Pareto equilibrium solution algorithm based on the metrics planning method and its application to multi-objective aerospace optimization

In high-dimensional multi-objective optimization problems, there are many Pareto solutions obtained by using high-dimensional multi-objective optimization algorithms, but there is only one meaningful optimal solution for the engineering problem; to find the unique solution, this paper develops a high-dimensional Pareto equilibrium solution algorithm based on the metrics planning method. First, the optimization problem of high-dimensional objectives is integrated into a single-objective problem based on the reference point according to the metrics planning method. Then, the weighting values of each objective function in the integrated single-objective problem are calculated using the weight allocation method. Finally, optimization experiments on the test functions show that the approach can effectively find the ideal optimal solution located in the set of Pareto solutions of the high-dimensional multi-objective optimization problem. This paper further applies the algorithm to the multi-objective optimization design of a liquid rocket engine injector and obtains the ideal Pareto optimal solution, which indicates that the high-dimensional Pareto equilibrium solution algorithm based on metrics planning in this paper is an effective method to help engineers find the meaningful solution from the numerous solutions, and it is promising in multi-objective aerospace optimization problems.