Iterative Parametric Dynamic Programming and Its Application in Reliability Optimization

This paper considers a class of optimization problems that is nonseparable in the sense of dynamic programming. Iterative parametric dynamic programming is proposed where multiobjective optimization is used as a separation strategy and the optimal solution is sought in a multilevel fashion. At the lower level, the auxiliary weighted pth-power Lagrangian problem is solved using dynamic programming. The upper level adjusts the value of the weighting vector in the weighted pth-power Lagrangian problem based on the calculated optimal search direction. The two-level solution process repeats until the optimal solution of the nonseparable optimization problem is attained by the optimal solution of an auxiliary weighted pth-power Lagrangian problem. Application of the proposed iterative parametric dynamic programming in constrained reliability optimization ;problems is presented.