# Modeling and Multi-Objective Optimization Design of High-Speed on/off Valve System
## 1 Introduction
The AFSA is a population-based intelligent optimization algorithm, fundamentally inspired by the follow, swarm, prey, and random behaviors of fish [19; 20; 21]. This algorithm is applicable to various continuous and combinatorial optimization problems. Suppose an artificial fish is currently in state Z, with a visual field set to V, and at a given moment, its viewed position is Zv. If the state at the viewed position is better than the current state of the artificial fish, the fish can move one step towards Zn; otherwise, it continues to search within its visual field for other positions. The perception ability of artificial fish to the surrounding environment increases with the number of explorations, and the improvement of perception ability can help AF make the next decision. The optimization design of HSVs remains a highly challenging process, primarily due to the dependence of metaheuristic optimization algorithms on accurate system modeling. HSV systems exhibit highly nonlinear characteristics, even without considering the influence of driving circuits, and can be modeled as third-order systems [22]. Precisely predicting the opening and closing time presents significant difficulties. Currently, to conserve computing resources, the widely accepted approach involves approximating functions, making it challenging to achieve high accuracy [23]. In recent years, advanced artificial intelligence methods, particularly those based on neural networks, have made significant advancements and found applications in various fields. Neural network-based methods allow for the direct establishment of black box models by mapping system-related parameters through the training process [24]. Given their strong generalization ability and high prediction accuracy, backpropagation neural networks (BPNN) are an ideal choice for fitting HSV systems [25]. The purpose of this study is to design and validate an HSV model with a permanent magnet structure, focusing on the key performance indicators of rapid opening and closing. In pursuit of this objective, a novel HSV with a permanent magnet bias structure is proposed. The subsequent sections of this paper are organized as follows: Section 2 introduces the proposed valve structure and utilizes system dynamics software for modeling, whereby various design parameters are incorporated to simulate valve response time and flow rate. Section 3 presents the design of the backpropagation neural network (BPNN) structure, followed by its training using simulation data and an analysis of the training accuracy. Section 4 addresses the multi-objective optimization problem, wherein non-dominant solution set screening and storage are incorporated into the artificial fish swarm algorithms (AFSA) algorithm. The improved AFSA is employed to optimize the design of six key parameters in the HSV, facilitating the attainment of Pareto optimal solutions and enabling the selection of parameters based on engineering requirements. Section 5 validates the proposed valve model through an experimental assessment of switching time and pressure drop. Finally, Section 6 presents the corresponding conclusions.