An uncertain structural optimization method based on nonlinear interval number programming and interval analysis method

An optimization method is proposed to solve uncertain structural problems based on a nonlinear interval number programming method and an interval analysis method. A nonlinear interval number programming method is suggested to transform the uncertain optimization problem to a deterministic multi-objective optimization problem based on an order relation of interval. For each specific design vector, an interval analysis method is applied to calculate the interval of the objective function caused by uncertainty, and whereby the optimization nesting problem can be solved. A non-constraint and single-objective optimization problem is then formulated through the linear combination method of multi-objective optimization and the penalty function method. An intergeneration projection genetic algorithm is employed to seek for Pareto optimum of the uncertain problem. The presented method is applied to a benchmark test of ten-bar truss and a practical automobile frame, and the optimization results demonstrate its efficiency.