V.N. Panovskiy - Student, Moscow Aviation Institute (National Research University). E-mail: panovskiy.v@yandex.ru

Interval explosion method, which was created by the author, for the solution of the global constrained optimization problem is consi-dered. Also this algorithm can be used to solve the problem of determination of optimum program control of discrete and continuous dynamic systems. In the modern mathematics a great attention is given to the solution of problems of global optimization and to the synthesis of optimal control of dynamic systems. These problems arise during designing of planes, helicopters and spacecrafts, when the necessity of optimization of characteristic parameters and of creation of control systems arises. Existing numerical methods use different approaches, but their application is connected with various difficulties: the big computing loadings, requirements to problem statement, difficulties in reaching convergence. Thus, development of new methods of the optimi-zation, which combine the newest mathematical approaches, is the extremely important. Besides, it is necessary to notice that it is the extremely important to use and develop heuristic methods. Despite the lack of its strict substantiation, these methods give an acceptable solution of a problem in the majority of almost significant cases. Heuristic algorithms do not guarantee finding the solution and can give an incorrect solution in certain cases. However an essential advantage of such algorithms is their low computing complexity. This allows to apply them to the solution of problems of the raised difficulty (for example, the problems belonging to NP class). In aggregate with key singularities of the interval analysis (handling of ranges instead of isolated points, low insistence to problem statement) development of heuristic interval algorithms is the extremely perspective direction. Interval explosion method combines explosion heuristics and interval analysis. Such combination allows to create algorithm, which has advantages from both of approaches. The developed algorithm has small amount of parameters and there is no need in complicated tuning. Accurate result can be easily obtained. The proposed algorithm was implemented in a software program. IDE - Microsoft Visual Studio, programming language - C#. In the given work the algorithm and the software of interval explosion method for the solution of problems of global constrained op-timization and of synthesis of optimal program control of discrete and continuous determined dynamic systems were created. Also so-lutions of applied problems (command navigation problem), which demonstrate the effectiveness of the algorithm, are demonstrated.

 

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