Adjiman C.S., Androulakis I.P., and Floudas C.A., 1998a, A global optimization method, BB, for general twice--differentiable NLPs -- II. Implementation and computational results. Comp. Chem. Engng. 22, 1159--1178.  Home/Search   Document Not in Database   Summary   Related Articles   Check

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Adjiman C.S., Androulakis I.P., and Floudas C.A., 1998a, A global optimization method, BB, for general twice--differentiable NLPs -- II. Implementation and computational results. Comp. Chem. Engng. 22, 1159--1178.

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Adjiman, C. S.; Androulakis, I. P.; Floudas, C. A. A Global Optimization Method, ffBB, for General Twice--Differentiable NLPs -- II. Implementation and Computational Results Computers chem. Engng. 1998, in press.

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Adjiman C.S., Androulakis I.P., and Floudas C.A., 1997b, A global optimization method, ffBB, for general twice-- differentiable NLPs -- II. implementation and computational results. Computers chem. Engng., accepted for publication.

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Adjiman C.S., Androulakis I.P., and Floudas C.A., 1997a, A global optimization method, ffBB, for general twice--differentiable NLPs -- II. Implementation and computational results.

....optimality guarantees of the algorithm. However, their accuracy and computational requirements differ so that no method can be shown to perform consistently better than others for all problems. Their use is illustrated on an unconstrained and a constrained example. The second part of this paper (Adjiman et al. 1997) is devoted to the discussion of issues related to the implementation of the ffBB algorithm and to extensive computational studies illustrating its potential applications. 1 Institut fur Mathematik,Universitat Wien, Strudlhofgasse 4, A 1090 Wien, Austria 2 Author to whom all correspondence ....

....example, the scaled Gerschgorin approach (Method II.1) with d i = x U i Gamma x L i ) gives the best results both in terms of number of iterations and CPU time. Its performance and that of other methods are further assessed by solving a variety of problems presented in Part II of this paper (Adjiman et al. 1997). Single Up. One Up. Iter Method Iter. CPU t U Iter. CPU t U sec. sec. Gerschgorin (I.1) 74 37.5 0.5 31 41.6 0.0 E Matrix (I.2) E = 0 61 30.6 1.6 25 37.2 0.2 E Matrix (I.2) E = diag( DeltaH) 61 29.2 1.0 25 35.4 0.1 Mori Kokame (I.3) 69 32.8 1.9 25 31.5 0.2 Lower bounding Hessian (I.4) ....

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C. S. Adjiman, I. P. Androulakis, and C. A. Floudas. A Global Optimization Method, ffBB, for General Twice--Differentiable NLPs -- II. Implementation and Computational Results. accepted for publication, 1997.

....problems, including the effects of solvation, through the use of a deterministic global optimization algorithm. This branch and bound based global optimization algorithm, known as ffBB, is applicable to a large class of nonlinear optimization problems that have twice differentiable functions [1, 2, 3, 4, 5, 6]. MODELING Potential Models Many models have been developed using a classical description of molecules in terms of atomic bonds and effective interactions. In general, these models, also known as force fields, are expressed as summations of empirically derived potential functions. Thermodynamic ....

.... with twice differentiable functions [12] The application of this algorithm to the minimization of potential energy functions was first introduced for microclusters [21, 22] and small acyclic molecules [23, 24] The ffBB approach has also been extended to constrained optimization problems [2, 3, 4, 6]. In more recent work, the algorithm has been shown to be successful for isolated peptide systems [7, 25] Minimization of Energy using ffBB The ffBB global optimization algorithm effectively brackets the global minimum solution by developing converging lower and upper bounds. These bounds are ....

C. S. Adjiman, I. P. Androulakis and C. A. Floudas, A global optimization method, ffBB, for general twice-differentiable NLPs - II. Implementation and computational results, Comput. Chem. Eng., (accepted for publication), (1997).

....of rules have been developed for the selection of a continuous branching variable. Their aim is to determine which variable is responsible for the largest separation distances between the convex underestimating functions and the original nonconvex functions. These efficient rules are exposed in [AAF7b]. 4.1.3. Variable Bound Updates. Variable bound updates performed before the generation of the convex MINLP have been found to greatly enhance the speed of convergence of the ffBB algorithm for continuous problems [AAF7b] For continuous variables, the variable bounds are updated by minimizing or ....

....and the original nonconvex functions. These efficient rules are exposed in [AAF7b] 4.1.3. Variable Bound Updates. Variable bound updates performed before the generation of the convex MINLP have been found to greatly enhance the speed of convergence of the ffBB algorithm for continuous problems [AAF7b]. For continuous variables, the variable bounds are updated by minimizing or maximizing the chosen variable subject to the convexified constraints being satisfied. In spite of its computational cost, this procedure often leads to significant improvements in the quality of the underestimators and ....

C. S. Adjiman, I. P. Androulakis, and C. A. Floudas, A global optimization method, ffBB, for general twice--differentiable NLPs -- II. Implementation and computational results, accepted for publication, 1997b.

....as stochastic. Two smoothing methods, namely the diffusion equation and packet annealing techniques, claim to be deterministic. However, as will be shown, a number of approximations must be made to practically implement these methods. Another exception, the ffBB (branch and bound) approach [2, 3, 4, 5, 6, 9], has specifically been developed to deterministically treat global optimization problems such as those found in protein folding and peptide docking. The following discussion is based on a classification of the global optimization approaches into five areas combinatorial, genetic algorithms, ....

....heuristic methods in a branch and bound framework should prove to increase the efficiency in locating global minimum energy conformations. A deterministic branch and bound method, ffBB, has been developed and applied to general global optimization problems involving twice differentiable functions [2, 3, 4, 5, 6, 9]. The application of the ffBB algorithm to the global minimization of energy functions was first introduced for microclusters [108, 109] and small acyclic molecules [110, 111] The approach has also been extended to general constrained optimization problems [3, 4, 5, 6, 9] The ffBB global ....

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C. S. Adjiman, I. P. Androulakis and C. A. Floudas, A global optimization method, ffBB, for general twice-differentiable NLPs - II. Implementation and computational results, Comput. Chem. Eng., (in press), (1998).

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Adjiman C.S., Androulakis I.P., and Floudas C.A., 1997b, A global optimization method, ffBB, for general twice--differentiable NLPs -- II. Implementation and computational results. in preparation.

....of rules have been developed for the selection of a continuous branching variable. Their aim is to determine which variable is responsible for the largest separation distances between the convex underestimating functions and the original nonconvex functions. These efficient rules are exposed in [AAF7b] 4.5.3 Variable Bound Updates Variable bound updates performed before the generation of the convex MINLP have been found to greatly enhance the speed of convergence of the ffBB algorithm for continuous problems [AAF7b] For continuous variables, the variable bounds are updated by minimizing ....

....and the original nonconvex functions. These efficient rules are exposed in [AAF7b] 4.5. 3 Variable Bound Updates Variable bound updates performed before the generation of the convex MINLP have been found to greatly enhance the speed of convergence of the ffBB algorithm for continuous problems [AAF7b] For continuous variables, the variable bounds are updated by minimizing or maximizing the chosen variable subject to the convexified constraints being satisfied. In spite of its computational cost, this procedure often leads to significant improvements in the quality of the underestimators ....

C. S. Adjiman, I. P. Androulakis, and C. A. Floudas, A global optimization method, ffBB, for general twice--differentiable NLPs -- II. Implementation and computational results, accepted for publication, 1997b.

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C. S. Adjiman, I. P. Androulakis, and C. A. Floudas. A Global Optimization Method, ffBB, for General Twice--Differentiable NLPs -- II. Implementation and Computational Results. Comput. chem. engng., 22(9):1159--1179, 1998b.

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