A derivation of the number of minima of the Griewank function

Applied Mathematics and Computation

Volumn 204, Issue 2, 2008, Pages 694-701

  Cho, Huidae ^a   Olivera, Francisco ^a   Guikema, Seth D ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b Johns Hopkins University   (United States)

Author keywords

Griewank function; Local minima; Multi modal optimization; Optimization

Indexed keywords

LEARNING SYSTEMS; NUMERICAL METHODS;

GRIEWANK FUNCTION; LOCAL MINIMA; MULTI-MODAL OPTIMIZATION; OPTIMIZATION;

INFORMATION DISSEMINATION;

EID: 53449096187     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.07.009     Document Type: Article

References (15)

1. Griewank A.O. Generalized descent for global optimization. Journal of Optimization Theory and Applications 34 1 (1981) 11-39
2. J. Kennedy, Stereotyping: Improving particle swarm performance with cluster analysis, in: Proceedings of the Congress on Evolutionary Computation, IEEE Service Center, Piscataway, New Jersey, 2000, pp. 1507-1512.
3. T. Krink, J.S. Vesterstrøm, J. Riget, Particle swarm optimisation with spatial particle extension, in: Proceedings of the Congress on Evolutionary Computation, vol. 2, Honolulu, Hawaii, 2002, pp. 1474-1479.
4. J. Riget, J.S. Vesterstrøm, A diversity-guided particle swarm optimizer-the ARPSO, Technical Report 2002-02, Department of Computer Science, Aarhus Universitet, Bgn. 540, Ny Munkegade DK-8000 Aarhus C, Denmark, 2002.
5. X.-F. Xie, W.-J. Zhang, Z.-L. Yang, A dissipative particle swarm optimization, in: Proceedings of the Congress on Evolutionary Computation, Honolulu, Hawaii, 2002, pp. 1456-1461.
6. R. Brits, A.P. Engelbrecht, F. van den Bergh, Scalability of Niche PSO, in: Proceedings of the 2003 IEEE Swarm Intelligence Symposium, 2003, pp. 228-234. .
7. Locatelli M. A note on the Griewank test function. Journal of Global Optimization 25 (2003) 169-174
8. N. Khemka, C. Jacob, Exploratory toolkit for evolutionary and swarm-based optimization, in: Proceedings of the 6th International Mathematica Symposium, Banff, Alberta, Canada, 2004.
9. He S., Wu Q.H., Wen J.Y., Saunders J.R., and Paton R.C. A particle swarm optimizer with passive congregation. BioSystems 78 (2004) 135-147
10. Acan A., and Gunay A. Enhanced particle swarm optimization through external memory support. in: Proceedings of the Congress on Evolutionary Computation 2 (2005) 1875-1882
11. Monson C.K., and Seppi K.D. Bayesian optimization models for particle swarms. Proceedings of the Genetic and Evolutionary Computation Conference (2005), ACM Press, NY, New York 193-200
12. Meissner M., Schmuker M., and Schneider G. Optimized particle swarm optimization (OPSO) and its application to artificial neural network training. BMC Bioinformatics 7 (2006) 125-136
13. Monson C.K., and Seppi K.D. Adaptive diversity in PSO. Proceedings of the Genetic and Evolutionary Computation Conference (2006), ACM Press, NY, New York 59-66
14. Brits R., Engelbrecht A.P., and van den Bergh F. Locating multiple optima using particle swarm optimization. Applied Mathematics and Computation 189 (2007) 1859-1883
15. Wang X., Gao X.Z., and Ovaska S.J. A hybrid optimization algorithm based on ant colony and immune principles. International Journal of Computer Science & Applications 4 3 (2007) 30-44