Differential evolution on the CEC-2013 single-objective continuous optimization testbed

Differential evolution (DE) is one of the most powerful continuous optimizers in the field of evolutionary computation. This work systematically benchmarks a classic DE algorithm (DE/rand/1/bin) on the CEC-2013 single-objective continuous optimization testbed. We report, for each test function at different problem dimensionality, the best achieved performance among a wide range of potentially effective parameter settings. It reflects the intrinsic optimization capability of DE/rand/1/bin on this testbed and can serve as a baseline for performance comparison in future research using this testbed. Furthermore, we conduct parameter sensitivity analysis using advanced non-parametric statistical tests to discover statistically significantly superior parameter settings. This analysis provides a statistically reliable rule of thumb for choosing the parameters of DE/rand/1/bin to solve unseen problems. Moreover, we report the performance of DE/rand/1/bin using one superior parameter setting advocated by parameter sensitivity analysis.

[1]  Francisco Herrera,et al.  A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization , 2009, J. Heuristics.

[2]  Jouni Lampinen,et al.  A Fuzzy Adaptive Differential Evolution Algorithm , 2005, Soft Comput..

[3]  N. Hansen,et al.  Real-Parameter Black-Box Optimization Benchmarking: Experimental Setup , 2010 .

[4]  Qingfu Zhang,et al.  Differential Evolution With Composite Trial Vector Generation Strategies and Control Parameters , 2011, IEEE Transactions on Evolutionary Computation.

[5]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[6]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[7]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[8]  Mehmet Fatih Tasgetiren,et al.  Differential evolution algorithm with ensemble of parameters and mutation strategies , 2011, Appl. Soft Comput..

[9]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[10]  Xin Yao,et al.  Scalability of generalized adaptive differential evolution for large-scale continuous optimization , 2010, Soft Comput..

[11]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[12]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[13]  Maliha S. Nash,et al.  Handbook of Parametric and Nonparametric Statistical Procedures , 2001, Technometrics.

[14]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[15]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[16]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[17]  Amit Konar,et al.  Two improved differential evolution schemes for faster global search , 2005, GECCO '05.

[18]  Andries Petrus Engelbrecht,et al.  Self-adaptive Differential Evolution , 2005, CIS.