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Cultural convergence is quicker to solve structural problems, according to UK chemists. Samantha Chong and Maryjane Tremayne of the University of Birmingham have combined principles from social and biological evolution to create, what they refer to as a Cultural Differential Evolution hybrid global optimization technique that can be used to solve crystal structures much faster than conventional evolutionary techniques. Their new, approach could be used to solve a variety of global optimization problems in chemistry, nanoscience and bioinformatics. The use of evolutionary algorithms is a relatively new approach to solving problems based on mimicking the principles of "natural selection" and "survival of the fittest". It is growing in popularity among researchers hoping to find a fast and effective approach to previously intractable problems. However, evolutionary algorithms, like their natural counterpart, can be slow. The Birmingham team reasoned that the much more rapid social evolution experienced by humans at an almost everyday level that is embodied in cultural algorithms, such as fashion sense, might be usefully hybridised with an evolutionary algorithm. The resulting system would combine the power of natural selection but allow the evolutionary process to be accelerated by adding a "cultural" bias based on prior knowledge and understanding to the results. Chong and Tremayne operate the so-called Differential Evolution (DE) method with a cultural bias to help them obtain an optimised structure for powder diffraction data. The DE algorithm generates a randomly distributed collection of potential structural candidates. These are reproduced by combining properties of pairs and including a "mutation" in the child structures, a process carried out in a single step. The child structures are then compared to the parents and only the "fitter" of the two retained. Over several generations the team can thus find a global energy minimum. However, the new approach is more sophisticated than this simplified description would suggest. In a conventional DE algorithm, boundary conditions relating to molecular movements, are held fixed as the next generations appear. In Chong and Tremayne's modified approach, they allow previous generations to influence the boundaries and so restrict the search only to low-lying regions of the structure space. This use of dynamic boundaries is tantamount to the influence past fashions have on future trends and so excludes those structural offspring that do not at least follow the prevailing culture to some degree. In other words, they can narrow down the number of likely structural candidates much more rapidly than is possible with a conventional approach that simply compares parent and child and discards the least fit of each pair. The researchers have demonstrated the efficacy of the cultural evolution on a test structure, baicalein, a flavone constituent of the Asian herbal medicine "Sho-saiko-to" and an unknown crystal structure, alpha-methyl-alpha-propyl succinimide(II). The team first determined the structure of baicalein using a conventional DE approach. They then applied the dynamic boundaries of the cultural approach and obtained the same known structure in half the time. They then analysed the powder diffraction pattern for the succinimide of unknown structure and determined it to be P21/c, with Z = 1. They ran their cultural algorithm several times using optimal parameters until convergence was reached. The CDE calculation converged after only 461 generations, whereas the optimum DE calculation required almost 1000 generations. The final structure was then obtained through a Rietveld analysis. "[The approach] allows the algorithm to follow population clustering that, while unlikely to expand in terms of parameter range, may shift in terms of absolute parameter values as the population evolves," say the researchers, "Our work describes the first application of the concept of cultural evolution in a chemical or crystallographic context, and demonstrates the major gains in optimization efficiency that can be achieved by combining the dictates of biological and social evolution." Related links:
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