Multiple optimization objectives and the Pareto set often arise from engineering structural optimization. Normalization methods (such as the weighting method) have the disadvantage that the weighted value is not set by the decision maker but the designer and is greatly influenced by the opinion of the designer. On this basis, in this paper a non-dominated sorting genetic algorithm-analytic hierarchy process (NSGA-AHP) method is proposed for decision making and analysis of the Pareto solution set of the multiple-objective optimization in a structural optimal model. In addition, illustrated by the example of a disc brake, a multiple-objective optimization model for a disc brake has been here developed. Besides, the NSGA-AHP method is adopted for the analysis optimization. The research results show that the NSGA-AHP method can be utilized to select the Pareto solution set in an effective way and that this method is effective in solving a multiple-objective problem in the structural optimization design.

The requirements of frequency-selective surface (FSS) between high transparency in pass band and high reflectance in stop band are contradictory, when they have loaded medium on one side and receive a large range of illumination. In order to solve the contradiction, this paper employs a discrete particle swarm optimization approach (hereafter referred to as a DPSO). In order to seek a balanced FSS with high transparency in pass band and high reflectance in stop band, the periodic intervals and geometrical dimensions of FSS-structures are optimized and designed by using the DPSO method. Simulation and test results indicate that the FSS of super dense Y loop elements in a half-loaded medium structure is presented in this paper: the transparency in pass band and stop band are 80% and 30% respectively. The DPSO method will offer an excellent FSS for the radome which receives a large range of illumination, and on the other hand, it provides a theoretical guidance for the requirements of FSS between high transparency in pass band and high reflectance in stop band.