A decomposition method for optimization of large-system reliability

The authors consider a decomposition approach for optimization of the reliability of a large system with a general network structure. A three-level methodology is developed for optimal allocation of available resources among subsystems in order to ensure maximization of system reliability. The decentralized nature of this methodology greatly reduces the complexity of the large problem and facilitates seeking the optimal solution. Two examples show that the complexity of a large system can be greatly reduced by solving several smaller-dimensional subproblems iteratively. Subproblems whose dimensions are small can be efficiently solved by an existing nonlinear programming method. Another important feature of the approach is the possible simplification of the objective function during the solution. This leads in some cases to an analytic solution for the lower-level optimization problems in the three-level decomposition solution