×

Experimental investigation of local searches for optimization of grillage-type foundations. (English) Zbl 1156.90376

Čiegis, Raimondas (ed.) et al., Parallel scientific computing and optimization. Advances and applications. New York, NY: Springer (ISBN 978-0-387-09706-0/hbk). Springer Optimization and Its Applications 27, 103-112 (2009).
Summary: In grillage-type foundations, beams are supported by piles. The main goal of engineering design is to achieve the optimal pile placement scheme in which the minimal number of piles is used and all the reactive forces do not exceed the allowed values. This can be achieved by searching for the positions of piles where the difference between the maximal reactive forces and the limit magnitudes of reactions for the piles is minimal. In this study, the values of the objective function are given by a separate modeling package. Various algorithms for local optimization have been applied and their performance has been investigated and compared. Parallel computations have been used to speed-up experimental investigation.
For the entire collection see [Zbl 1151.65001].

MSC:

90B40 Search theory
90-08 Computational methods for problems pertaining to operations research and mathematical programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Arfken, G., Weber, H.: Mathematical Methods for Physicists, 6th edn., chap. 7.3, pp. 489-496. Academic Press (2005) · Zbl 1066.00001
[2] Baravykaitė, M.; Belevičius, R.; Čiegis, R., One application of the parallelization tool of master-slave algorithms, Informatica, 13, 4, 393-404 (2002) · Zbl 1031.68146
[3] Belevičius, R.; Valentinavičius, S.; Michnevič, E., Multilevel optimization of grillages, Journal of Civil Engineering and Management, 8, 2, 98-103 (2002)
[4] Broyden, C. G., The convergence of a class of double-rank minimization algorithms 1. General considerations, IMA Journal of Applied Mathematics, 6, 1, 76-90 (1970) · Zbl 0223.65023
[5] Čiegis, R.: On global minimization in mathematical modelling of engineering applications. In: A. Törn, J. Žilinskas (eds.) Models and Algorithms for Global Optimization, Springer Optimization and Its Applications, vol. 4, pp. 299-310. Springer (2007) · Zbl 1267.90182
[6] Čiegis, R.; Baravykaitė, M., Belevičius, R.: Parallel global optimization of foundation schemes in civil engineering, Lecture Notes in Computer Science, 3732, 305-312 (2006) · doi:10.1007/11558958_36
[7] Davidon, W. C., Variable metric method for minimization, SIAM Journal on Optimization, 1, 1, 1-17 (1991) · Zbl 0752.90062 · doi:10.1137/0801001
[8] Erdelyi, A.: Asymptotic Expansions. Dover (1956) · Zbl 0070.29002
[9] Fletcher, R., A new approach to variable metric algorithms, Computer Journal, 13, 3, 317-322 (1970) · Zbl 0207.17402 · doi:10.1093/comjnl/13.3.317
[10] Fletcher, R.: Practical Methods of Optimization, 2nd edn. John Wiley & Sons (2000) · Zbl 0905.65002
[11] Fletcher, R.; Powell, M. J.D., A rapidly convergent descent method for minimization, Computer Journal, 6, 1, 163-168 (1963) · Zbl 0132.11603
[12] Goldfarb, D., A family of variable-metric methods derived by variational means, Mathematics of Computation, 24, 109, 23-26 (1970) · Zbl 0196.18002 · doi:10.2307/2004873
[13] Lagarias, J. C.; Reeds, J. A.; Wright, M. H.; Wright, P. E., Convergence properties of the Nelder-Mead simplex method in low dimensions, SIAM Journal of Optimization, 9, 1, 112-147 (1998) · Zbl 1005.90056 · doi:10.1137/S1052623496303470
[14] Morse, P. M.; Feshbach, H., Methods of Theoretical Physics, chap. 4.6, 434-443 (1953), New York: McGraw-Hill, New York · Zbl 0051.40603
[15] Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd edn. Cambridge University Press (1992) · Zbl 0778.65002
[16] Shanno, D. F., Conditioning of Quasi-Newton methods for function minimization, Mathematics of Computation, 24, 111, 647-656 (1970) · Zbl 0225.65073 · doi:10.2307/2004840
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.