Evolutionary Intelligence

, Volume 4, Issue 1, pp 17–29 | Cite as

Composed compact differential evolution

  • Giovanni Iacca
  • Ernesto Mininno
  • Ferrante NeriEmail author
Special Issue


This paper proposes a novel algorithm for solving continuous complex optimization problems with a relatively low memory consumption. The proposed approach, namely Composed compact Differential Evolution, consists of a set of compact Differential Evolution units which simultaneously search the decision space from various perspectives. A randomization in the virtual population allows the algorithm to behave, on one hand, as a multiple local search with a multi-start logic integrated within it. On the other hand, the compact units communicate among each other by means of a ring topology and propagation of information. More specifically, the most promising elite solutions and scale factor values of each compact unit are migrated to the neighbour unit so that the search of the global optimum is performed. In other words, while each single compact unit performs a local search by exploiting the direction suggested by each elite solution, the entire structure combines the achievement of each local search operation towards the direction of the global search. The proposed algorithm is characterized by a limited memory consumption and is memory-wise equivalent to a population-based algorithm with a small population. Numerical results show that the proposed approach outperforms other compact algorithms and various modern population-based structures.


Differential evolution Distributed algorithms Compact algorithms Randomization Scale factor inheritance 


  1. 1.
    Larrañaga P, Lozano JA (2001) Estimation of distribution algorithms: a new tool for evolutionary computation. Kluwer, NorwellGoogle Scholar
  2. 2.
    Harik GR, Lobo FG, Goldberg DE (1999) The compact genetic algorithm. IEEE Trans Evol Comput 3(4):287–297CrossRefGoogle Scholar
  3. 3.
    Rastegar R, Hariri A (2006) A step forward in studying the compact genetic algorithm. Evol Comput 14(3):277–289CrossRefGoogle Scholar
  4. 4.
    Harik G (1999) Linkage learning via probabilistic modeling in the ECGA. Technical Report 99010, University of Illinois at Urbana-Champaign, Urbana, ILGoogle Scholar
  5. 5.
    Harik GR, Lobo FG, Sastry K (2006) Linkage learning via probabilistic modeling in the extended compact genetic algorithm (ECGA). In: Pelikan M, Sastry K, Cantú-Paz E (eds) Scalable optimization via probabilistic modeling vol 33 of studies in computational intelligence. Springer, pp 39–61Google Scholar
  6. 6.
    Sastry K, Goldberg DE (2000) On extended compact gentic algorithm. Technical Report 2000026, University of Illinois at Urbana-Champaign, Urbana, ILGoogle Scholar
  7. 7.
    Sastry K, Xiao G (2001) Cluster optimization using extended compact genetic algorithm. Technical Report 2001016, University of Illinois at Urbana-Champaign, Urbana, ILGoogle Scholar
  8. 8.
    Sastry K, Goldberg DE, Johnson DD (2007) Scalability of a hybrid extended compact genetic algorithm for ground state optimization of clusters. Mater Manuf Process 22(5):570–576CrossRefGoogle Scholar
  9. 9.
    Aporntewan C, Chongstitvatana P (2001) A hardware implementation of the compact genetic algorithm. In: Proceedings of the IEEE congress on evolutionary computation, 1:624–629Google Scholar
  10. 10.
    Gallagher JC, Vigraham S, Kramer G (2004) A family of compact genetic algorithms for intrinsic evolvable hardware. IEEE Trans Evol Comput 8(2):111–126CrossRefGoogle Scholar
  11. 11.
    Jewajinda Y, Chongstitvatana P (2008) Cellular compact genetic algorithm for evolvable hardware. In: Proceedings of the international conference on electrical engineering/electronics, computer, telecommunications and information technology, 1:1–4Google Scholar
  12. 12.
    Gallagher JC, Vigraham S (2002) A modified compact genetic algorithm for the intrinsic evolution of continuous time recurrent neural networks. In: Proceedings of the genetic and evolutionary computation conference, pp 163–170Google Scholar
  13. 13.
    Ahn CW, Ramakrishna RS (2003) Elitism based compact genetic algorithms. IEEE Trans Evol Comput 7(4):367–385CrossRefGoogle Scholar
  14. 14.
    Rudolph G (2001) Self-adaptive mutations may lead to premature convergence. IEEE Trans Evol Comput 5(4):410–414CrossRefGoogle Scholar
  15. 15.
    Mininno E, Cupertino F, Naso D (2008) Real-valued compact genetic algorithms for embedded microcontroller optimization. IEEE Trans Evol Comput 12(2):203–219CrossRefGoogle Scholar
  16. 16.
    Cupertino F, Mininno E, Naso D (2006) Elitist compact genetic algorithms for induction motor self-tuning control. In: Proceedings of the IEEE congress on evolutionary computation, pp 3057–3063Google Scholar
  17. 17.
    Cupertino F, Mininno E, Naso D (2007) Compact genetic algorithms for the optimization of induction motor cascaded control. In: Proceedings of the IEEE international conference on electric machines and drives, 1:82–87Google Scholar
  18. 18.
    Fossati L, Lanzi PL, Sastry K, Goldberg DE (2007) A simple real-coded extended compact genetic algorithm. In: Proceedings of the IEEE congress on evolutionary computation, pp 342–348Google Scholar
  19. 19.
    Lanzi P, Nichetti L, Sastry K, Goldberg DE (2008) Real-coded extended compact genetic algorithm based on mixtures of models. In: Linkage in evolutionary computation, vol 157 of studies in computational intelligence. Springer, pp 335–358Google Scholar
  20. 20.
    Mininno E, Neri F, Cupertino F, Naso D (2011) Compact differential evolution. IEEE Trans Evol Comput (to appear)Google Scholar
  21. 21.
    Neri F, Tirronen V (2010) Recent advances in differential evolution: a review and experimental analysis. Artif Intell Rev 33(1):61–106CrossRefGoogle Scholar
  22. 22.
    Neri F, Mininno E (2010) Memetic compact differential evolution for cartesian robot control. IEEE Comput Intell Mag 5(2):54–65CrossRefGoogle Scholar
  23. 23.
    Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13:398–417CrossRefGoogle Scholar
  24. 24.
    Tasoulis DK, Pavlidis NG, Plagianakos VP, Vrahatis MN (2004) Parallel differential evolution. In: Proceedings of the IEEE congress on evolutionary computation, pp 2023–2029Google Scholar
  25. 25.
    Weber M, Neri F, Tirronen V (2009) Distributed differential evolution with explorative-exploitative population families. Genet Program Evol Mach 10(4):343–371CrossRefGoogle Scholar
  26. 26.
    Weber M, Tirronen V, Neri F (2010) Scale factor inheritance mechanism in distributed differential evolution. Soft Comput Fusion Found Method Appl 14(11):1187–1207Google Scholar
  27. 27.
    Gautschi W (1972) Error function and fresnel integrals. In: Abramowitz M, Stegun IA (eds) Handbook of mathematical functions with formulas, graphs, and mathematical tables, Chap. 7. pp 297–309Google Scholar
  28. 28.
    Cody WJ (1969) Rational chebyshev approximations for the error function 23(107):631–637Google Scholar
  29. 29.
    Price KV, Storn R, Lampinen J (2005) Differential evolution: a practical approach to global optimization. Springer, BerlinzbMATHGoogle Scholar
  30. 30.
    Feoktistov V (2006) Differential evolution in search of solutions. SpringerGoogle Scholar
  31. 31.
    Lampinen J, Zelinka I (2000) On stagnation of the differential evolution algorithm. In: Oŝmera P (eds) Proceedings of 6th international mendel conference on soft computing, pp 76–83Google Scholar
  32. 32.
    Brest J, Greiner S, Bošković B, Mernik M, Žumer V (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657CrossRefGoogle Scholar
  33. 33.
    Zhang J, Sanderson AC (2009) Jade: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958CrossRefGoogle Scholar
  34. 34.
    Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y-P, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical Report 2005005, Nanyang Technological University and KanGAL, Singapore and IIT Kanpur, IndiaGoogle Scholar
  35. 35.
    Vesterstrøm J, Thomsen R (2004) A comparative study of differential evolution particle swarm optimization and evolutionary algorithms on numerical benchmark problems. In: Proceedings of the IEEE congress on evolutionary computation, 3:1980–1987Google Scholar
  36. 36.
    Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3:82–102CrossRefGoogle Scholar
  37. 37.
    Igel C, Suttorp T, Hansen N (2006) A computational efficient covariance matrix update and a (1 + 1)-CMA for evolution strategies. In: Proceedings of the genetic and evolutionary computation conference. ACM Press, pp 453–460Google Scholar
  38. 38.
    Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics Bull 1(6):80–83CrossRefGoogle Scholar
  39. 39.
    Yuan B, Gallagher M (2005) Experimental results for the special session on real-parameter optimization at cec 2005: a simple, continuous eda, pp 1792–1799Google Scholar
  40. 40.
    Molina D, Herrera F, Lozano M (2005) Adaptive local search parameters for real-coded memetic algorithm. In: Proceedings of the IEEE congress on evolutionary computation, pp 888–895Google Scholar
  41. 41.
    Noman N, Iba H (2008) Accelerating differential evolution using an adaptive local search. IEEE Trans Evol Comput 12(1):107–125CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Giovanni Iacca
    • 1
  • Ernesto Mininno
    • 1
  • Ferrante Neri
    • 1
    Email author
  1. 1.Department of Mathematical Information TechnologyUniversity of JyväskyläAgoraFinland

Personalised recommendations