## 1 Introduction  
Blind source separation (BSS) is a signal processing method that can obtain the source signals to be processed from the mixed signal observed without confirming the characteristics and quantity of the source signals, as well as the mixing matrix of the transmission channel [1]. Its objective is to reconstruct the source signal as closely as feasible using an estimation method. BSS has important theoretical significance and practical application value in various fields, such as speech, communication, biomedical engineering, and earthquake detection. Although BSS has many characteristics and advantages, it has some limitations. Because of the lack of pre-examined knowledge, the research on blind source separation is based on many assumptions. However, there is a possibility that actual source signals do not meet these assumption conditions, resulting in poor separation effects that affect the spread of blind-sound separation techniques. Independent component analysis (ICA) algorithms for blind source separation were first developed by [PERSON] and [PERSON] in 1995 [2]. They also presented hypothetical conditions for the application of ICA methods. Since then, the research on linear mixed signal separation has been transformed into exploring the objective function of ICA and its optimization method. Until now, the ICA algorithm is still the mainstream algorithm for processing blind source separation. However, in practical environments, some source signals may not meet the assumptions of the ICA method, such as image processing in the field of face recognition, financial impact factors that affect the market, communication-related interference, etc. In recent years, researchers' interest has been drawn to Bounded Component Analysis (BCA), which offers a new approach to blind source separation. In BCA, the assumptions of ICA are replaced by the compactness and Cartesian separability of the source signals, which are more relaxed than that of ICA and can still be separated without requiring source signals to be independent of each other. After that, the BCA algorithm was improved by other academics. [PERSON] suggested that the best way to separate a single source signal from a mixed signal is to minimize the convex perimeter function [3]. [PERSON] established the concepts of main hyper ellipsoids and boundary hyper rectangles and developed a BCA approach with volume ratio maximization as its main objective [4]. The correlation coefficients between source signals are well tolerated by this approach [5]. The computational complexity of all these BCA approaches is high in terms of the objective function. To solve this problem, [PERSON] et al. [6] proposed a normalized boundary objective function that simplified the objective function of BCA and verified the effectiveness of this method via simulation and experiment. [PERSON] et al. [7] proposed that the PCA algorithms can be applied to temporal or spatially dependent sources, as well as independent sources. Today, the PCA algorithm has been successfully applied in many engineering fields. [PERSON] [8] used the PCA algorithm to improve the accuracy of gas turbine noise source recognition, and [PERSON] developed a digital Self-Interference Cancellation algorithm based on bounded component analysis to improve the bit error rate performance of the In-Band Full Duplex system [9]. In conclusion, the research on the blind source separation algorithm based on BCA is fundamentally transformed into an examination of the objective function and its optimization method of BCA. This algorithm is sensitive to initial values and has unstable solution accuracy during the optimization process. For this problem, some scholars propose using swarm intelligence algorithms with stronger global convergence to optimize the objective function. Genetic algorithms were used to solve the BSS problem for the first time by [PERSON] et al. in 1997 [10]. In 2004, the Particle Swarm Optimization (PSO) technique was effectively applied by [PERSON] et al. [11] to optimize the objective function.