A sequential nonlinear interval number programming method for uncertain structures

A sequential nonlinear interval number programming (SNINP) method is suggested to deal with the uncertain optimization problems. A general uncertain optimization model is investigated in which the objective function and constraints are both nonlinear and uncertain. A nonlinear interval number programming (NINP) method is employed to transform the uncertain optimization problem into a deterministic two-objective optimization problem. Then using the linear combination method and the constraint penalty function method, a deterministic single-objective and non-constraint optimization problem is formulated in terms of a penalty function. Combining this NINP method with a modified approximation management framework (AMF), an efficient SNINP method is then constructed. At each iterative step, an approximation optimization problem is created based on the Latin Hypercube Design (LHD) and the quadratic polynomial response surface approximation (RSA), and it can then be solved by the NINP method efficiently. The trust region method is used to manage the sequence of the approximation optimization problems based on a reliability index. An efficient method is suggested to calculate the actual penalty function and whereby the reliability index, and based on it the current design space can be updated. Two numerical examples are presented to demonstrate the effectiveness of the present method.