Abstract
A modified version of particle swarm optimization algorithm is proposed for minimization of maximal real part of a polytopic system eigenvalues. New initialization procedure and special projection operation are introduced to keep all particles working effectively inside a simplex of feasible positions. The algorithm is tested on several benchmarks and statistical evidences for its’ high efficiency are provided.
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References
Lewis, A.S.: The mathematics of eigenvalue optimization. Math. Program., Ser. B 97, 155–176 (2003)
Chesi, G.: Measuring the Instability in Continuous-Time Linear Systems with Polytopic Uncertainty. In: 52nd IEEE Conference on Decision and Control, pp. 1131–1136 (2013)
Apkarian, P., Noll, D., Prot, O.: Trust region spectral bundle method for nonconvex eigenvalue optimization. SIAM. J. Optim. 19(1), 281–306 (2009)
Chen, X., Qi, H., Qi, L., Teo, K.L.: Smooth convex approximation to the maximum eigenvalue function. Jour. of Global Optimization 30, 253–270 (2004)
Blanco, A.M., Bandoni, J.A.: Eigenvalue and Singular Value Optimization. In: ENIEF 2003 - XIII Congreso sobre Métodos Numéricos y sus Aplicaciones, pp. 1256–1272 (2003)
Eberhart, R.C., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39–43. IEEE Service Center, Piscataway (1995)
Parsopoulos, K., Vrachatis, M.N.: Particle swarm optimization and intelligence: advances and applications, Hershey, New York (2009)
Parsopoulos, K.E., Vrahatis, M.N.: UPSO: A unified particle swarm optimization scheme. In: Proc. Int. Conf. Comput. Meth. Sci. Eng. (ICCMSE 2004). Lecture Series on Computer and Computational Sciences, vol. 1, pp. 868–873. VSP International Science Publishers, Zeist (2004)
Cao, Y.J.: Eigenvalue optimization problems via evolutionary programming. Electronics Letters 33(7), 642–643 (1997)
Kabziński, J.: Swarm Capability of Finding Eigenvalues. In: Ramsay, A., Agre, G. (eds.) AIMSA 2012. LNCS, vol. 7557, pp. 172–177. Springer, Heidelberg (2012)
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Kabziński, J., Kacerka, J. (2014). Optimization of Polytopic System Eigenvalues by Swarm of Particles. In: Agre, G., Hitzler, P., Krisnadhi, A.A., Kuznetsov, S.O. (eds) Artificial Intelligence: Methodology, Systems, and Applications. AIMSA 2014. Lecture Notes in Computer Science(), vol 8722. Springer, Cham. https://doi.org/10.1007/978-3-319-10554-3_17
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DOI: https://doi.org/10.1007/978-3-319-10554-3_17
Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-10554-3
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