Sensitivity of a genetic algorithm to the mutation rate parameter value: results for a crystallographic test

Wojciech Paszkowicz 

Polish Academy of Sciences, Institute of Physics, al. Lotników 32/46, Warszawa 02-668, Poland

Abstract

Genetic algorithms (GAs) represent a family of powerful global-search methods applicable to solving high-complexity optimisation tasks in science, technology and everyday life. The global-optimisation strategies based on the genetic approach mimic the evolution of living organisms. Applications in materials science, physics, chemistry, crystallography, technology, industry, medicine, economy, communication can be found in literature. In crystallography and related fields, the GAs are used e.g. for molecular design, for structure prediction, and for solving structures. Moreover, they constitute an important tool for image analysis, e.g. in medicine, and can be used for analysis of various kinds of data collected at 2D detectors.
Mutation is one of operators employed in GAs. Typically, it consists of flipping a single bit with a small probability (mutation rate, M). Using this operator ascertains that whole parameter space is searched. The value of M is either fixed at the level ~1% - ~5%, or is adjusted during calculations. In the present study, the role of M value for the success and for the calculation speed is studied on a test example of powder-diffraction data of an orthorhombic crystal. The convergence of the algorithm was determined for 20000, 30000, 60000 and 100000 function calls (during ~200-400 generations) on the basis of multiple test calculations. The probability of finding the global optimum is found to be strongly influenced by the M value. When M equals 1.8%, the chance for successful finding the global optimum is 0.2, only (in remaining cases the algorithm converged to some local minimum). The process of reaching the global minimum is fast then (stopping criterion of 20000 calls is sufficient). For the M value being twice as high (3.7), the chance for success increases to 0.8, but at expense of calculation time (stopping criterion of 100000 calls). The study demonstrates how sensitive is the algorithm to the value of the mutation rate.

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Presentation: poster at E-MRS Fall Meeting 2004, Symposium D, by Wojciech Paszkowicz
See On-line Journal of E-MRS Fall Meeting 2004

Submitted: 2004-07-17 15:21
Revised:   2009-06-08 12:55
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