Reliability Optimization by Generalized Lagrangian-Function and Reduced-Gradient Methods

Nonlinear optimization problems for reliability of a complex system are solved using the generalized Lagrangian function (GLF) method and the generalized reduced gradient (GRG) method. GLF is twice continuously differentiable and closely related to the generalized penalty function which includes the interior and exterior penalty functions as a special case. GRG generalizes the Wolfe reduced gradient method and has been coded in FORTRAN title ``GREG'' by Abadie et al. Two system reliability optimization problems are solved. The first maximizes complex-system reliability with a tangent cost-function; the second minimizes the cost, with a minimum system reliability. The results are compared with those using the Sequential Unconstrained Minimization Technique (SUMT) and the direct search approach by Luus and Jaakola (LJ). Many algorithms have been proposed for solving the general nonlinear programming problem. Only a few have been demonstrated to be effective when applied to large-scale nonlinear programming problems, and none has proved to be so superior that it can be classified as a universal algorithm. Both GLF and GRG methods presented here have been successfully used in solving a number of general nonlinear programming problems in a variety of engineering applications and are better methods among the many algorithms.