Stochastic global optimization

Rinnooy Kan, A. H. G. and G. T. Timmer. Stochastic Global Optimization Methods, Part 2 Multi Level Methods. Math Prog 39 57-78 (1987). 

Norkin, W.I., Pflug, G.Ch., and Ruszczysk, A. (1998) A branch and bound method for stochastic global optimization. Mathematical Programming, 83, 425. 

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. 

Of course, besides stochastic global optimization methods, there are also many deterministic methods [138-140]. Typical applications of these to clusters have so far been possible only for trivially small clusters, for example, LJ7 in Ref. [ 141 ] or LJ 13 in Ref. [ 142]. Clearly, this is no match at all for the stochastic methods that have now reached LJ309 in the CSA work of Lee et al. [133]. 

Rangaiah, G.P. (ed.) (2010) Stochastic Global Optimization Techniques and Applications in Chemical... 

Poplewski, G. and Jezowski, J.M. (2010) Application of adaptive random search optimization for solving industrial water allocation problem, in Stochastic Global Optimization Techniques and Applications in Chemical Engineering (ed. G.P. Rangaiah), World Scientific, Singapore. 

Figure 5 shows an example of fitted data to an equivalent circuit using Fricke and modified Fricke model. During the first step of data analysis, data are fitted to an equivalent circuit described by a model equation. For the estimation of the model parameters an evolutionary algorithm is used, described in (Buschel, Troltzsch, and Kanoun 2011, Kanoun, Troltzsch, and Trankler 2006). This algorithm is based on a stochastic global optimization method. 

Multi-objective integrated design and control using stochastic global optimization methods... 

The paper presents a developed version of an algorithm for safe ship trajectory plarming using stochastic global optimization method, what has allowed to include the COLREGs, a greater number of static obstacles and moving objects, dynamic properties of the vessel, the determination of a safe trajectory to the specified endpoint and consistent solutions from the perspective of all the vessels involved in the coUision situation. 

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. 

So far, only techniques, starting from some initial point and searching locally for an optimum, have been discussed. However, most optimization problems of interest will have the complication of multiple local optima. Stochastic search procedures (cf Section 4.4.4.1) attempt to overcome this problem. Deterministic approaches have to rely on rigorous sampling techniques for the initial configuration and repeated application of the local search method to reliably provide solutions that are reasonably close to globally optimal solutions. 

W. Wenzel and K. Hamacher. Stochastic tunneling approach for global optimization of complex potential energy landscapes. Phys. Rev. Lett, 82 3003, 1999. 

A genetic algorithm is a stochastic global search method that mimics the metaphor of natural biological evolution. This Darwinian evolution theory is a well known paradigm that has been proved to be robust when applied to search and optimization problems [5]. Evolution is determined by a natural selection of individuals (based on their fitness) which, is expected to be better throughout a determined number of generations by means of recombination and mutation operations. 

The first part briefly introduces the stochastic expected value programming theory. With the discussing on the expected value model which is a convex programming, Theorem 4.2 is put forward and proved. Furthermore we get the conclusion that if the expected value model is a convex programming and there exists an optimal solution, then any local optimal solution will be the global optimal solution. 

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