Article Outline
Introduction
Formulation
Methods
A Global Terrain Method for Optimization at the Small Length Scale
A Funneling Method for Optimization at the Large Length Scale
A Multi-Scale Global Optimization Method
Application
Small Scale Terrain Optimization
Large Scale Funneling Optimization
Robustness
Reliability – Avoiding Traps at Local Minima
References
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Aluffi-Pentini F, Parisi V, Zirilli F (1985) Global optimization and stochastic differential equations. J Opt Theory Appl 47:1–16
Bahren J, Protopopescu V (1996) Generalized TRUST algorithms for global optimization. In: Floudas CA, Pardalos PM (eds) State of the Art in Global Optimization. Kluwer, Dordrecht, pp 163–180
Baker J (1986) An algorithm for the location of transition states. J Comput Chem 7:385–395
Bilbro GL (1994) Fast stochastic global optimization. IEEE Trans Sys Man Cyber 4:684–689
Cerjan CJ, Miller WH (1981) On finding transition states. J Chem Phys 75:2800–2806
Deaven DM, Tit N, Morris JR, Ho KM (1996) Structural optimization of Lennard-Jones clusters by a genetic algorithm. Chem Phys Lett 256:195–200
DeJong K (1975) An analysis of the behavior of a class of genetic adaptive systems. Ph.D. Thesis, Univ. of Michigan, Ann Arbor, Princeton
Doye JPK, Miller MA, Wales DJ (1999) Evolution of the potential energy surface with size for Lennard-Jones clusters. J Chem Phys 111:8417–8428
Doye JPK, Wales DJ (2002) Saddle points and dynamics of Lennard-Jones clusters, solids and supercooled liquids. J Chem Phys 116:3777–3788
Gibson KD, Scheraga HA (1987) Revised algorithm for the build-up procedure for predicting protein conformation by energy minimization. J Comput Chem 8:826–834
Gregurick SK, Alexander MH, Hartke B (1996) Global geometry optimization of (Ar) n and B(Ar) n clusters using a modified genetic algorithm. J Chem Phys 104:2684–2691
Hansen ER (1980) Global optimization using interval analysis – The multidimensional case. Numer Math 34:247–270
Henkelman G, Johannesson G, Jonsson H (2000) Methods for finding saddle points and minimum energy paths. In: Schwartz SD (ed) Progress in Theoretical Chemistry and Physics. Kluwer, Dordrecht, 5:269–300
Holland JH (1992) Genetic algorithms. Sci Am 267:66
Jones DT, Taylor WR, Thornton JM (1992) A new approach to protein folding recognition. Nature 358:86–89
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680
Levy AV, Montalvo A (1985) The tunneling algorithm for the global minimization of functions. SIAM J Sci Stat Comp 6:15–29
Lucia A, Yang F (2002) Global terrain methods. Comput Chem Eng 26:529–546
Lucia A, Yang F (2003) Multivariable terrain methods. AIChE J 49:2553–2563
Lucia A, DiMaggio PA, Depa P (2004) A geometric terrain methodology for global optimization. J Global Optim 29:297–314
Lucia A, DiMaggio PA, Depa P (2004) Funneling algorithms for multi-scale optimization on rugged terrains. Ind Eng Chem Res 43:3770–3781
Maranas CD, Floudas CA (1992) A global optimization approach to Lennard-Jones microclusters. J Chem Phys 97:7667–7678
Maranas CD, Floudas CA (1995) Finding all solutions to nonlinearly constrained systems of equations. J Global Optim 7:143–182
Matro A, Freeman DL, Doll JD (1994) Locating transition states using double-ended classical trajectories. J Chem Phys 101:10458–10463
Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092
Muller K, Brown LD (1979) Location of saddle points and minimum energy paths by a constrained simplex optimization procedure. Theoret Chim Acta 53:75–93
Niesse JA, Mayne HR (1996) Global geometry optimization of atomic clusters using a modified genetic algorithm in space-fixed coordinates. J Chem Phys 105:4700–4706
Onuchic JN, Luthey-Schulten Z, Wolynes PG (1997) Theory of protein folding: the energy landscape perspective. Annu Rev Phys Chem 48:545–600
Piela L, Kostrowicki J, Scheraga HA (1989) The multiple minima problem in conformational analysis of molecules. Deformation of the potential energy hypersurface by the diffusion equation method. J Phys Chem 93:3339–3346
Pincus MR, Klausner RD, Scheraga HA (1982) Calculation of the three dimensional structure of the membrane-bound portion of melittin from its amino acid sequence. Proc Natl Acad Sci USA 79:5107–5110
Scheraga HA (1974) Prediction of protein conformation. In: Anfinsen CB, Schechter AN (eds) Current Topics in Biochemistry. Acad Press, New York, p 1
Schnepper CA, Stadtherr MA (1996) Robust process simulation using interval methods. Comput Chem Eng 20:187–199
Sevick EM, Bell AT, Theodorou DN (1993) A chain of states method for investigating infrequent events in processes occurring in multistate, multidimensional systems. J Chem Phys 98:3196–3212
Sun AC, Seider WD (1992) Homotopy-continuation algorithm for global optimization. In: Floudas CA, Pardalos PM (eds) Recent Advances in Global Optimization. Princeton Univ Press, Princeton, pp 561–592
Wales DJ, Doye JPK (1997) Global optimization by basin hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J Phys Chem A 101:5111–5116
Westerberg KM, Floudas CA (1999) Locating all transition states and studying the reaction pathways of potential energy surfaces. J Chem Phys 110:9259–9295
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
Lucia, A. (2008). Multi-Scale Global Optimization Using Terrain/Funneling Methods . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_434
Download citation
DOI: https://doi.org/10.1007/978-0-387-74759-0_434
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-74758-3
Online ISBN: 978-0-387-74759-0
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering