Abstract
The differential evolution algorithm (DE) is a simple and effective global optimization algorithm. It has been successfully applied to solve a wide range of real-world optimization problem. In this paper, the proposed algorithm uses two mutation rules based on the rand and best individuals among the entire population. In order to balance the exploitation and exploration of the algorithm, two new rules are combined through a probability rule. Then, self-adaptive parameter setting is introduced as uniformly random numbers to enhance the diversity of the population based on the relative success number of the proposed two new parameters in a previous period. In other aspects, our algorithm has a very simple structure and thus it is easy to implement. To verify the performance of MDE, 16 benchmark functions chosen from literature are employed. The results show that the proposed MDE algorithm clearly outperforms the standard differential evolution algorithm with six different parameter settings. Compared with some evolution algorithms (ODE, OXDE, SaDE, JADE, jDE, CoDE, CLPSO, CMA-ES, GL-25, AFEP, MSAEP and ENAEP) from literature, experimental results indicate that the proposed algorithm performs better than, or at least comparable to state-of-the-art approaches from literature when considering the quality of the solution obtained.
Similar content being viewed by others
References
Brest J, Greiner S, Boskovic B, Mernik M, Zumer V (2006) Self adapting control parameters in differential evolution: a comparativestudy on numerical benchmark problems. IEEE Trans Evolut Comput 10(6):646–657
Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6:58–73
Das S, Suganthan PN (2011) Differential evolution: a survey of the atate-of-the-art. IEEE Trans. Evolut Comput 15(1):4–31
Das S, Abraham A, Chakraborty UK, Konar A (2009) Differential evolution using a neighborhood based mutation operator. IEEE Trans Evol Comput 13(3):526–553
Dorigo M, Maniezzo V, Colorni A (1996) The ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B 26(1):29–41
Garcia-Martinez C, Lozano M, Herrera F, Molina D, Sanchez AM (2008) Global and local real-coded genetic algorithms based on parent-centric crossover operators. Eur J Oper Res 185:1088–1113
Ghosh A, Das S, Chowdhury A, Giri R (2011) An improved differential evolution algorithm with fitness-based adaptation of the control parameters. Inf Sci 181(18):3749–3765
Gong WY, Cai ZH, Jiang LX (2008) Enhancing the performance of differential evolution using orthogonal design method. Appl Math Comput 206(1):56–69
Gong W, Cai Z, Ling CX (2010) DE/BBO: a hybrid differential evolution with biogeography-based optimization for global numerical optimization. Soft Comput. 15(4):645–665
Hansen N, Ostermeier A (2001) Completely derandomized self adaptation in evolution strategies. Evol Comput 9(2):159–195
Horn J, Nafpliotis N, Goldberg DE (1994) A niched Pareto genetic algorithm for multiobjective optimization. Evol Comput 1:82–87
Li XT, Wang JN, Yin MH (2013) Enhancing the performance of cuckoo search algorithm using orthogonal learning method. Neural Comput Appl. doi:10.1007/s00521-013-1354-6
Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295
Liu J, Lampinen J (2005) A fuzzy adaptive differential evolution algorithm. Soft Comput Fusion Found Methodol Appl 9(6):448–462
Mallipeddi R, Mallipeddi S, Suganthan PN (2010) Ensemble strategies with adaptive evolutionary programming. Inf Sci 180(9):1571–1581
Montgomery J, Chen S (2010) An analysis of the operation of differential evolution at high and low crossover rates. In: IEEE Congress on Evolutionary Computation (CEC), IEEE, pp 1–8
Neri F, Tirronen V (2009) Scale factor local search in differential evolution. Memetic Comput J 1(2):153–171
Noman N, Iba H (2008) Accelerating differential evolution using an adaptive local search. IEEE Trans Evol Comput 12(1):107–125
Omran MGH, Engelbrecht AP, Salman A (2007) Differential evolution based particle swarm optimization. IEEE Swarm Intel. Symp. (SIS 2007) 4:112–119
Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evolut Comput 13(2):398–417
Rahnamayan S, Tizhoosh HR, Salama MMA (2008) Opposition-based differential evolution. IEEE Transactions on Evolutionary Computation 12(1):64–79
Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous space. J Global Optim 11:341–359
Suman B (2004) Study of simulated annealing based algorithms for multiobjective optimization of a constrained problem. Comput Chem Eng 8:1849–1871
Sun J, Zhang Q, Tsang E (2004) DE/EDA: a new evolutionary algorithm for global optimization. Inf Sci 169:249–262
Wang Y, Cai ZX, Zhang QF (2011a) Differential evolution with composite trail vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66
Wang Y, Cai ZX, Zhang QF (2011b) Enhancing the search ability of differential evolution through orthogonal crossover. Inf Sci 18(1):153–177
Yang XS, Deb S (2009) Cuckoo search via Levy flights. In: World Congress on Nature & Biologically Inspired Computing (NaBIC 2009). IEEE Publication, USA, pp 210–214
Yang Z, He J, Yao X (2008) Making a difference to differential evolution. In: Michalewicz Z, Siarry P (eds) Advances in metaheuristics for hard optimization. Springer, Berlin, pp 397–414
Zhang Q, Muhlenbein H (2004) On the convergence of a class of estimation of distribution algorithms. IEEE Trans Evol Comput 8(2):127–136
Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evolut Comput 13(5):945–958
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, X., Yin, M. Modified differential evolution with self-adaptive parameters method. J Comb Optim 31, 546–576 (2016). https://doi.org/10.1007/s10878-014-9773-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-014-9773-6