Abstract
We consider the problems of designing reliable complex systems. Software has been developed for calculating the reliability of a complex system if the structure of the system and the reliability of its elements are determined. The reliability of systems can be increased due to a better selection of its components, by redundancy of elements, and by optimization of the structure of a complex system. Optimization models of such problems are built for these problems. The reliability function is a multivariate polynomial and the problem variables are Boolean or integer. Such optimization problems are quite difficult for numerical solutions, as they contain many local extrema. To solve small problems, you can use the OpenSolver for Excel. For systems with hundreds and thousands of elements, we suggest using the exact quadratic regularization method. The effectiveness of the obtained results is confirmed by computational experiments.
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