The System Reliability Optimization Problems by means of lmproved Surrogate Constraints Method

It is often difficult to obtain optimal or high quality solutions to multidimensional nonlinear integer programming problems when they have many decision variables or they have a large number of dimensions. Surrogate constraint techniques are known to be very effective in solving the multidimensional problems. These methods translate the multidimensional problem into a problem with a single dimension by using a surrogate multiplier. When the optimal solution to the surrogate problem is not the optimal solution to the original problem, it is said that there exists a surrogate duality gap between the translated one dimensional problem and the original multidimensional problem. Nakagawa has recently proposed an improved surrogate constraint (ISC) method that can close the surrogate duality gap and hence provide optimal solutions to problems which previously could not be solved due to the size of their surrogate duality gap. By applying this ISC method to multidimensional nonlinear knapsack problems we can obtain an optimal solution to the coherent systems reliability optimization problem of Fyffe-HinesLee that previously could not be solved due to the existence of a surrogate duality gap. We also found that we could efficiently find the optimal solution to the system reliability optimization problem of Prasad-Kuo. Furthermore it is clear that this method can also be used to solve large-scale problems, as the problems with 250 variables can be solved using this method.