Deterministic global algorithm

We start with continuous variable optimization and consider in the next section the solution of NLP problems with differentiable objective and constraint functions. If only local solutions are required for the NLP problem, then very efficient large-scale methods can be considered. This is followed by methods that are not based on local optimality criteria we consider direct search optimization methods that do not require derivatives as well as deterministic global optimization methods. Following this, we consider the solution of mixed integer problems and outline the main characteristics of algorithms for their solution. Finally, we conclude with a discussion of optimization modeling software and its implementation on engineering models. 

With even fewer runs relative to the number of input variables, Bettonvil and Kleijnen (1996) used a sequential bifurcation algorithm (see Chapter 13) to analyze a large deterministic global-climate model. The output is the worldwide CO2 circulation in the year 2100. The model has 281 input variables, 15 of which were identified as important after 154 runs. The sequential bifurcation algorithm makes several strong assumptions to enable an experiment with fewer runs than input variables (a supersaturated design—see Chapter 8). Each variable is considered at only two levels, and effects are assumed to be linear and additive. Moreover, the direction (sign) of each effect must be known a priori. The sequential bifurcation... 

Floudas, C. A., Deterministic Global Optimization Theory, Algorithms and Applications, Kluwer, Dordrecht, 1999. 

A common characteristic of deterministic global optimization algorithms is the progressive reduction of the domain space until the global solution has been... 

Figure 53. Deterministic global optimization algorithm for binding site structure prediction.

In particular, this review has focused on the use of ab initio models, which give rise to a series of complex mathematical problems. A second important component has been the application of deterministic global optimization, namely the aBB algorithm, for solving the resulting problems. In this review we have analyzed and discussed many issues related to the modeling of protein... 

II with a new chapter (for the second edition) on global optimization methods, such as tabu search, simulated annealing, and genetic algorithms. Only deterministic optimization problems are treated throughout the book because lack of space precludes discussing stochastic variables, constraints, and coefficients. 

Abstract This contribution focuses upon the application of evolutionary algorithms to the non-deterministic polynomial hard problem of global cluster geometry optimization. The first years of method development in this area are sketched briefly followed by a characterization of the current state of the art by an overview of recent application work. Strengths and weaknesses of this approach are highlighted by comparison with alternative methods. Last but not least, current method development trends and desirable future development directions are summarized. 

In this work, two types of solution methods have been tested the deterministic method known as outer approximation (Duran and Grossman, 1986), and the stochastic algorithm Tabu search (Glover, 1986,1997). While outer approximation guarantees that the global optimum will be found within a finite number of steps for a convex MINLP, the formulation... 

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