A reliability-based method for optimization programming problems

In this study, a method is developed to solve general stochastic programming problems. The method is applicable to both linear and nonlinear optimization. Based on a proper linearization, a set of probabilistic constraints (performance functions) can be transformed into a corresponding set of deterministic constraints. this is accomplish by expanding all the constraints about the most probable failure point. The use of the proposed method allows the simplification of any stochastic programming problems into a standard linear programming problem. Numerical examples are applied to the area of probability- based optimum structural design.