Redundancy Allocation for Series-Parallel Systems Using a Column Generation Approach
An optimization method based on column generation decomposition is described and demonstrated for the redundancy allocation problem to maximize system reliability. The redundancy allocation problem is a well-known nonlinear integer programming problem, which involves the maximization of system reliability by selecting components and redundancy levels as part of engineering design. The proposed solution method is based on the formulation of a restricted master problem and generation of possible better solutions through a set of sub-problems. The main advantages of our approach over previously studied heuristic methods are that it considers the objective function directly without any approximations, it has superior computation time, and it is flexible. Flexibility means that there is no need for assumptions like convexity and linearity of the objective function or constraints, restrictions on the number of constraints, and restrictions on component mixing. However, it is necessary to assume that the objective function and constraints are separable in decision variables. Numerical results are presented and discussed based on previously studied examples. The overall quality of the solutions matches or surpasses most of the existing heuristic methods with less computation time in the majority of the presented cases.
column generation redundancy allocation problem system reliability optimization