Application of Uniform Design for Mixture Experiments in Multi-objective Optimization

When the number of experimental points and variables in uniform design for mixture experiments is too large, the requirements of uniformity and calculation efficiency are hard to be satisfied simultaneously. In this paper based on the transformation of U-type matrix method, the uniformity is improved by cutting method, and the calculation efficiency problem is solved by genetic algorithm. So the uniform design for mixture experiments with good uniformity and arbitrary number of experimental points and variables is able to be generated. Then it is applied to the multi-objective optimization algorithm based on physical programming to improve optimization quality and generate evenly distributed Pareto front. Finally, the effectiveness of the improved uniform design for mixture experiments in multi-objective optimization is verified by a numerical example with three objectives.