Reliability optimization of systems by a surrogate-constraints algorithm

A method for solving the problem of optimizing both, redundancy (number of redundant components) and component reliability in each stage of a system under multiple constraints is presented. A mixed-integer nonlinear programming formulation and the surrogate dual method are used. The solution of the surrogate dual problem is not always feasible in the original problem, that is, a `surrogate gap´ exists. Two countermeasures to surrogate gaps are considered: (1) modifying the original problem to tighten the constraints, with the modification being continued until the solution of the surrogate dual problem of the modified problem becomes feasible in the original problem, and (2) decreasing component reliabilities in the vertical direction to the tangential plane of the objective function. The method applies to reliability optimization problems for general systems, enabling complex systems such as communication networks to be treated. Some computational results are shown and compared with other approaches; they show the efficiency of the method