## 4 Performance Analysis
### Engineering Applications  
There are numerous multimodal optimization problems in engineering applications, such as the multi-template matching problem in image recognition. These problems have wide-ranging applications in fields such as medicine, transportation, and industrial automation and thus hold considerable research value. For instance, in the realm of electronics manufacturing, the PCB multi-template matching problem involves employing template matching technology to precisely locate various components on the PCB, including resistors, capacitors, and integrated circuits, ensuring that they are correctly placed. Moreover, PCB multi-template matching can be utilized to detect defects on the PCB, such as soldering issues, open circuits, or short circuits, facilitating early identification and repair and thereby ensuring product quality. While traditional template matching can only be used to identify a single matching position, in practical engineering applications, there are typically multiple matching positions. Additionally, traditional template matching algorithms often necessitate the traversal of every pixel, which can lead to substantial costs and time consumption. Therefore, the ability to identify multiple peaks simultaneously using fewer pixels could significantly reduce the costs and enhance the efficiency of businesses. Evolutionary algorithms can effectively address this issue of traditional template matching. Evolutionary algorithms seek the optimal solution through randomized populations, employing operations such as crossover and mutation, thus circumventing the need to inspect every pixel. This approach offers a significant advantage in terms of efficiency. When multiple regions within the target image match the template, the relationship between the template's pixel positions and the matching degree forms a multimodal optimization problem. Consequently, the TCDE algorithm can be employed to effectively solve this problem. A similarity evaluation function must be employed to transform PCB multi-template matching into a multi-peak optimization problem. Normalized cross-correlation (NCC) is a technique that involves quantifying the similarity between each pixel of a target image and a template. The NCC matching method involves calculating the cross-correlation between the target image and the template, normalizing the result, and then assessing the similarity between each pixel in the target image and the template. This process mitigates the effects of varying brightness and contrast levels, enhancing the accuracy of the similarity measurement. Consequently, NCC has long been recognized as a standard method for similarity measurement in feature matching and target recognition. This indicates that the TCDE algorithm is effective in the PCB multi-template matching problem. \[NCC(x,y)=\frac{\sum\limits_{i=0}^{m-1}\sum\limits_{j=0}^{n-1}[F(x+i,y+j)- \overline{F}]\times[T(i,j)-\overline{T}]}{\sqrt{\sum\limits_{i=0}^{m-1}\sum \limits_{j=0}^{n-1}[F(x+i,y+j)-\overline{F}]^{2}\times\sum\limits_{i=0}^{m-1} \sum\limits_{j=0}^{n-1}[T(i,j)-\overline{T}]^{2}}}. \tag{19}\]  
Template matching can be transformed into a multimodal optimization problem through the use of normalized cross-correlation (NCC) matching. The normalized cross-correlation matching between a target image \(F\) of size \(M\times N\) and a template \(T\) of size \(m\times n\) at position \((x,y)\) is defined by Equation (19), where \(F(x,y)\) and \(T(x,y)\) represent the grayscale values at position \((x,y)\) in the target image and the template image, respectively. \(F\) and \(T\) denote the average grayscale values of overlapping regions between the target image and the template image and the grayscale average value of the template image, respectively. The template moves within the range of the target image, and the matching degree between corresponding pixels of \(T\) and \(F\) is calculated using the NCC method. \(NCC(x,y)\) is a normalized value within the range \((-1,1)\).