×

A differential evolution algorithm with self-adapting strategy and control parameters. (English) Zbl 1231.90383

Summary: This paper presents a differential evolution algorithm with self-adaptive trial vector generation strategy and control parameters (SspDE) for global numerical optimization over continuous space. In the SspDE algorithm, each target individual has an associated strategy list (SL), a mutation scaling factor \(F\) list (FL), and a crossover rate \(CR\) list (CRL). During the evolution, a trial individual is generated by using a strategy, \(F\), and \(CR\) taken from the lists associated with the target vector. If the obtained trial individual is better than the target vector, the used strategy, \(F\), and \(CR\) will enter a winning strategy list (wSL), a winning \(F\) list (wFL), and a winning \(CR\) list (wCRL), respectively. After a given number of iterations, the FL, CRL or SL will be refilled at a high probability by selecting elements from wFL, wCRL and wSL or randomly generated values. In this way, both the trial vector generation strategy and its associated parameters can be gradually self-adapted to match different phases of evolution by learning from their previous successful experience. Extensive computational simulations and comparisons are carried out by employing a set of 19 benchmark problems from the literature. The computational results show that overall the SspDE algorithm performs better than the state-of-the-art differential evolution variants.

MSC:

90C56 Derivative-free methods and methods using generalized derivatives
90C59 Approximation methods and heuristics in mathematical programming
90C26 Nonconvex programming, global optimization

Software:

CEC 05
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Abbass HA. The self-adaptive Pareto differential evolution algorithm. In: Proceedings of the 2002 congress on evolutionary computation, 2002, Honolulu, HI, USA, May 2002, p. 831-6.
[2] Brest, J.; Greiner, S.; Boskovic, B.; Mernik, M.; Zumer, V., Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems, IEEE transactions on evolutionary computation, 10, 646-657, (2006)
[3] Das S, Konar A, Chakraborty UK. Two improved differential evolution schemes for faster global search. In: ACM-SIGEVO proceedings of genetic and evolutionary computation conference (GECCO-2005), Washington DC, USA, 2005, p. 991-8.
[4] Gämperle, R.; Müller, S.D.; Koumoutsakos, P., A parameter study for differential evolution, (), 293-298
[5] Hansen N. Compilation of results on the 2005 CEC benchmark function set, May 4, 2006 〈http://www.ntu.edu.sg/home/epnsugan/index_files/CEC-05/compareresults.pdf〉.
[7] Huang VL, Qin AK, Suganthan PN. Self-adaptive differential evolution algorithm for constrained real-parameter optimization, IEEE-CEC-06, July 2006, Canada.
[8] Ilonen, J.; Kamarainen, J.K.; Lampinen, J., Differential evolution training algorithm for feed-forward neural networks, Neural processing letters, 17, 93-105, (2003)
[9] Joshi, R.; Sanderson, A.C., Minimal representation multisensor fusion using differential evolution, IEEE transactions on systems, man, and cybernetics (part A), 29, 63-76, (1999)
[10] Lampinen J, Zelinka I. On stagnation of the differential evolution algorithm. In: Ošmera P, editor. Proceedings of MENDEL 2000, sixth international Mendel conference on soft computing, 2002, p. 76-83.
[11] Liang JJ, Suganthan PN, Deb K. Novel composition test functions for numerical global optimization. In: IEEE swarm intelligence symposium 2005, Pasadena, California, June 2005, p. 68-75.
[12] Liu, J.; Lampinen, J., A fuzzy adaptive differential evolution algorithm, Soft computing, 9, 448-462, (2005) · Zbl 1076.93513
[13] Omran MGH, Salman A, Engelbrecht AP. Self-adaptive differential evolution. In: Computational intelligence and security, PT 1, Proceedings of the lecture notes in artificial intelligence, 2005, p. 192-9.
[14] Onwubolu, G.C., Design of hybrid differential evolution and group method of data handling networks for modeling and prediction, Information sciences, 178, 3616-3634, (2008)
[15] Pan, Q.K.; Wang, L.; Qian, B., A novel differential evolution algorithm for bi-criteria no-wait flow shop scheduling problems, Computers and operations research, 36, 2498-2511, (2009) · Zbl 1157.90423
[16] Price, K.V., An introduction to differential evolution, (), 79-108
[17] Price, K.; Storn, R., Differential evolution: a simple evolution strategy for fast optimization, Dr. Dobb’s journal of software tools, 22, 18-24, (1997)
[18] Price, K.; Storn, R.; Lampinen, J., Differential evolution—a practical approach to global optimization, (2005), Springer Berlin
[19] Qin, A.K.; Huang, V.L.; Suganthan, P.N., Differential evolution algorithm with strategy adaptation for global numerical optimization, IEEE transactions on evolutionary computations, 13, 398-417, (2009)
[20] Qin AK, Suganthan PN. Self-adaptive differential evolution algorithm for numerical optimization. In: IEEE congress on evolutionary computation (CEC 2005), Edinburgh, Scotland, IEEE Press, September 2005, p. 1785-91.
[21] Rogalsky T, Derksen RW, Kocabiyik S. Differential evolution in aerodynamic optimization. In: Proceedings of 46th annual conference of Canadian Aeronautics and Space Institute, Montreal, Quebec, May, 1999, p. 29-36.
[22] Rönkkönen J, Kukkonen S, Price KV. Real-parameter optimization with differential evolution. In: 2005 IEEE congress on evolutionary computation (CEC 2005), Edinburgh, Scotland, IEEE Press, September 2005, p. 506-13.
[23] Storn R, Price K. Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report TR-95-012, ICSI 〈http://http.icsi.berkeley.edu/∼storn/litera.html〉, 1995. · Zbl 0888.90135
[24] Storn, R.; Price, K.V., Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces, Journal of global optimization, 11, 341-359, (1997) · Zbl 0888.90135
[25] Storn R. On the usage of differential evolution for function optimization. In: Biennial conference of the North American Fuzzy Information Processing Society (NAFIPS), Berkeley, 1996, p. 519-23.
[26] Suganthan PN, Hansen N, Liang JJ, et al. Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical report, Nanyang Technological University, Singapore, May 2005 and Kangal report #2005005, IIT Kanpur, India.
[27] Teo, J., Exploring dynamic self-adaptive populations in differential evolution, Soft computing, 10, 637-686, (2006)
[28] Wang, L.; Pan, Q.-K.; Suganthan, P.N., A novel hybrid discrete differential evolution algorithm for blocking flow shop scheduling problems, Computers and operations research, (2008)
[29] Yao, X.; Liu, Y.; Lin, G., Evolutionary programming made faster, IEEE transactions on evolution computation, 3, 82-102, (1999)
[30] Zaharie D. Control of population diversity and adaptation in differential evolution algorithms. In: Matousek R, Osmera P, editors. Proceedings of Mendel 2003, ninth international conference on soft computing, Brno, Czech Republic, June 2003, p. 41-6.
[31] Zaharie D, Petcu D. Adaptive pareto differential evolution and its parallelization. In: Proceedings of the fifth international conference on parallel processing and applied mathematics, Czestochowa, Poland, September 2003, p. 261-8. · Zbl 1128.68549
[32] Zhang, M.; Luo, W.J.; Wang, X., Differential evolution with dynamic stochastic selection for constrained optimization, Information sciences, 178, 3043-3074, (2008)
[33] Conover, W.J., Practical nonparametric statistics, (1980), John Wiley & Sons, (p. 225-6)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.