The selection of materials is carried out first. In 2015, Deng et al.38 grew large-area graphene films on copper foil by using an R2R chemical vapor deposition process. These films were thermally laminated onto nanowire precoated ethylene vinyl acetate copolymer (EVA)/ethylene terephthalate (PET) films. The copper foil was preserved for reuse by R2R electrochemical layering. The packaging structure minimizes the wire-to-wire resistance and graphene grain boundary resistance and enhances the adhesion of nanowires and graphene to the plastic substrate, resulting in excellent photoelectric performance, corrosion resistance and mechanical flexibility. In 2010, Junxia et al. introduced a new process for the recycling of EVA and PET composite plastic films by improving the traditional floatation and sinking process to realize the continuous production of plastic separation and recycling.To ensure that the BCI is comfortable and reliable, electrodes can be fabricated using PET plus surface EVA polymers. The PET film provides good mechanical strength and chemical stability, while the EVA polymers provide good adhesion and water resistance.Therefore, PET and EVA were finally selected as the materials for the electronic film. The PET film was chosen for its good mechanical strength and chemical stability, which can effectively protect the internal circuits from external shocks and chemical corrosion. The EVA polymer material, on the other hand, provides excellent adhesion and water resistance to ensure the stability and reliability of the electronic film under different environmental conditions.First, lines are printed on the PET film to create electrode connections. Minute electrode patterns are precisely formed on the surface of the PET film to ensure that the electrodes are aligned and connected as designed. In addition, the mechanical strength and chemical stability of the PET film make it an ideal substrate material for holding and protecting microelectrode arrays. Next, the PET film is coated with a layer of EVA polymer, which has excellent adhesion properties, adheres firmly to the PET film, and provides good water resistance to protect the electrodes from moisture and liquids. The flexibility of EVA also improves the overall flexibility of the electronic film, making it more suitable for use in head-worn devices. The prepared electronic film is then processed using injection molding electronics (IME) technology, which combines the electronic film with the injection molding material to form an integrated structure.Liquid silicone rubber (LSR) was chosen as the injection molding material to ensure a comfortable wearing experience. LSR is a soft and flexible material that provides a good wearing experience, and its biocompatibility and durability make it an ideal material for head-worn devices39.It can be seen that the EVA and PET polymer materials have good adhesion. In this paper, an EVA film layer is applied to the surface of a PET shell using in-mold electronic decoration technology to improve the safety and stability of a BCI. The IME membrane has good electrical properties and high transparency and can achieve efficient stimulation and monitoring of nerve tissue. Figure 3 shows the PVT diagram of the PET and EVA materials used in this work.A pressure‒volume‒temperature (PVT) diagram is a diagram that describes the behavior of a material under different pressure, volume and temperature conditions. Specifically, the PVT diagram contains the following information: pressure (P), volume (V), and temperature (T).As shown in Fig. 4, the PET material has good chemical stability and mechanical strength to protect the electrode array and prevent signal loss. At the same time, the EVA polymer material can fill the gap between the electrodes, improving the efficiency of signal transmission.Figure 4Comparison of the PVTs of the PET and EVA images.Second, the use of PET and EVA materials can effectively prevent the electrode array from being disturbed and damaged by the external environment and reduce artifacts caused by mechanical motion, thus improving the reliability of the BCI.Finally, the use of IME technology to produce electrode arrays can realize high-precision and efficient manufacturing. Moreover, PET and EVA materials are also easy to process and manufacture, making the entire production process simpler and more controllable.Latin hypercube sampling (LHS)LHS is a statistical method for generating quasi-random parameter values from multidimensional distributions in programming that is designed to create a fair distribution between input variables to reduce the number of iterations during computational fluid dynamics (CFD) simulations. The key to the Latin hypercube method is the proper stratification of the probability distribution of the input parameters. This stratification divides the cumulative curve into equal partitions from 0 to 1.0, which is the range of the probability scale. A sample is then taken from each stratum or interval of the input distribution. The Latin hypercube sampling technique involves sampling without substitution. In a sense, the number of layers performed by the sequence is equal to the number of iterations performed on the selected sample. For example, for an input distribution with five levels, there would be five iterations. In this sampling method, another important key is to maintain independence between variables. This independence is achieved by randomly selecting input parameters in the distribution and as variables from an interval that will never be used in the future. This method avoids unnecessary correlations between parameters.$$ x_{i}^{k} = \frac{{\pi_{k} \left( i \right) – 1 + U_{I}^{K} }}{N},i = 1, \ldots ,N,k = 1, \ldots n $$They are random sampling points on the interval [0,1]. It is obvious that for each dimension k = 1…N, only one point falls in the interval (i − 1)/N and i/N, i = 1…N. Of course, this stratification is established by superimposing layered samples on one dimension and is not expected to provide good uniformity in dimension.The parameters in the injection molding process were considered to be coordinates in multidimensional space by the Latin hypercube sampling method. Several sampling points were selected as parameter combinations by using this sampling method, and then a mold flow simulation was performed to obtain corresponding product quality indicators, such as size, shape, and surface finish. By analyzing the experimental data, the optimal injection molding parameter combination was determined to achieve the best product quality and production efficiency. In addition, the Latin hypercube sampling method can also be used to analyze and optimize the uncertain factors in the injection molding process, such as batch differences in the raw materials, ambient temperature and other factors, thereby improving the stability and reliability of the manufacturing process. When using this method for parameter optimization, it is necessary to select the appropriate number of sampling points and distribution mode to ensure the representativeness and reliability of the obtained parameter combination. At the same time, different sampling point settings and experimental designs may be required for different injection products and requirements.Multistrategy differential evolution algorithm (MSDE)When the differential evolution algorithm solves complex optimization problems, it needs to consider how to ensure the global search ability and convergence of the algorithm, but the variational strategy of the classical differential evolution algorithm has obvious characteristics and shortcomings. Therefore, in this section, to improve the convergence of the algorithm and maintain the diversity of the population, three adjustment strategies are adopted, and a multistrategy differential evolution algorithm is designed by combining the elite sharing strategy, the perturbation back-solving strategy and the adaptive adjustment strategy.Elite sharing strategyThe existing differential evolution algorithm uses the information of the current optimal individual and the possible direction of descent to design the differential mutation operator. However, this mutation operator weakens individual diversity by producing all offspring with the genetic fragments of the optimal individual. Therefore, to maintain the diversity of the population, the population is divided into several subgroups by the clustering algorithm so that the optimal individuals of the subgroups can participate in the variation process of other subgroups, thus realizing the genetic interaction among the subgroups and slowing the crisis of rapid reduction in individual genetic diversity. The specific process is as follows:First, the k-means clustering method is used to divide the population into s subgroups, denoted as \({X}_{k}^{G}=\left\{{X}_{k1}^{G},{X}_{k2}^{G},\cdots {X}_{km}^{G}\right\}\), where \({k}_{m}\) represents the size of the Kth subgroup k = 1,2,5. Then, the optimal individuals in each subgroup are selected to form the candidate solution set \(\left\{{X}_{b1}^{G},{X}_{b2}^{G},\cdots {X}_{bm}^{G}\right\}\). Finally, \({X}_{bi}^{G}\) is used to generate the offspring individuals of subgroup \({X}_{j}^{G}\), i.e.,$${V}_{KJ}^{G}={X}_{kr}^{G}+F({X}_{bi}^{G}-{X}_{ks}^{G})$$where \(i\ne j\) and \({X}_{kr}^{G},{X}_{ks}^{G}\in {X}_{j}^{G}\). Notably, too small a scale to generate subpopulations using clustering may cause the above mutation operation to fail. Therefore, when the size of the subgroup is less than 3, this type of subgroup is randomly merged into other subgroups.The K-means algorithm is a clustering analysis algorithm based on the principle of distance and proximity and is solved by multiple iterations. The main steps are as follows: First, K objects are randomly generated as the initial clustering center; second, the distance between each object and K objects is calculated, and each object is assigned to the nearest clustering center according to the distance value. Finally, the group is formed.Perturbation reverse solution strategyWhen differential evolution (DE) is used to solve complex multimodal optimization problems, it is difficult for the population to be uniformly distributed in the high-dimensional decision space, so the algorithm often stagnates due to the rapid decline in population diversity during the process of evolution. To avoid such problems, DE searches the decision space as widely as possible in the early stages of evolution to maintain population diversity. The algorithm in this section uses the reverse solution technique for poorly performing individuals rather than population initialization and therefore has a better effect on maintaining individual diversity throughout the evolutionary process. However, it should be noted that this method may have a symmetry problem due to the reverse solution, resulting in a higher gene repetition rate or similarity rate of individual offspring. To avoid the above problems, the random perturbation technique is combined with the inverse solution to perform a random perturbation on the inverse solution.Let \(x=\left({x}_{1},{x}_{2},\cdots {x}_{D}\right)\), where D is the dimension of the decision variable, and the reverse solution is defined as follows:$${\widehat{x}}_{j}={x}_{j}^{U}+{x}_{j}^{L}-{x}_{j}$$where \({x}_{j}^{U}\) and \({x}_{j}^{L}\) represent the upper and lower limits of component \({x}_{j}\), respectively.Notably, \({\widehat{x}}_{j}\) and \({x}_{j}\) are symmetric with respect to the center of the interval \(\left[{x}_{j}^{L},{x}_{j}^{U}\right]\). If x is near the center point, then there may be too many redundant points in the process, which reduces the ability of the algorithm to explore new regions. To overcome this shortcoming, the following perturbation reverse solution is established as follows:$${\widehat{x}}_{j}={x}_{j}^{U}+{x}_{j}^{L}-{x}_{j}\pm \frac{1}{2}rand\cdot min\left\{{x}_{j}-{x}_{j}^{L},{x}_{j}^{U}-{x}_{j}\right\}$$Clearly, the above equation can produce different solutions even if there are the same individuals in the population.Adaptive adjustment strategyThe appropriate setting of parameters in the differential evolution algorithm can improve the performance of the algorithm. To obtain satisfactory algorithm performance, one of the factors to be considered is whether there is a significant difference between the fitness values of the parent individual and the offspring individual. In addition, the probability of the parent being selected as the next generation individual and the a priori success parameter values contain potentially useful information and are therefore considered in the parameter setting process of the algorithm. Based on the above considerations, a simple and effective nonparametric hypothesis test is used to propose an adaptive parameter adjustment strategy. The specific procedure is described as follows:First,, assume we have hypothesis \({H}_{0}\): there is no significant difference between the fitness values of the parent individual and the offspring individual. Then, we have the opposite hypothesis \({H}_{1}\): there is a significant difference between the fitness values of the parent individual and the offspring individual.Second, for a given significance level, the Wilcoxon signed rank test was used to test whether the original hypothesis \({H}_{0}\) was valid.Then, the probability of the parent individual being selected as the next generation individual is calculated, denoted as p;Finally, the Wilcoxon signed rank test results and probability value p were used to design the relevant parameter values F and CR, i.e.,$$ F^{{G + 1}} = \left\{ {\begin{array}{*{20}c} {F^{G} + \delta ,} & {If\,the\,null\,hypothesis\,is\,not\,true\,and\,p < 0.5} \\ {F^{G} – \delta ,} & {If\,the\,null\,hypothesis\,is\,not\,true\,and\,p \ge 0.5} \\ {F^{G} ,} & {otherwise} \\ \end{array} } \right., $$$$ CR^{{G + 1}} = \left\{ {\begin{array}{*{20}c} {CR^{G} + \delta ,} & {If\,the\,null\,hypothesis\,is\,not\,true\,and\,p < 0.5} \\ {CR^{G} – \delta ,} & {If\,the\,null\,hypothesis\,is\,not\,true\,and\,p \ge 0.5} \\ {CR^{G} ,} & {otherwise} \\ \end{array} } \right. $$In the above equation, \(\delta \) represents the increase or decrease step size of the related parameters. Clearly, \(\delta \) should increase with decreasing evolutionary algebra, that is,\(\delta =\frac{0.1}{{e}^{\tau \left(\frac{G}{{G}_{max}}\right)-\beta }}\)
1.
If the original hypothesis H is rejected, then there is a significant difference between the goal value of the generation individual and the goal value of the offspring individual, and the probability value meets \(p<0.5\). This indicates that there is a high possibility of producing high-quality offspring individuals, which means that the current parameter is valid. Therefore, the values of the variation factor F and crossover probability value CR should increase in the next generation of evolution.
2.
If the probability value of the original hypothesis \({H}_{0}\) meets \(p>0.5\), then there is a significant difference between the goal value of the parent individual and the goal value of the offspring individual; however, the offspring individuals produced are poor. Therefore, the values of related parameters should be reduced in the evolution process of the next generation.
3.
If the original hypothesis \({H}_{0}\) is accepted, then the algorithm search tends to be stable, and the original parameters remain unchanged. Finally, considering the range of empirical values of parameters, if they exceed this range, then the parameter values are modified by the following rules:$$ \left\{ {\begin{array}{*{20}c} {F^{{G + 1}} = 1.2,} & {if\,F^{{G + 1}} \ge 1.2} \\ {F^{{G + 1}} = 0.2,} & {if\,F^{{G + 1}} \le 0.2} \\ \end{array} } \right. $$$$ \left\{ {\begin{array}{*{20}c} {CR^{{G + 1}} = 1} & {if\,CR^{{G + 1}} \ge 1} \\ {CR^{{G + 1}} = 0,} & {if\,CR^{{G + 1}} \le 0} \\ \end{array} } \right. $$
In the proposed algorithm, several subpopulations are generated by the K-means clustering method. Elite individuals are selected from the subpopulation to participate in the mutation process of other subpopulations, and the elite sharing strategy is applied to produce offspring. It is expected that better individuals will be found through gene recombination so that high-quality gene fragments can be transferred to individuals in another subpopulation and interactions between genes can be realized. At the same time, the value of the variation factor F and the crossover probability CR are important factors affecting the performance of the differential evolution algorithm, and whether there is a significant difference between the individual target value of the parent and the offspring has a certain influence on the parameter setting. The Wilcoxon signed rank test with the nonparametric hypothesis can be used to assess whether there is a significant difference between the parent and offspring targets. Therefore, it is effective to use the results of the Wilcoxon signed rank test to design adaptive fitting parameters. Furthermore, the reverse perturbation strategy is applied to individuals with poor fitness in the early stage of evolution to improve the search ability of the algorithm. The differential evolution algorithm based on the reverse perturbation strategy, elite sharing strategy and adaptive adjustment strategy is referred to as SOSESDE.The MSDE algorithm is a common optimization algorithm that searches for the best solution through a variety of different strategies. In this application, the algorithm must first define the objective function and the parameter space of the optimization problem. Then, an initial set of individuals is generated based on different strategies, and these individuals are evaluated and selected according to the objective function. Next, the individuals are updated and evolved according to the strategies using differential evolution algorithms. In each generation of evolution, the best individuals are selected, and new individuals are generated according to different strategies. This process is repeated until the stopping condition is met or the maximum evolutionary algebra is reached.The MSDE algorithm can play an important role in the optimization of injection molding BCIs by means of the elite sharing strategy, the perturbation reverse solution strategy and the adaptive adaptation strategy. It improves the search ability and optimization effect by increasing the diversity of the search space, preserving excellent solutions, and flexibly adjusting the strategy weight.Among them, the elite sharing strategy is a core multistrategy differential evolution algorithm. It maintains excellent individuals in the population by preserving the best solution in each generation and using it as a reference object for cross-variation by other individuals in the population. The purpose of this method is to prevent the algorithm from falling into the local optimum prematurely and to speed up the convergence to the global optimum.In addition, the perturbation backtracking strategy is also an important part of the multistrategy differential evolution algorithm. In this strategy, the solution vector is randomly perturbed and updated toward smaller objective function values. This approach can effectively increase the exploration capacity of the search space and further improve the effect of optimization. The adaptive adjustment strategy is a key element of the multistrategy differential evolution algorithm. By adaptively adjusting the weight or probability distribution of different strategies, the algorithm can automatically adapt to different problem characteristics and optimization requirements during the search process. By dynamically adjusting the probability of using strategies, the algorithm can balance global search and local search to better cope with the complexity and diversity of problems.