Reliability Optimization Problems with Multiple Constraints

This paper presents a class of reliability optimization problems with multiple-choice constraints. We assume that at least one design alternative can be chosen as redundancy for each subsystem. A 2-phase solution method is presented for solving these problems. In phase I, we decompose a problem into n subproblems. These subproblems can be solved by dynamic programming, independently. That is, these subproblems can be solved by parallelism. In phase II, we solve a 0-1 multiple-choice knapsack problem which is generated from phase I. We use a combinatorial tree which always satisfies the multiple-choice constraints. The 2-phase solution method is illustrated with a numerical example.