## 4 Case Study
### Evaluated Variables  
The features of the objects database are dependent on the type of museum. Collected objects in the database of any museum can be divided into different categories according to the collections' characteristics. Every object's criteria are judged by the planner's perception and knowledge, depending on the factors of history, attraction, story, rarity, etc. These factors are considered evaluated variables. There are two categories of scores within six variables proposed to evaluate and calculate in advance for production and optimization of layout instances. Category I is concerned with the properties of every object, and Category II is concerned with the relationship between exhibits, the gallery, and the arrangement with the entire exhibition space. Every score (\(\lambda\)) of variables is ranked on a scale of 1-10, and the total score \(\lambda^{(*)}\) is to sum up six scores. The definition of every type of score (\(\lambda\)) is as follows:  
1. Category I: The attributions of each object. There are four variables to evaluate every train in the objects database. These types of scores are Story_score, Age_score, Sort_score, and Rarity_score. 2. Story_score (\(\Lambda_{\text{Story}}\)): The history of each train is different from others, and the story score of everyone can be scaled according to aspects of special social event, contact with celebrities, manufacturers, etc. The average value for all selected exhibits based on certain aspects can be calculated. 3. Age_score (\(\Lambda_{\text{Age}}\)): Taking 2020 A.D. as the calculated base year, the older train gets the highest score: (2020 - start using the year of the train)/(2020 - the oldest year of start using year in objects database) \(\times\) 10. 4. Sort_score (\(\Lambda_{\text{Sort}}\)): Trains with stronger engines, notable figures, and colorful appearances are more attractive to visitors, which gets a higher score. 5. Rarity_score (\(\Lambda_{\text{Rarity}}\)): Depending on the amount of each type of train. The fewer the amount, the higher the score. If there is only one of any given type of train, that train is awarded the highest score (10). 6. Category II: Relationship with the display object and space. According to the layout patterns of ELP and the dynamic size of different selected objects, the exhibits cannot exceed the area's boundary. There are two variables to evaluate the selected exhibits within the gallery. These two scores are Space-gap_score (\(\lambda_{\text{Space-gap}}\)) and Ratio_score (\(\lambda_{\text{Ratio}}\)). Figure 5: Some pictures of collecting trains for National Railway Museum in Taiwan (adapted from TWA). Space-gap_score (\(\lambda_{\text{Space-gap}}\)): The smaller the gap between the train and the place area, the higher the score. This means that the train appropriately fits the space. The score of Space-gap (\(\lambda_{\text{Space-gap}}\)) is (L + W)/2. * Where: L = 10 \(-\)  | (place area in length) \(-\) (real object in length) | ; W = 10 \(-\)  | (place area in width) \(-\) (real object in width) |. * Ratio_score (\(\lambda_{\text{Ratio}}\)): The percentage of display area to a gallery's floor area is about 20%, and it gives visitors better benefits in the initial time spent visiting (i.e., 6\(\sim\)20 min) to engage in the narrative theme of the museum. The score of the ratio is the display area to 20% of the gallery. The score of ratio (\(\lambda_{\text{Ratio}}\)) is (\(\Sigma\) L \(\times\) W (i.e., sum of display area)/floor area of the gallery) \(\times\)10. 3. The total score of a layout instance: The final score \(\lambda^{(*)}\) of each layout instance is the sum of Category I and Category II (Equation (1)): \[\lambda^{(*)}=(\Sigma\lambda_{\text{i}})/6=((\Sigma\lambda_{\text{Story}}+ \Sigma\lambda_{\text{Age}}+\Sigma\lambda_{\text{Sort}}+\Sigma\lambda_{\text{ Rarity}}+\Sigma\lambda_{\text{Space-gap}}+\Sigma\lambda_{\text{Ratio}})/ \text{n}_{\text{i}})/6\] (1) where: \(n_{i}\) is the number of trains in a gallery; \(i\) is the ordinal number of trains.