## 1 Introduction
### Design Parameters  
With respect to the five objectives, the design parameters should be defined in order to support the formulation of the simplified modelling problem. Drawing on prior research conducted by [PERSON] and [PERSON] [4], it is possible to simplify the design of earphones into a selection problem comprising eight variables: the type, magnet, voice coils, and diaphragm of both the primary and secondary drivers (4 \(\times\) 2 = 8 parameters), while the depiction of a single driver can be observed in the Figure 1.  
A concise overview of the primary components of the drivers and their associated options can be found below. At the core of earphone design are the drivers, which consist of a magnet and voice coil. The magnet's function is to produce a magnetic field that interacts with the voice coil, which then moves, producing sound. The type of magnet used can significantly impact the quality of sound produced by the earphones. A stronger magnet generates a more powerful air movement with the same number of turns of the coil, resulting in better coverage of the frequency range and enhancing the overall sound quality of the earphones. Conversely, a weaker magnet may result in suboptimal sound production, particularly in the lower frequency range. It is thus essential to carefully consider the type of magnet used in earphone design to achieve optimal results. In more detail, the magnet in  
Figure 1: Depiction of the components for a single driver [8]. the earphone driver is responsible for creating a magnetic field that interacts with the voice coils, which are essentially wires that are wrapped around a cylindrical former. The voice coils in earphone drivers become magnetized when an electrical current flows through them, allowing them to interact with the magnetic field produced by the magnet. As a result, the diaphragm moves, creating sound waves. The strength of the magnet used in earphone design can significantly impact the quality of sound produced [9]. Next, apart from the selection of types of magnets, the material of the coils is essential to earphone designs. Actually, the coils are in direct contact with the diaphragm and produce the driving force needed to vibrate the surrounding air through electromagnetic induction. Although most coils are made of copper, the quality of the copper used can vary and play a role in the earphones' sound quality. The conductivity of the material used in the coils affects the current generated with the same voltage, leading to a larger driving force [10]. Lastly, the diaphragm is an essential component of the earphone core, as it directly interacts with the air or conduction media. As the human ear perceives sound waves generated by the diaphragm, the interaction between the membrane's movement and the perception of humans is crucial for product design. However, the relationship between the two is complex and nonlinear, making it challenging to design earphones [11]. Additionally, the diaphragm is a crucial component of earphone drivers, responsible for converting the electrical signals from the voice coils into sound waves. The selection of materials for the diaphragm can significantly impact the sound quality of the earphones. Various materials are used in diaphragm construction, including mylar, titanium, paper, and carbon fiber, among others. Each material has its own unique properties and can produce a distinct sound profile. However, despite the wide range of materials available for diaphragm construction, the association between the material used and the resulting sound quality remains somewhat of a mystery. This is because the interaction between the diaphragm material and other components of the driver, such as the magnet and voice coils, is highly complex and not yet fully understood. Furthermore, the sound quality produced by earphones is also influenced by factors such as ear canal resonance, sound leakage, and environmental noise, making it challenging to isolate the impact of the diaphragm material alone.