Abstract: The subject of the research is the methods of optimization, in particular, methods of random search for the global extremum of functions. The object of the research is the problems of the random search connected with the replacing the flow of equally distributed truly random numbers with pseudorandom sequences. The authors have created a simulative example that can clearly demonstrate limitations of the method of equal random search in case when the period length of a pseudo-random sequence used is comparable to potentially achievable number of target function calculations in the given group of traditional calculations. The authors demonstrate that there are serious limitations of the random number generator installed in the VBA-subsystem of the Microsoft Office package when using the option of random search in algorithms. When synthesizing the model target function, the author has used the methods of algebra and analysis. The main results of the research is the statement about impractibility of using the pseudo-random number generator installed in the VBA-subsystem of the Microsoft Office package in random search algorithms and recommendations on how to replace the installed sensor with the new generation generators such as Mersenne twister. 
 

Abstract: Evaluation of risks of system development is an urgent task for a for a variety of disciplines such as economics and sociology, technology and ecology, the system studied at the intersection of different disciplines. Often the parameters of such systems are discrete, set of possible states is bounded. The application package “MultiMIR” was designed to evaluate risks of development in such systems. An important difference of “MultiMIR” from other application is in achievement of polynomial computational complexity for some classes of systems, while most analogues offer only exponential complexity. The article describes: purpose of the application, main ideas used as a basis for algorithms, application architecture. The author gives an overview of ways of using the application. The conceptual basis of the theory used in the development of algorithms implemented in “MultiMIR” is in theoretical probabilistic approach. As a specific mathematical apparatus the author has chosen formalism of theory of multisets, which, in author’s opinion, has the richest expressive possibilities for the study in the described the subject area. As a programming system used in the development of the first version of the application the author used VBA-subsystem office with Microsoft Office. The selection of the programming system is dictated by the features and preferences of the primary target of the package: banking and financial analysts. Using “MultiMIR” allowed for the first time to provide accurate calculation of such non-linear measures of risk as expected utility, distorted probability measure, "Value at Risk", and so on for medium and large homogeneous portfolios term financial instruments without involving time-consuming analytical methods. Unlike traditionally used for this purpose Monte Carlo method, approached based on the described above application allows obtaining an exact solution using a comparable amount of CPU resource. “MultiMIR” application can also be used for verification of reliability of the results obtained using Monte Carlo methods considered classical in the financial risk management.