## 2 The Related Work  
This section introduces the development of feed-forward neural networks (FNN) and related works. This paper first discusses the history of artificial neural networks (ANNS) and the use of feed-forward neural networks in real-world applications. It next discusses random weight feed-forward neural networks, their optimization, and ultimately our optimization strategy. This paper first introduces the origin of artificial neural networks (ANNS) and the practical application of feed-forward neural networks, then introduces the optimization and application of random weight feed-forward neural networks, and finally presents our optimization scheme. An artificial neural network (ANN), also referred to as a neural network (NN), is a mathematical model of hierarchically distributed information processing by imitating the behavior characteristics of animal brain neural network [24], through the relationship between various neurons, mainly by regulating the relationship between a large number of internal nodes, to achieve the purpose of data processing [25]. The logician [PERSON] and psychologist [PERSON] created the mathematical MP models and neural networks in 1943. The age of artificial neural network research began when they proposed the formal mathematical description of neurons and the network structure approach through the MP model, and demonstrated that a single neuron can carry out logical functions [26]. Artificial neural networks have many model structures, and feed-forward neural networks are only one of them [27]. [PERSON] created the perceptron, an artificial neural network, in 1957. The perceptron is a simple neural network in which each neuron is arranged in layers and is only connected to the previous layer. The output of the previous layer is received and exported to the next layer, and there is no feedback between neurons in each layer. This is the earliest form of a feed-forward neural network (FNN). The feed-forward neural network is one of the most popular and rapidly evolving artificial neural networks due to its straightforward construction. The study of feed-forward neural networks started in the 1960s, and both theoretical and practical advancements have been made. The FNN can be regarded as a multilayer perceptron. With all the links between layer and layer, it is a kind of typical deep learning model. The performance of the traditional model, with large data samples and outstanding performance, can solve the problems that some traditional machine learning models cannot understand. However, deep learning models with small data samples are complex, making the process difficult to explain. The FNN also shares these characteristics, so it is mainly used in scenarios with large datasets. A feed-forward neural network-based approach for creating rocket trajectories online is presented in [28], and the trajectory is roughly estimated utilizing the neural network's nonlinear mapping capability. In [29], the study of source term inversion of nuclear accidents uses deep feed-forward based neural networks. The Bayesian MCMC technique is used to examine the DFNN's prediction uncertainty when the input parameters are unclear. In [30], with the chaotic encryption of the polarization division multiplexing OFDM/OQAM system, the feed-forward neural network is used to increase data transmission security and realize a huge key space. In [31], a feed-forward backpropagation artificial neural network is used to predict the force response of linear structures, which helps researchers understand the mechanical response properties of complex joints with special nonlinearities. In [32], the initial weight approach and the construction algorithm are combined to form a novel method of feed-forward neural network multi-class classification that can achieve high success rates. In [33], hybrid MVO and FNN were improved for fault identification of WSN cluster head data. It is clear that feed-forward neural networks are used in a variety of industries.