An improved robust multi-objective optimization of structure with random parameters

Abstract

The robust multi-objective optimization is conventionally achieved by minimizing expected values and standard deviations of performance functions by imposing equal importance to each individual gradient of the performance function. But, it is well established in the literature that all the gradients are not of equal importance to capture the presence of uncertainty. In this work, an improved sensitivity importance–based robust multi-objective optimization approach is proposed. The basic idea is to improve the robustness of the performance by defining a new index using the importance factors, proportional to the importance of the gradients of the performance. The efficiency of the proposed robust multi-objective optimization approach is investigated by optimizing a vibrating platform for maximum frequency and minimum cost. The minimization of the associated standard deviation of cost and frequency is also treated as objective functions. Noting the limitations of the conventional weighted sum method or ε-constraint method for solution of such robust multi-objective optimization problems, non-dominated sorting genetic algorithm II has been adopted for solution. The proposed robust multi-objective optimization yields more efficient Pareto fronts, that is, making a design less-sensitive to the variation in the input variables compared to the conventional robust multi-objective optimization approach.