Research On High Dimensional Multi-objective Optimization Algorithm And Its Application In Financial Field

In application engineering,scientific research,social life,especially in many fields such as resource scheduling,production tasks,resource allocation,financial management,etc.,it is often necessary to design optimization solutions based on multiple goals,which can ultimately be attributed to solving high-dimensional Target optimization problem.As the number of targets increases,the non-dominated solution individuals in the solution set increase exponentially.On the one hand,the search ability of traditional highdimensional multi-objective optimization algorithms is obviously insufficient;on the other hand,it will cause difficulties in visualizing the frontier of high-dimensional targets,thereby affecting user decision-making.Therefore,the study of high-dimensional multiobjective optimization algorithms,such as the design of investment portfolio schemes in the financial industry,has very important practical application value.The non-dominated sorting genetic algorithm with elite strategy(NSGA-II)is widely used to solve multi-objective optimization problems due to its strong computing power,high adaptability,and strong robustness.However,when the NSGA-II algorithm is used to optimize the high-dimensional multi-objective optimization problem,the convergence speed of the optimal solution set is slow and the accuracy is insufficient.This paper uses t-random neighbor embedding algorithm(t-SNE)to optimize the traditional NSGA-II algorithm,and studies the high-dimensional multi-objective optimization algorithm,which is expected to reduce computational complexity and improve prediction accuracy.The main research contents are as follows:(1)A t-SNE-based high-dimensional multi-objective optimization algorithm(tSNE-NSGAII)is proposed by using the t-SNE optimization NSGA-II algorithm to downscale complex high-dimensional data,which is difficult to process,into more manageable multidimensional data.After initializing the population of the target set each time,t-SNE is used to analyze and process the high-dimensional targets to reduce the number of targets by discarding redundant target sets.Comparing this algorithm with the NSGA-II algorithm and the decomposition-based multi-objective evolutionary algorithm(MOEAD),the convergence speed of the t-SNE-NSGAII algorithm is significantly improved when the number of targets is greater than 5.When the number of targets was10,the spatial distribution improved by 18.3% and 17.3%,respectively.(2)Although the t-SNE-NSGAII algorithm can greatly reduce the computational complexity of the algorithm when simplifying the target set,it may also lose some meaningful attributes in the target set,leading to a decrease in the accuracy of the algorithm.For this reason,a high-dimensional multi-objective optimization algorithm(tSNESUM-NSGAII)based on the t-SNE weighted sum is proposed by merit retention of both redundant objectives and initialized populations.Experiments demonstrate that the accuracy and convergence of the t-SNESUM-NSGAII algorithm are significantly improved compared with the t-SNE-NSGAII algorithm when the number of objectives exceeds 5.When the number of targets is 10,the spatial distribution is improved by 38.7%.(3)Taking the financial industry as an example,its investment areas and fund types are complex,and designing an optimal portfolio solution is essentially a high-dimensional multi-objective optimization problem.Using the optimization algorithm proposed in this paper,it is found that the overall performance of the scheme of the t-SNESUM-NSGAII algorithm is improved by nearly 41% over that of the NSGA-II algorithm,and the overall performance of the scheme of the t-SNE-NSGAII algorithm is improved by nearly 27.9%over that of the NSGA-II algorithm.