C. Eberhart,et al.  Tracking and optimizing dynamic systems with particle swarms , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[50]  Martin Middendorf,et al.  A hierarchical particle swarm optimizer for noisy and dynamic environments , 2006, Genetic Programming and Evolvable Machines.

[51]  Rakesh Angira,et al.  Optimization of dynamic systems: A trigonometric differential evolution approach , 2007, Comput. Chem. Eng..

[52]  Fabrício Olivetti de França,et al.  A dynamic artificial immune algorithm applied to challenging benchmarking problems , 2009, IEEE Congress on Evolutionary Computation.

[53]  Zbigniew Michalewicz,et al.  Evolutionary optimization in non-stationary environments , 2000 .

[54]  Francisco Herrera,et al.  Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power , 2010, Inf. Sci..

[55]  Dumitru Dumitrescu,et al.  A collaborative model for tracking optima in dynamic environments , 2007, 2007 IEEE Congress on Evolutionary Computation.

[56]  Hartmut Schmeck,et al.  Designing evolutionary algorithms for dynamic optimization problems , 2003 .

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

[58]  Rainer Storn,et al.  Differential Evolution-A simple evolution strategy for fast optimization , 1997 .

[59]  Helen G. Cobb,et al.  An Investigation into the Use of Hypermutation as an Adaptive Operator in Genetic Algorithms Having Continuous, Time-Dependent Nonstationary Environments , 1990 .