Reliability Optimization with the Lagrange-Multiplier and Branch-and-Bound Technique

A method has been developed for constrained reliability optimization problems. This method incorporates the Lagrange multiplier method and the branch-and-bound technique. The Lagrange multiplier method treats the number of redundancies as real numbers. Once a real number solution is obtained, the branch-and-bound technique is used to obtain the integer solution. With our method, a 4-stage series system with two linear constraints is illustrated for the redundancy allocation problem, and a 5-stage series system with three nonlinear constraints is illustrated for the reliability-redundancy allocation problem. The results show that our method is better than previous methods for both the redundancy allocation problem and the mixed integer-type reliability-redundancy allocation problem. Our method also provides more reasonable explanations when solving reliability optimization problems.