Global optimization algorithms

The example considered here involves the use of a branch-and-bound global optimization algorithm known as aBB (Adjiman et al., 1998) as carried out by Klepeis et al. (1998) who calculated the minimum energy for a number of peptides. To simplify an inherently very complicated optimization problem, particularly in view of the limited data known about solvation parameters, they formulated the energy minimization... 

Floudas CA, Pardalos PM. A Collection of Test Problems for Constrained Global Optimization Algorithms. New York Springer-Verlag, 1990. Stephanopoulos G. Chemical Process Control. Englewoods Cliffs, NJ Prentice Hall, 1984. 

Remark 1 The mathematical model is an MINLP problem since it has both continuous and binary variables and nonlinear objective function and constraints. The binary variables participate linearly in the objective and logical constraints. Constraints (i), (iv), (vii), and (viii) are linear while the remaining constraints are nonlinear. The nonlinearities in (ii), (iii), and (vi) are of the bilinear type and so are the nonlinearities in (v) due to having first-order reactions. The objective function also features bilinear and trilinear terms. As a result of these nonlinearities, the model is nonconvex and hence its solution will be regarded as a local optimum unless a global optimization algorithm is utilized. 

C. A. Floudas and V. Visweswaran. A global optimization algorithm (GOP) for certain classes of nonconvex NLPs I. theory. Comp. Chem. Eng., 14 1397, 1990. 

P. M. Pardalos and J. B. Rosen. Constrained global optimization Algorithms and applications, volume 268 of Lecture Notes in Computer Science. Springer Verlag, Berlin, Germany, 1987. 

S. Smith, E. Eskow, and R. B. Schnabel, Adaptive Asynchronous Stochastic Global Optimization Algorithms for Sequential and Parallel Computation, Computer Science Report CV-CS-449-89. University of Colorado, Boulder, 1989. 

The global optimization algorithm described above uses a spatial branch-and-bound procedure (steps 2 to 4). Like many branch-and-bound methods, the algorithm consists of a set of branching rules, together with upper bounding and lower bounding procedures. 

Floudas, C. A., and Visweswaran, V. A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs-I Theory, Comput. Chem. Eng. 4, 1397-1417 (1990). 

Quesada, 1., and Grossmann, I. E. Global Optimization Algorithm of Process Networks with Multicomponent Flows." Comput. Chem. Eng. 19, 1219-1242 (1995a). 

Altomare et al. combined Z)M with SA. The peaks of the electron density map provided by DM are used to reduce the number of DOFs of the global optimization algorithm according to three protocols ... 

DST methods are particularly competitive for organic compounds, which are more resistant to the traditional approaches and whose structural models can be easily guessed. At present, the complexity of crystal structures solved by direct-space methods is essentially limited by the number of DOFs that can be handled by the global optimization algorithms within a reasonable amount of time. In prospect, improvement of both search algorithms and computer power may overcome this limitation. The major pitfalls for the use of DST are (a) they are time consuming (b) they are dependent on the existence of reliable prior structural information. Partially incorrect models may compromise the success of the procedure independent of the computer time spent (c) they are sensitive to the accuracy of the peak profile parameterization through peak-shape and peak-width functions. ... 

As a test of the computational methods, we used a six-hump "camel-back" function as the terrain on which we will find a mountain pass. The function is used to test many global optimization algorithm and has well known mountain passes. The function takes the form... 

Lee S. and Grossmann l.E. 2001. A global optimization algorithm for nonconvex generalized disjunctive programming and applications to process systems, Comput. Chem. Eng., 25,1675-1697. 

Qnesada I. and Grossmann I.E. 1995. A global optimization algorithm for hnear fractional and bilinear programs, J. Global Optimization, 6(1), 39-76. 

Mockus, J., Eddy, W., Mockus, A., Mockus, L. and Reklaitis, G. Bayesian Heuristic Approach to Dsicrete and Global Optimization Algorithm, Ksualization, Software, and Applications. Kluwer Academic Publishers, Dordrecht, The Netholands, 1996. 

Castro, P.M. and Teles, J.P. (2013) Comparison of global optimization algorithms for the design of water using networks. Computers and Chemical Engineering, 52, 249-261. 

DE is st(x hastic global optimization algorithm derived from the concept of natural selection and evolution [32]. It uses a special kind of differential operator, which invoked to create new offspring from parent chromosomes, to instead the classical crossover or mutation. DE can be applied to solve a variety of optimization problems that are not well suited for standard optimization algorithms. 

The Simulated Annealing (SA) optimization routine implements the continuous simulated annealing global optimization algorithm (Corana, Marchesi, Martini, Ridella, 1987). 

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