## 2 Related Work
### Review of Optimization Approaches in Financial Applications  
Genetic algorithms (GAs) are optimization algorithms widely used for solving complex problems in a variety of fields [42; 43]. In the financial field, many applications utilize GAs to improve and search for near-optimal solutions in limited time [44]. For example, [PERSON] et al. propose an optimization algorithm to address the diverse group stock portfolio optimization problem to obtain a diverse group stock portfolio using the grouping genetic algorithm (GGA) [18]. To identify good group trading strategy portfolios, [PERSON] et al. propose an algorithm to not only obtain a reliable group trading strategy portfolio but also to find appropriate stop-loss and take-profit points based on the GGA [17]. [PERSON] proposes a methodology for effective stock selection using support vector regression (SVR) and a GA [45]. He was first to use the SVR to generate surrogates for actual stock returns that, in turn, serve to provide reliable stock rankings. The GA is then used to optimize the parameters for the proposed model. [PERSON] et al. propose an approach for feature selection utilizing the GA, and use the selected features to construct a long short-term memory (LSTM) neural network model for stock prediction [13]. The results showed that the GA-LSTM model outperforms all baseline models for time series prediction. [PERSON] et al. propose a spatiotemporal convolutional neural network-based relational network (STCNN-RN) model for stock anomaly detection [46]. To improve the accuracy of the STCNN-RN model, the GA is then employed to identify outlier time points for use in the model to identify abnormal behaviors. They indicate that the model is effective on a multiple financial time series dataset for finding anomalous situations. For pairs trading optimization, [PERSON] et al. propose a pairs trading structure based on deep reinforcement learning (DRL) and a GA [47]. They first apply the distance method (DM) and the cointegration approach (CA) to generate trading pairs from the given pair pool, after which trading actions are determined using the simple thresholds (ST) strategy, the GA, and DRL. They propose five pairs trading strategies for trading, including the DM-ST, CA-DM-ST, and CA-ST benchmark strategies, and the improved strategies CA-GA-ST and CA-DRL. In CA-GA-ST, the GA is utilized to find appropriate parameter settings, and in CA-DRL, DRL is employed to construct an agent using pairs trading rules and the differences between the two assets. They indicate that CA-DRL is superior to other strategies. [PERSON] et al. propose an intelligent system using mixed integer programming (MIP) and the multi-objective genetic algorithm (NSGA-II) for multivariate pairs trading [48]. It uses MIP to generate trading pairs. The risk and return are used as two conflicting objective functions when finding Pareto solutions using NSGA-II. The results indicate that multi-objective multivariate pairs trading outperforms traditional approaches. [PERSON] et al. propose an intelligent model for pairs trading based on GA [49]. In their approach, the GA is utilized to find the parameters of moving averages, Bollinger Bands, and stock weight coefficients for the model. Experimental results indicate that GA-based pairs trading effectively improves the performance of pairs trading and outperforms the benchmark in terms of return. In addition, [PERSON] proposes the genetic Bollinger Band and correlation-coefficient based pairs trading algorithm (GBCPT), using a GA for pairs trading [28]. GBCPT encodes the parameters into a chromosome, including the correlation coefficient threshold, the entry width of the Bollinger channel, and the exit width of the Bollinger channel. The last two parameters are used to determine the width of the Bollinger Bands.