A probabilistic multi-objective optimization mechanical design

Abstract

Optimization design of machinery is usually a multi-objective one inevitably. At present, the popular mechanical optimization design is limited by the intrinsic shortcomings of the previous multi-objective optimization methods, which leads to the difficulty of non-comprehensive and nonsystematic optimal solutions in the viewpoint of probability theory. In the linear weighting “additive” method, there is inherent problems of normalization and introduction of subjective factors, and the final results depend on the normalization method to a great extent; the Pareto solution set is a “set” instead of an exact solution. In this paper, the probability—based multi-objective optimization, discretization with uniform design and sequential optimization are combined to establish a new approach of multi-objective optimization mechanical design based on probability theory; the probabilistic multi-objective optimization is used to transform the multi-objective optimization problem into single-objective optimization one from the perspective of probability theory; the discretization by means of uniform design provides an effective sampling to simplify the mathematical processing, which is especially important for dealing with multi-objective optimization problems with continuous objective functions; the sequential optimization algorithm is used to conduct the successive deep optimization. Furthermore, the implementation steps are illustrated with two examples. The results show that the approach can not only give excellent optimization results, but also provide a relatively simple processing.