# Differential Evolution for High-Dimensional Function Optimization

## Notes

- DE:
- parameters:
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: vector dimension;latex error! exitcode was 2 (signal 0), transscript follows:

: population size;latex error! exitcode was 2 (signal 0), transscript follows:

: crossover rate;latex error! exitcode was 2 (signal 0), transscript follows:

: scaling factor;

- citations: 1, 2, 5, 6, 7, 8;

- parameters:
- CC:
- problem decomposition;
- subcomponent optimization;
- cooperative combination;

- scheme DE/rand/1/bin:
- mutation:
differential variation:

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;latex error! exitcode was 2 (signal 0), transscript follows:

;

- crossover:
latex error! exitcode was 2 (signal 0), transscript follows:

;

- selection:
latex error! exitcode was 2 (signal 0), transscript follows:

;

- where:
latex error! exitcode was 2 (signal 0), transscript follows:

: uniform random betweenlatex error! exitcode was 2 (signal 0), transscript follows:

andlatex error! exitcode was 2 (signal 0), transscript follows:

;

- citations: 1, 8;

- mutation:
- NSDE the same as DE/rand/1/bin but with the following amendments:
- mutation:
latex error! exitcode was 2 (signal 0), transscript follows:

;

- where:
latex error! exitcode was 2 (signal 0), transscript follows:

: Gaussian random with meanlatex error! exitcode was 2 (signal 0), transscript follows:

and standard deviationlatex error! exitcode was 2 (signal 0), transscript follows:

;latex error! exitcode was 2 (signal 0), transscript follows:

: Cauchy random with scale parameterlatex error! exitcode was 2 (signal 0), transscript follows:

;

- citations: 14, 15, 16, 17;

- mutation:
- SaNSDE:
auto-adapted parameters:

latex error! exitcode was 2 (signal 0), transscript follows:

,latex error! exitcode was 2 (signal 0), transscript follows:

;- citations: 5, 8;

- DECC:
- parameters:
latex error! exitcode was 2 (signal 0), transscript follows:

: fitness evaluations;latex error! exitcode was 2 (signal 0), transscript follows:

: 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;

- parameters:
- non-separable functions:
- citations: 9, 10;

- benchmarks without DECC:
- parameters:
latex error! exitcode was 2 (signal 0), transscript follows:

: 30;- runs: 25;

- conclusion: SaNSDE better than NSDE; NSDE better than DE;
- citations: 15, 18, 17, 19;

- parameters:
- benchmarks with DECC:
- parameters:
latex error! exitcode was 2 (signal 0), transscript follows:

: 500 or 1000;latex error! exitcode was 2 (signal 0), transscript follows:

: 100 (fixed);latex error! exitcode was 2 (signal 0), transscript follows:

: 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;

- parameters:

## 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;