Multiple objectives escaping bird search optimization and its application in stock market prediction based on transformer model.

Stock market prediction has long attracted the attention of academia and industry due to its potential for substantial financial returns. Despite the availability of various forecasting methods, such as CNN, LSTM, BiLSTM, GRU, and Transformer, the hyperparameter optimization of these models often faces limitations, particularly in single-objective optimization, where they can easily fall into local optima. To address this issue, this paper proposes an innovative multi-objective optimization algorithm-the Multi-Objective Escape Bird Algorithm (MOEBS)-and introduces the MOEBS-Transformer architecture to enhance the efficiency and effectiveness of hyper-parameter optimization for Transformer models. This study first validates the performance of MOEBS through a series of multi-objective benchmark tests on standard problem sets such as ZDT, DTLZ, and WFG, comparing it with other multi-objective optimization algorithms (e.g., MOMVO, MSSA, and MOEAD) using evaluation metrics such as GD, Spacing, IGD, and HV for comprehensive analysis. In the context of stock price prediction, we select the closing price datasets of Amazon, Google, and Uniqlo, using MOEBS to optimize the core hyper parameters of the Transformer while considering multiple objectives, including training set RMSE, testing set RMSE, and testing set error variance. In the experiments, this paper first compares CNN, LSTM, BiLSTM, GRU, and traditional Transformer models to establish the Transformer as the optimal model for stock market prediction. Subsequently, the study compares the MOEBS-Transformer with Transformer models optimized using various hyperparameter optimization methods, including MOMVO-Transformer, MSSA-Transformer, and MOEAD-Transformer. Additionally, it evaluates Transformer models optimized through conventional methods: Random Search (RS-Transformer), Grid Search (GS-Transformer), and Bayesian Optimization (BO-Transformer). By assessing the performance of these models using R