Reliability-Based Multiobjective Design Optimization under Interval Uncertainty

Abstract

This paper studies the reliability-based multiobjective optimization by using a new interval strategy to model uncertain parameters. A new satisfac- tion degree of interval, which is significantly extended from (0, 1) to (-¥, +¥), is introduced into the non-probabilistic reliability-based optimization. Based on a predefined satisfaction degree level, the uncertain constraints can be effectively transformed into deterministic ones. The interval number programming method is applied to change each uncertain objective function to a deterministic two-objective optimization. So in this way the uncertain multiobjective optimization problem is transformed into a deterministic optimization problem and a reliability-based multi- objective optimization is then established. For sophisticated engineering problems, the objectives and constraints are modeled by using the response surface (RS) ap- proximation method to improve the optimization efficiency. Thus the reliability- based multiobjective optimization is combined with the RS approximation models to form an approximation optimization problem. For the multiobjective optimiza- tion, the Pareto sets can be obtained with different satisfactory degree levels. Two numerical examples and one real-world crashworthiness design for vehicle frontal structure are presented to demonstrate the effectiveness of the proposed approach.