Sobol' Sequences Application in Dynamic Stochastic Systems Optimization

摘要

The paper overviews modern methods of optimization of systems parameters at design stage, based on application of LP_(τ) sequences or Sobol' sequences with uniform distribution density and best property of evenness among modern uniform grids. Very often projected systems are complicated and bad formalized or even non-formalized. For such case accurate mathematical methods for searching of solution of multi-parameter multi-criteria optimization problem in modern computational mathematics are absent. If indices of quality are non-formalized and haven't strict expressions for derivatives of functions, it is useful the using of uniform distributed sequences for complicated functions testing in the procedures of searching of approximate “rational” solution of optimization problems. Usually “rational” solution represents some improvement of criteria values without application of accurate procedures for searching of extremum. The best property of grids evenness may give a significant acceleration of searching procedures. In the paper different procedures, demanded for examination of space of systems parameters, are considered and compared. An application of classical I.M. Sobol' and R. B. Statnikov procedure, PLP- search and LP_(τ)-search with averaging algorithms for optimization of dynamic stochastic systems is discussed. The latest algorithm is the most suitable for optimization of non-formalized systems, adequately describing only by means of simulation models. Such variant of approximate optimization algorithm is named optimization-simulation. It is the most convenient for design of complicated modern devices and only for them optimization problem may be formulated and solved for case of criterion, given in form of continuous curve. Examples of optimization problems decisions for complex technical systems are shown.