Improving differential evolution with a new selection method of parents for mutation

Abstract

In differential evolution (DE), the salient feature lies in its mutationmechanismthat distinguishes it from other evolutionary algorithms. Generally, for most of the DE algorithms, the parents for mutation are randomly chosen from the current population. Hence, all vectors of population have the equal chance to be selected as parents without selective pressure at all. In this way, the information of population cannot be fully exploited to guide the search. To alleviate this drawback and improve the performance of DE, we present a new selection method of parents that attempts to choose individuals for mutation by utilizing the population information effectively. The proposed method is referred as fitnessand- position based selection (FPS), which combines the fitness and position information of population simultaneously for selecting parents in mutation of DE. In order to evaluate the effectiveness of FPS, FPS is applied to the original DE algorithms, as well as several DE variants, for numerical optimization. Experimental results on a suite of benchmark functions indicate that FPS is able to enhance the performance of most DE algorithms studied. Compared with other selection methods, FPS is also shown to be more effective to utilize information of population for guiding the search of DE.

Keywords

differential evolution / mutation operator / parents selection / population information / numerical optimization

References

[1] Storn R, Price K. Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 1997, 11(4): 341–359

[2] Das S, Suganthan P N. Differential evolution: a survey of the state-ofthe-art. IEEE Transactions on Evolutionary Computation, 2011, 15(1):4–31

[3] Plagianakos V, Tasoulis D, Vrahatis M. A review of major application areas of differential evolution. Advances in Differential Evolution,2008, 143: 197–238

[4] Zhou Y, Wang J. A local search-based multiobjective optimization algorithm for multiobjective vehicle routing problem with time windows. IEEE Systems Journal, 2014, 99: 1–14

[5] Wang J, Cai Y. Multiobjective evolutionary algorithm for frequency assignment problem in satellite communications. Soft Computing, 2015,19(5): 1229–1253

[6] Neri F, Tirronen V. Recent advances in differential evolution: a survey and experimental analysis. Artificial Intelligence Review, 2010, 33(1/2): 61–106

[7] Qin A, Huang V, Suganthan PN. Differential evolution algorithm withstrategy adaptation for global numerical optimization. IEEE Transactionson Evolutaionry Computation, 2009, 13(2): 398–417

[8] Brest J, Greiner S, Boskovíc B, Mernik M, Zumer V. Self-adaptingcontrol parameters in differential evolution: a comparative study onnumerical benchmark problems. IEEE Transactions on EvolutionaryComputation, 2006, 10(6): 646–657

[9] Yu W, Shen M, Chen W, Zhan Z, Gong Y, Lin Y, Liu O, Zhang J. Differential evolution with two-level parameter adaptation. IEEE Transactionson Cybernetics, 2014, 44(7): 2168–2267

[10] Tang L, Dong Y, Liu J. Differential evolution with an individualdependent mechanism. IEEE Transactions on Evolutionary Computation, 2014, 99

[11] Zhang J, Sanderson A. JADE: adaptive differential evolution with optional external archive. IEEE Transactions on Evolutionary Computation, 2009, 13(5): 945–958

[12] Cai Y, Wang J. Differential evolution with neighborhood and directioninformation for numerical optimization. IEEE Transactions on Cybernetics, 2013, 43 (6): 2202–2215

[13] Das S, Abraham A, Chakraborty U K, Konar K. Differential evolutionusing a neighborhood-based mutation operator. IEEE Transactions on Evolutionary Computation, 2009, 13(3): 526–553

[14] Wang J, Liao J, Zhou Y, Cai Y. Differential evolution enhanced with multiobjective sorting based mutation operators. IEEE Transactions on Cybernetics, 2014, 46(12): 2792–2805

[15] Wang Y, Cai Z, Zhang Q. Differential evolution with composite trialvector generation strategies and control parameters. IEEE Transactionson Evolutionary Computation, 2011, 15(1): 55–66

[16] Sun J, Zhang Q, Tsang EPK. DE/EDA: a new evolutionary algorithm for global optimization. Information Sciences, 2005, 169(3): 249–262

[17] Xin B, Chen J, Zhang J, Fang H, Peng Z. Hybridizing differential evolution and particle swarm optimization to design powerful optimizers: a review and taxonomy. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, 2012, 42(5): 744–767

[18] Li Y, Zhan Z, Gong Y, Chen W, Zhang J, Li Y. Differential evolution with an evolution path: a deep evolutionary algorithm. IEEE Transactionson Cybernetics, 2014, 99

[19] Dorronsoro B, Bouvry P. Improving classical and decentralized differential evolution with new mutation operator and population topologies. IEEE Transactions on Evolutionary Computation, 2011, 15(1): 67–98

[20] Weber M, Tirronen V, Neri F. Scale factor inheritance mechanismin distributed differential evolution. Soft Computing, 2010, 14(11):1187–1207

[21] Noman N, Iba H. Accelerating differential evolution using an adaptivelocal search. IEEE Transactions on Evolutionary Computation, 2008,12(1): 107–125

[22] Epitropakis MG, Tasoulis DK, Pavlidis NG, Plagianakos PV, Vrahatis MN. Enhancing differential evolution utilizing proximity based mutation operators. IEEE Transactions on Evolutioanry Computation, 2011,15(1): 99–119

[23] Gong W, Cai Z. Differential evolution with ranking-based mutation operators. IEEE Transactions on Cybernetics, 2013, 43(6): 2066–2081

[24] Wang H, Rahnamayan S, Hui S, Omran MG. Gaussian barebones differential evolution. IEEE Transactions on Cybernetics, 2013, 43(2):634–647

[25] Cai Y, Wang J, Chen Y, Tian W, Hui T. Adaptive direction informationin differential evolution for numerical optimization. Soft Computing, 2014

[26] Mallipeddi R, Suganthan P N, Pan Q, Tasgetiren M. Differential evolution algorithm with ensemble of parameters and mutation strategies. Applied Soft Computing, 2011, 11(2): 1679–1696

[27] Gong W, Cai Z, Ling CX, Li H. Enhanced differential evolution with adaptive strategies for numerical optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2011, 41(2):397–413

[28] García-Martínez C, Rodríguez F, Lozano M. Role differentiation andmalleable mating for differential evolution: an analysis on large-scale optimization. Soft Computing, 2011, 15(11): 2109–2126

[29] Chen G, Low C, Yang Z. Preserving and exploiting genetic diversityin evolutionary programming algorithms. IEEE Transactions on Evolutionary Computation, 2009, 13(3): 661–673

[30] Cai Y, Wang J, Yin J. Learning-enhanced differential evolution for numerical optimization. Soft Computing, 2012, 16(2): 303–330

[31] Baeck T, Fogel D B, Michalewicz Z. Handbook of evolutionary computation. New York: Taylor & Francis, 1997

[32] Suganthan P N, Hansen N, Liang J, Deb K, Chen Y, Auger A, Tiwari S. Problem definitions and evaluation criteria for the CEC 2005 specialsession on real-parameter optimization. KanGAL Report Number2005005. 2005

[33] Rahnamayan S, Tizhoosh H R, Salama M M A. Opposition based differential evolution. IEEE Transactions on Evolutionary Computation, 2008, 12(1): 64–79

[34] Wilcoxon F. Individual comparisons by ranking methods. Biometrics, 1945, 1(6): 80–83

[35] García S,Fernández A, Luengo J, Herrera F. A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft Computing, 2009, 13(10): 959–977

[36] Derrac J, García S, Molina D, Herrera F. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm and Evolutionary Computation, 2011, 1(1): 3–18

[37] Alcalá-Fdez J, Sánchez L, García S. KEEL: A software tool to assess evolutionary algorithms to data mining problems. Soft Computing, 2009, 13(3): 307–318

[38] Das S, Suganthan P N. Problem definitions and evaluation criteria for CEC 2011 competition on testing evolutionary algorithms on realworld optimization problems. Technical Report. 2010

[39] Chow C K, Yuen S Y. An evolutionary algorithm that makes decisionbased on the entire previous search history. IEEE Transactions on Evolutionary Computation, 2011, 15(6): 741–769

[40] Zhou X, Wu Z, Wang H, Rahnamayan S. Enhancing differential evolution with role assignment scheme. Soft Computing, 2013, 18(11): 2209–2225

[41] Guo WZ, Liu G G, Chen G L, Peng S J. A hybrid multi-objective PSOalgorithm with local search strategy for VLSI partitioning. Frontiers of Computer Science, 2014, 8(2): 203–216

[42] Zhang Y, Gong D W. Generating test data for both paths coverage and faults detection using genetic algorithms: multi-path case. Frontiers of Computer Science, 2014, 8(5): 726–740

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg