Stochastic global search

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 Genetic Algorithms is a stochastic global search method that mimics the metaphor of natural biological evolution. GAs operate on a population of potential solutions... 

The second problem can be overcome by using a stochastic search. Thus Corana s simulating annealing SA [89], a sophisticated global search method arising from the Metropolis algorithm [90] was employed. A synthetic seven species problem was constructed and the elements in T-jx were correctly determined using SA. The recovered spectra are essentially identical to the synthetic 7 pure component spectra. [91]... 

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. 

The result is a tool which combines the global search capabilities of stochastic algorithms with the pattern recognition and tuning abilities of the user. The solutions obtained provide good initial points for subsequent rigorous optimization with a mixed integer nonlinear model. 

Zabinsky, Z.B. (2003). Stochastic Adaptive Search for Global Optimization, Kluwer, Boston, 224 p. 

Figure 8.1 Stochastic global solution search algorithm of the algorithmic process.

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. 

To approximately locate the global minimum i.e., to obtain a good quality crystal structure solution) in a reasonable amount of time, grid search methods should be replaced by the stochastic ones, based on a random sampling of the parameter space. This technique, called Monte Carlo MC), has been widely used in other scientific fields to simulate the behavior of complex systems. Its application to crystal structure determination from powder diffraction data has been developed by many authors the main strategies are outlined below. 

Ferguson and Raber s RIPS (Random Incremental Pulse Search) program also performs its stochastic search in Cartesian coordinate space. Two modes of operation are possible, the first to locate just the global minimum energy conformation and the second to perform a complete search of the conformational space. In the hunt for the global energy minimum, the lowest energy structure found to... 

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