Complex Benchmark Functions

The quality of the optimization procedures (existing and new) is often evaluated using reference standard problems, such as complex functions. 

These complex test functions can be categorized as follows  

AstudUlo et al., Chemical Optimization Algorithm for Fuzzy Controller Design, SpringerBriefs in Computational Intelligence, DOI 10.1007/978-3-319-05245-8 5, The Author(s) 2014 

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Table 5.1 shows the complex benchmark functions used in this work to evaluate the performance of the chemical reaction algorithm. 

The performance of the chemical reaction algorithm (CRA) was evaluated on a set of complex benchmark functions and a type-1 and type-2 fuzzy logic fracking controller. The results were compared with those obtained with another nature inspired paradigms. 

For the complex benchmark functions, simulations showed how the algorithm was able to reach smaller values than GAs, PSO and SGA obtaining good results with a basic set of values a population of only 10 elements and a maximum of 10 iterations per experiment, except for the Rosenbrock s valley function in which a Genetic Algorithm with a population of 150 individuals and 200 generations obtained better results than the CRA. 

In this book, a novel optimization method inspired by a paradigm from nature is introduced. The chemical reactions are used as a paradigm to propose an optimization method that simulates these natural processes. The proposed algorithm is described in detail and then a set of typical complex benchmark functions is used to evaluate the performance of the algorithm. Simulation results show that the proposed optimization algorithm can outperform other methods in a set of benchmaik functions. 

During the last years, more and more researchers have applied density functional theory to small transition-metal complexes and benchmarked the results against either high level wave function based methods or experimental data. A particular set of systems for which reasonably accurate benchmark data are available are the cationic M+-X complexes, where X is H, CH3 or CH2. Let us start our discussion with the cationic hydrides of the 3d transition-metals. 

The identification of the monooxo MVI0(OSer)(dithiolate)2 and the des-oxo MIV(OSer)(dithiolate)2 (M = Mo, W) centers as key intermediates in the catalytic cycle of the DMSOR (1, 33, 76, 77) has prompted Holm and coworkers (78-80) to investigate the synthesis and properties of chemical analogues of these centers. The complexes resulting from these endeavors have provided important structural, spectroscopic, and functional benchmarks that have significantly improved our understanding of the nature and function of the catalytic centers of the DMSOR family of enzymes. 

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