Innovation Strategy Generation for Building Design Based on the Optimization Algorithm for Dynamic Sorting of Extension Set

Based on extension set, our innovation strategy generation method for building design can automatically generate an innovation strategy for building design through the transform of building design problems, preliminary screening of building cases based on correlation function, and dynamic storing of building cases based on extension set.

As shown in Figure 1, our strategy consists of three modules: BCL construction (Module 1), optimization of dynamic sorting algorithm of the BCL (Module 2), and innovation strategy generation for building design (Module 3). In Module 1, online building cases are captured by LocoySpider, and processed to form a BCL. In Module 2, the dynamic sorting algorithm is optimized by the extension set theory; In Module 3, the innovation strategy for building design is generated from the BCL.

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Figure 1. Our innovation strategy generation method for building design based on extension set

2.1 BCL construction

The building case is the collective name of the knowledge, experience, and design strategies that architects have accumulated or developed in solving building design problems. On a webpage, a building case is presented in the form of building plan, design text, building drawings, images, models, photos, and videos. The specific features of a building case are listed in Table 1.

To facilitate temporal analysis, the architect should collect both the latest published cases and the past data (e.g. building comments). The collected data must be pertinent, broad, and typical.

Table 1. Features of a building case

Note: The architect can determine the features of a building case according to the contents of the webpage and his/her own needs.

Cloud computing greatly simplifies the operations of architects, thanks to its stable network environment, preset function modules, and low economic cost [14, 15]. For dynamic update of the BCL, LocySpider and MySQL were installed on Alibaba Cloud [16], and a detailed plan was prepared to collect data daily and update the BCL early every morning. The data were collected in the following steps:

Step 1. Based on the distribution of URLs, the rules for URL collection are designed, and used to acquire all URLs.

Step 2. The general features (e.g. project name, project type, completion time, and total building area) have already been extracted, and displayed at the top or bottom of the webpage. The architect needs to observe the distribution law of each feature in Table 1, and set up the corresponding collection rules.

Step 3. Many features hidden in the text description of the project have not been extracted in advance. For these features, the language habits of the architect are analyzed before listing as many rules as possible.

Step 4. The building comments can be divided into comment contents and relevant indices. Comment contents reflect the users’ recognition of the building case. With the aid of sentiment analysis software, the sentiment of comment contents is categorized automatically into three types: positive, neutral, and negative. Relevant indices fall into two categories: focus indices (e.g. number of views, and number of comments) and recognition indices (e.g. number of favorites, number of likes, and number of reposts).

Step 5. The data export rules are set up, and used to automatically import the collected data to MySQL database.

Data processing mainly solves the redundancy, missing, and format inconsistency of the collected data [17]. The redundant data are eliminated by the duplication check function of MySQL database, which can detect duplicate URLs in the collected data and delete duplicate items. The missing data, the result of failing to extract all the building features, are deduced from other features, padded with global constants, filled with central metrics, or supplemented manually. The inconsistent formats are unified by setting up conversion tables, namely, geographic location-latitude and longitude conversion table, Chinese and English conversion table, synonyms conversion table, and measurement unit conversion table. Through data processing, the architect can turn the messy original data into orderly, high-quality building data.

To sum up, this paper establishes a BCL from four perspectives (i.e. conceptual design, logical design, functional design, and database operation and maintenance) based on MySQL database and Navicat for MySQL, and thus ensures data stability [18].

2.2 Optimization of dynamic sorting algorithm of the BCL

2.2.1 Setting up a transform mechanism for building problems and query conditions

The starting point of building design is to identify the constraints stemming from the objectives and current conditions of the project. These constraints must be highlighted in the query for building cases.

The query conditions cover two main aspects: the building overview and the keywords. The former ensures that the found cases have a similar overview to the current project; the latter ensures that the found cases face the same difficulties as the current project.

Take the construction of a middle school next to a light rail station for example. There is a conflict between the noise generated by the station and the quiet learning environment required by the middle school. Thus, the building problem can be transformed into: setting the “construction type” in the query conditions to “educational building” (or any other building type that require a quite environment), and including “noise” or its synonyms in the keywords.

During retrieval, the system automatically expands keywords into synonym sets through divergence analysis of extenics, and then matches the synonyms with the project introduction. In this way, much fewer excellent building cases will be missed. The principle of divergence analysis is as follows:

Taking each keyword as a primitive, multiple primitives are extended from each primitive. The set of primitives extended from the same primitive must be non-empty:

$\begin{aligned} B &=\left(\begin{array}{llll}O, & c, & v\end{array}\right) \\ & \dashv\left\{\left(\begin{array}{lll}O, & c_{1}, & v_{1}\end{array}\right),\left(\begin{array}{lll}O, & c_{2}, & v_{2}\end{array}\right), \ldots,\left(O, c_{n}, v_{n}\right)\right\} \\ &=\left\{\left(\begin{array}{lll}O, & c_{i,} & v_{i}\end{array}\right), i=1,2, \ldots, n\right\} \end{aligned}$

e.g.

$B=$Noise$\dashv\{\text {Noise din noisy rackety..}\}$

2.2.2 Preliminary screening of building cases based on correlation function

In extenics, the correlation function indicates the degree to which things have a certain attribute. During the preliminary screening of building cases, the correlation function is adopted to calculate the similarity between the cases in the BCL and the query conditions, i.e. how much the building cases meet the query needs of the architect.

(1) Correlation degree of numeric features

Numeric features are calculated by a simple correlation function. The query condition is usually the numerical range. For example, the optimal range of floor area ratio is [0.5, 2], and the ideal value (the optimal value) is 1. Considering the scalability of the query, the acceptable interval for floor area ratio is generally set to [0.45, 2.05]. There are six typical situations of case retrieval, which can be solved by the following algorithms [10]:

(a) If the positive domain is a finite interval X=<a,b>, and the optimal point MÎX, then the correlation function can be expressed as:

$k(x)=\left\{\begin{array}{ll}\frac{x-a}{M-a}, & x \leq M; \\ \frac{b-x}{b-M}, & x \geq M .\end{array}\right.$   (1)

Algorithm (1) is suitable for case features, whose optimal values fall into a certain query interval. For example, if the architect needs to query for cases with a total building area of 4,000m², he/she can set the query interval to <3,500, 4,500>, with 4,000 as the optimal value.

(b) If the positive domain is a finite interval X=<a,+∞>, and the optimal point MÎX, then the correlation function can be expressed as:

$k(x)=\left\{\begin{array}{ll}\frac{x-a}{M-a}, & x \leq M; \\ \frac{M}{2 x-M}, & x \geq M .\end{array} \right.$     （2）

Algorithm (2) is suitable for case features, which meet the minimum query value and have an optimal value. For example, if the architect needs to query for cases with a green space ratio of 30%, he/she can set the query interval to <25%, ∞>, with 30% as the optimal value.

(c) If the positive domain is a finite interval X=<-∞,b>, and the optimal point MÎX, then the correlation function can be expressed as:

$k(x)=\left\{\begin{array}{ll}\frac{M}{2 M-x}, & x \leq M ; \\ \frac{x-b}{M-b}, & x \geq M .\end{array}\right.$    (3)

Algorithm (3) is suitable for case features, which meet the maximum query value and have an optimal value. For example, if the architect needs to query for cases with a floor area ratio of 2, he/she can set the query interval to <-∞, 2.5>, with 2 as the optimal value.

(d) If the positive domain is a finite interval X=<-∞,+∞>, and the optimal point MÎX, then the correlation function can be expressed as:

$k(x)=\left\{\begin{array}{ll}\frac{1}{1+M-x}, & x \leq M ; \\ \frac{1}{x+1-M}, & x \geq M .\end{array}\right.$    (4)

Algorithm (4) is suitable for case features, which have an optimal value by which the cases in the BCL are sorted. For example, if the architect needs to query for cases with a total building area of 4,000m², he/she can set the optimal value to 4,000, calculate the similarity of each case in the BCL to 4,000, and sort the cases by the similarity.

(e) If the value range is a finite interval <a,b], and the positive domain is X=<a₁,b] (a₁≥a, and b is the optimal point), the correlation function can be expressed as:

$k(x)=\frac{x-a_{1}}{b-a}$    (5)

Algorithm (5) has one more constraint than the above algorithms. It is suitable for expressing numerical features transformed from time features. For example, if the architect needs to query for the latest building cases, he/she can set the query conditions as “the past five years”, with “the past three years; the closer, the better” as the optimal condition.

(f) If the value range is a finite interval [a,b>, and the positive domain is X=<a,b₁] (b₁≤b, and a is the optimal point), the correlation function can be expressed as:

$k(x)=\frac{b_{1}-x}{b-a}$    (6)

Algorithm (6) has one more constraint than Algorithms (1)-(4). For example, if the architect needs to query for the cases with green space ratio no lower than 35%, he/she can set the query conditions as “[35%, 45%]”, with “[35%, 40%]; the closer to 35%, the better” as the optimal condition.

(2) Correlation degree of time features

The time features are usually stored in the form of “year-month-day”, e.g. “2013-02-14”. During the query for a building case, the time feature is often positively corelated with the design level of the building. These features should be transformed into numerical features, to compute the correlation between the completion time and query time. First, all time features should be transformed into the form of year by “year.(month-1)/12”. Hence, “2013-02-14” should be rewritten as “2013.08”. After the transform, the features can be processed by the correlation functions for numerical features.

(3) Correlation degree of location features

The location features are usually expressed in the form of state, country, province, city, etc., such as the construction location. The architect should convert these features into latitudes and longitudes, and calculate the correlation degree based on the actual distance. For example, “Ningbo City” should be converted into “28°51′-30°33′N; 120°55′- 122°16′E”.

(4) Correlation degree of nominal features

The calculation degree of nominal features cannot be calculated directly. However, these features are critical to the similarity calculation of buildings. Here, the correlation degree of such features is computed by Wu and Palmer’s calculation method for concept similarity based on node distance [19]:

$k(x,y)=\left\{ \begin{matrix}   \frac{2\times depth(Msc(x,y))}{Dis(x,y)+2\times depth(Msc(x,y))}, & x\ne y  \\   1, & x=y  \\\end{matrix} \right.$   (7)

where, Msc(x,y) is the nearest parent node to two concepts x and y; Dis(x,y) is the shortest distance between the two concepts (the minimum number of nodes on the path from x to y.); depth(Msc(x,y)) is the depth of the nearest parent node in the tree structure (the number of nodes from the parent node to the root node).

(5) Correlation degree of ordinal features

The features should be transformed into numerical features based on their ranks. For example, the four levels of building fire rating, I, II, III, and IV, can be converted into numbers 1, 2, 3, and 4, respectively, and then processed by the correlation functions for numerical features.

(6) Composite correlation degree

Multiple features are often involved in the calculation of case similarity. The weight of each feature should be assigned by architects or construction experts. Suppose λ₁, λ₂, …, λ_m, are the weight coefficients of features c₁, c₂, …, c_m, respectively, and satisfy $\sum_{i=1}^{m} \lambda_{i}=1$. The composite correlation degree between building cases can be calculated by:

$K(B)=\sum_{i=1}^{m} \lambda_{i} k_{i}\left(c_{i}(B)\right)=\sum_{i=1}^{m} \lambda_{i} k_{i}\left(x_{i}\right)$     (8)

2.2.3 Dynamic sorting of building cases based on extension set

The previous reports on case sorting often overlook the positive impact of architect’s retrieval behavior on the evaluation of case quality. To realize scientific sorting and dynamic evaluation of building cases, this paper quantifies the transform of things based on the extension set theory, and analyzes the retrieval behavior of architects. The basic principle is explained below:

Let U be the BCL, u be any case in U, k be a mapping from U to the real domain $\Re$, and T is a given transform. Then, an extension set on universe U [10] can be defined as:

$\tilde{E}(T)=\left\{\begin{array}{l}\left(u, y, y^{\prime}\right) | u \in U, y=k(u) \in\Re ; \\ y^{\prime}=T_k k(u)\end{array}\right\}$    (9)

where, y=k(u) and y’=T_kk(u) are the correlation function and extension function of $\tilde{E}(T)$, respectively.

If T=e, then the positive extension domain or positive qualitative change domain of $\tilde{E}(T)$ can be defined as:

$E+(T)=$$\left\{\left(u, y, y^{\prime}\right) | u \in U, y=k(u) \leq 0 ; \quad y^{\prime}=T_{k} k(u)>0\right\}$

During the current and subsequent evaluation periods, if the correlation degree of a case changes from negative to positive, then the case is strongly attractive.

The negative extension domain or negative qualitative change domain of $\tilde{E}(T)$ can be defined as:

$E-(T)=$$\left\{\left(u, y, y^{\prime}\right) | u \in U, y=k(u) \geq 0 ; \quad y^{\prime}=T_{k} k(u)<0\right\}$

During the current and subsequent evaluation periods, if the correlation degree of a case changes from positive to negative, then the case is strongly unattractive.

The positive stable domain or positive quantitative change domain of $\tilde{E}(T)$ can be defined as:

$E+(T)=$$\left\{\left(u, y, y^{\prime}\right) | u \in U, y=k(u)>0 ; \quad y^{\prime}=T_{k} k(u)>0\right\}$

During the current and subsequent evaluation periods, if the check frequency of a case increases from the already high level, then the case is slightly attractive.

The negative stable domain or negative quantitative change domain of $\tilde{E}(T)$ can be defined as:

$E-(T)=$$\left\{\left(u, y, y^{\prime}\right) | u \in U, y=k(u)<0 ; \quad y^{\prime}=T_{k} k(u)<0\right.$

During the current and subsequent evaluation periods, if the check frequency of a case decreases from the already low level, then the case is slightly unattractive.

The extension boundary of $\tilde{E}(T)$, i.e. the critical state of the above situations, can be defined as:

$E_{0}(T)=\left\{\left(u, y, y^{\prime}\right) | u \in U, y^{\prime}=T_{k} k(u)=0\right\}$

By the above definitions, the extension set describes the mutual transform between yes and no of building cases. It not only reflects the quantitative change (stable domain), but also illustrates the qualitative change (extension domain). The extension boundary is the limit of qualitative change. Beyond this boundary, building cases will undergo qualitative change.

For the retrieval behavior of the architect, the correlation between the evaluation values of a building case in the current and subsequent evaluation periods was defined as the correlation degree y, and the transform that causes the two evaluation values to change was defined as T. Then, the check frequency f of building case u in an evaluation period can be normalized by min-max method by:

$y=k(u)=2\left(f-f_{\min }\right) /\left(f_{\max }-f_{\min }\right)-1$    (10)

In this way, the building cases that meet the query conditions can be divided into the above five domains. Considering the increase/decrease of check frequency in positive/negative quantitative change domain, the dynamic evaluation results of building cases were divided into seven levels corresponding to the seven domains: positive qualitative change domain and positive quantitative change domain (increased correlation), positive quantitative change domain (decreased correlation), negative qualitative change domain, negative quantitative change domain (increased correlation), negative quantitative change domain (decreased correlation), and zero domain.

Based on weights, the correlation degrees and levels of building cases were summed up into the final evaluation result of case evaluation, laying the basis for case sorting.

2.2.4 Developing the BCL interface

To realize efficient retrieval of building cases and innovation strategies, in-depth design was carried out for important functions of the BCL, including online data acquisition, data analysis and processing, data format conversion, and data storage and query. The query interface of the BCL (Figure 2) was developed based on BlueGriffon v3.0.1, Microsoft IIS7.0 [20], and JSP10 [21].

Figure 2. The query interface of the BCL