Differential Evolution for High-Dimensional Function Optimization

Notes

• DE:
  • parameters:

    • : vector dimension;

    • : population size;

    • : crossover rate;

    • : scaling factor;

  • citations: 1, 2, 5, 6, 7, 8;
• CC:
  • problem decomposition;
  • subcomponent optimization;
  • cooperative combination;
• scheme DE/rand/1/bin:
  • mutation:

    • differential variation: ;

    • ;

  • crossover:

    • ;

  • selection:

    • ;

  • where:

    • : uniform random between and ;

  • citations: 1, 8;
• NSDE the same as DE/rand/1/bin but with the following amendments:
  • mutation:

    • ;

  • where:

    • : Gaussian random with mean and standard deviation ;

    • : Cauchy random with scale parameter ;

  • citations: 14, 15, 16, 17;
• SaNSDE:

  • auto-adapted parameters: , ;

  • citations: 5, 8;
• DECC:
  • parameters:

    • : fitness evaluations;

    • : sub-component dimension (between 30 and 100);

  • DECC-I:
    • the parameter permutation is constant throughout the cycles;
    • a weight is evolved (in parallel with the components) for the components;
  • DECC-II:
    • the permutation is randomized at the beginning of each cycle;
    • there is no need for the component weights;
• non-separable functions:
  • citations: 9, 10;
• benchmarks without DECC:
  • parameters:

    • : 30;

    • runs: 25;
  • conclusion: SaNSDE better than NSDE; NSDE better than DE;
  • citations: 15, 18, 17, 19;
• benchmarks with DECC:
  • parameters:

    • : 500 or 1000;

    • : 100 (fixed);

    • : 2m or 5m;

    • runs: 25;

  • evaluation: the fitness of an individual was estimated by combining it with the current best individuals from other subcomponents;

  • conclusion: DECC-I is better (not by much) than DECC-II;
  • citations: 9, 10;

Citations

• 1: Differential Evolution -- A Simple and Efficient Heuristic Strategy for Global Optimization over Continuous Spaces; R. Storn, K. Price; 1997;

• 2: A Comparative Study of Differential Evolution, Particle Swarm Optimization, and Evolutionary Algorithms on Numerical Benchmark Problems; J. Vesterstrom, R. Thomsen; 2004;

• 5: A Parameter Study for Differential Evolution; R. Gamperle, S. D. Muller, P. Koumoutsakos; 2002;

• 6: Critical values for the control parameters of differential evolution algorithms, D. Zaharie; 2002;

• 7: Self-adaptive Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems; J. Brest; 2006;

• 8: Self-adaptive Differential Evolution Algorithm for Numerical Optimizations; A. K. Qin, P. N. Suganthan; 2005;

• 9: Scaling Up Fast Evolutionary Programming with Cooperative Coevolution; Y. Liu, Q. Zhao, T. Higuchi; 2001;

• 10: A cooperative co-evolutionary approach to function optimization; A. M. Potter, K. A. De Jong; 2994;

• 11: A blended population approach to cooperative coevolution for decomposition of complex problems; D. Sofge, K. A. De Jong, A. Schultz; 2002;

• 13: Cooperative Co-evolutionary Differential Evolution for Function Optimization; Y. Shi, H. Teng, Z. Li; 2005;

• 18: Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization; P. N. Saughatan; 2005;

• 19: Real-Parameter Optimization with Differential Evolution; J. Ronkkonen, S. Kukkonen, K. V. Price; 2005;