## 3 Advanced AFSA Optimization Method
### Adaptive Chaotic Transformation  
AFSA is a very flexible and nimble swarm intelligence optimization method that has the advantages of powerful robustness and puissant global search ability [34; 36; 37]. However, the original AFSA may also converge too fast in the early stage during the optimization process in the indoor localization system composed of dual-receiving acoustic anchors, which makes it impossible to fully comprehend the acoustic signal sample set in the complex and flexible NLOS scenarios. At the same time, if the convergence speed of the algorithm is too slow in the later period, it may cause shortcomings in real-world situations. Therefore, a fresh upgrading strategy is required to address the weaknesses of AFSA. Figure 4: Some key devices. (**a**) USB adapters; (**b**) special devices for fixing acoustic anchors. In the traditional AFSA, the research object is the biological individuals valued by the fitness function. It will indirectly feedback on the number of trials required by an individual to complete an effective task. The optimization strategy proposed in this paper will focus on the four significant processes in the algorithm: initialization, AFSA_preying, AFSA_swarming, and AFSA_following, so as to improve the effectiveness of the advanced AFSA. The following steps will focus more on the optimization strategy of adaptive chaos transformation, adaptive GSA method, and physical attenuation factor to upgrade the classification performance of the DT model. For the initialization process of the original AFSA, it is necessary to amend parameters that control the initialization process or properties within a predictable and feasible domain. However, the strict requirements do not necessarily conform to all of the situations on LOS and NLOS acoustic signal characteristics in indoor localization systems. At the same time, the overall distribution of the training and test data sets constructed in the offline state does not always cope with the demands of the systems. Additionally, the fitness values of the two kinds of acoustic signals are not conducive to the global convergence of the algorithm when the distribution is uneven. Hence, we considered embedding the adaptive chaos transformation method to optimize the initialization strategy. According to the characteristics of the chaotic system and chaotic transformation [38], the randomness of samples and the algorithm traversal process are strengthened, so that the initialized artificial fish individuals are allocated, and the overall distribution is more consistent with the system optimization process. At the same time, this strategy will be conducive to the algorithm's global convergence speed. The typical formula of chaotic transformation can be written as:  
\[X_{t+1}=\mu\times X_{t}\times(1-X_{t}),X_{t}\in(0,1) \tag{6}\]  
In the aforementioned formula, \(\mu\) is used as the control parameter to ensure that as the initialization process goes on, the influence of chaos transformation will not be too inappreciable, thus losing the discrimination. In this paper, \(\mu=4\) is taken as a fixed value. \(X_{t}\) represents the fish individuals in the \(t\)-th optimization loop. Its overall value will gradually become uniformly distributed. Algorithm 1 below will reveal the main process of this adaptive initialization method, and it will also bring more explanations to the entire Chaotic Transformation process. According to the requirements of the advanced AFSA initialization, the original Equation (6) needs to be modified and incorporated into the initialization process. If the lines between \"/*.... */\" mean the code comment part (the color **green** is used to write them down), the whole pseudocode can be written as:  
1. /* Assuming X_FishRange shows the activity range of fish in the model, which is set as a matrix with two rows and three columns in this part. 2. The values in the first two columns in each row are the upper and lower limits of the mentioned fish school activities that can be quantified. 3.