Research of influence of calculation precision on the effectiveness of stochastic optimization methods

Abstract

This paper describes the influence of the varying computation precision when performing calculations using the optimizing algorithms. A comparative analysis of the computation speed and obtained result accuracy of the Rastrigin’s direct cone method with adapting of the step length and the angle of the cone's disclosure for varying precision was performed. It is shown that the speed of the optimization algorithm practically does not depend on used computation precision. The difference is observed only in accuracy of the obtained results. The investigation of optimizing algorithms behavior under the presence of noise, in particular due to rounding errors was conducted. It is shown that the optimizing algorithm under research becomes unsuitable after some noise level. Characteristics of the optimization algorithm during calculations with a single precision proved to be better then the characteristics of the algorithm when performing calculations with double precision. The analysis of possibilities of the effective graphics processors (GPU) application in order to conduct optimization was carried out. In particular, the difference in the speed of the GPU when performing calculations with a single and double precision was considered. To ensure the efficiency of calculations based on optimization algorithms, it is recommended to carry out calculations with the use of single precision, and increase the calculation precision in case of impossibility to achieve the desired accuracy of the result. There is considering the significantly higher performance of graphics processors when doing calculations with a single precision in comparison with calculations with double precision it is expedient to use a single calculation precision when graphic processors are used to solve considered problem. Double precision can be used if it is difficult to get sufficiently correct solution by single precision calculations. The results of numerical experiments confirm that the use of lower precision to perform optimization for macromodels creation has a slight influence on the speed of achieving of predetermined optimization accuracy.