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http://dx.doi.org/10.3795/KSME-A.2010.34.2.191

Development of a Branch-and-Bound Global Optimization Based on B-spline Approximation  

Park, Sang-Kun (Dept. of Mechanical Engineering, Chungju National Univ.)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.34, no.2, 2010 , pp. 191-201 More about this Journal
Abstract
This paper presents a new global optimization algorithm based on the branch-and-bound principle using Bspline approximation techniques. It describes the algorithmic components and details on their implementation. The key components include the subdivision of a design space into mutually disjoint subspaces and the bound calculation of the subspaces, which are all established by a real-valued B-spline volume model. The proposed approach was demonstrated with various test problems to reveal computational performances such as the solution accuracy, number of function evaluations, running time, memory usage, and algorithm convergence. The results showed that the proposed algorithm is complete without using heuristics and has a good possibility for application in large-scale NP-hard optimization.
Keywords
Global Optimization; Branch-and-Bound; B-spline Approximation;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By SCOPUS : 0
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1 Floudas, C.A., 2007, “Overview of aBB-based Approaches In Deterministic Global Optimization,” Workshop on Global Optimization, Imperial College London, 15-17 Dec.
2 Al-Khayyal, F.A. and Sherali, H.D., 2000, “On finitely terminating branch-and-bound algorithms for some global optimization problems,” SIAM J. Optimization, Vol.10, pp.1049-1057.   DOI   ScienceOn
3 Audet, C., Hansen, P., Jaumard, B., and Savard, G., 2000, “A Branch and Cut Algorithm for Nonconvex Quadratically Constrained Quadratic Programming,” Math. Programming, Vol.87, pp.131-152.   DOI
4 Park, S, 2009, “A Rational B-spline Hypervolume for Multidimensional Multivariate Modeling,” Journal of Mechanical Science and Technology, Vol.23, pp.1967-1981.   DOI   ScienceOn
5 Piegl, L. and Tiller, W., 1995, The NURBS Book, Springer-Verlag.
6 De Boor, C., 1978, A Practical Guide to Splines, New York, Springer-Verlag.
7 Stein, M., 1987, “Large Sample Properties of Simulations Using Latin Hypercube Sampling,” Technometrics, Vol.29, pp.143-151.   DOI
8 Huyer, W. and Neumaier, A., 1999, "Global Optimization by Multilevel Coordinate Search," Journal of Global Optimization, Vol. 14, pp.331-355.   DOI
9 Neumaier, A., 2004, “Complete Search in Continuous Global Optimization and Constraint Satisfaction,” pp.1-99 in: Acta Numerica, Cambridge Univ. Press.
10 Pinter, J.D., 1996, Global Optimization in Action, Kluwer, Dordrecht.
11 Floudas, C.A., 2000, Deterministic Global Optimization: Theory, Methods and Applications, Kluwer Academic Publishers.
12 Neumaier, A., 2004, “Complete Search in Continuous Global Optimization and Constraint Satisfaction,” in: Acta Numerica, Cambridge Univ. Press, pp.1-99.