An Interactive Personalized Garment Design Recommendation System Using Intelligent Techniques

Abstract

This paper presents a garment design recommendation system based on two mathematical models that permit the prediction and control of garment styles and structural parameters from a consumer’s personalized requirements in terms of fitting and aesthetics. Based on a formalized professional garment knowledge base, enabling the quantitative characterization of the relations between consumer profiles and garment profiles (colors, fabrics, styles, and garment fit), these two models aim at recommending the most relevant garment profile from a specific consumer profile, using reasoning with fuzzy rules and self-adjusting the garment patterns according to the feedback of the 3D virtual fitting effects corresponding to the recommended garment profile, using a genetic algorithm (GA) and support vector regression. Based on these knowledge-based models, the proposed interactive recommendation system enables the progressive optimization of the design solution through a series of human–machine interactions, i.e., the repeated execution of the cycle “design generation—virtual garment demonstration—user’s evaluation—adjustment” until the satisfaction of the end user (consumer or designer). The effectiveness of this interactive recommendation system was validated by a real case of pants customization. In a manner different from the existing approaches, the proposed system will enable designers to rapidly, accurately, intelligently, and automatically generate the optimal design solution, which is relevant in dealing with mass customization and e-shopping for fashion companies.

1. Introduction

In the context of the rapid development of innovative digital technologies (artificial intelligence, big data, virtual reality, cloud computing, etc.), e-mass customization (e-MC) has become a critical branding strategy of many fashion companies (garments, shoes, furniture, accessories, etc.) for optimizing their manufacturing processes when facing fierce international competition [1,2,3,4,5,6]. In practice, the interactions between fashion products and humans (consumers and designers) usually play a pivotal role in implementing e-MC. To enhance these interactions, fashion companies need to have a good understanding of the relations between consumers’ uncertain and vague requirements and product parameters and robust decision support for consumers’ online purchasing. For this purpose, many relevant computational tools, including recommendation systems [7,8,9,10,11,12,13,14,15,16,17,18,19,20], knowledge bases [21,22,23], decision-support systems [24,25,26,27], and 3D virtual try-on technologies [28,29,30,31,32,33] have been developed for solving various fashion design problems. For instance, to facilitate the general consumers in creating the preferred fashion design sketches, P.Y. Mok et al. developed an IGA-based knowledge model. They then presented a customized fashion sketch design support system [26]. Arzu et al. developed an intelligent system for fashion style selection for non-standard female figure types, combining a genetic algorithm and particle swarm optimization with a neural network classifier [34]. Zhou et al. proposed a recommendation model based on a hybrid method combining Kansei engineering with a traditional filtering algorithm to realize the personalized apparel recommendation services following users’ emotional needs [12]. An open case-based color recommendation system was put forward by Hong et al., enabling the helping of designers and consumers in obtaining the most appropriate color range of consumer products [9]. Takatera et al. created a fabric retrieval system for apparel e-commerce for designers based on Kansei technology [35]. For realizing jeans recommendation for a specific consumer, Zhang et al. created a jeans knowledge base and then set up a recommendation system using sensory evaluation and an intelligent data fusion method [21]. Yu et al. developed an aesthetic-aware clothing recommendation system to perform clothing recommendations following the personalized aesthetic preference of consumers [13]. Guan et al. explored an advanced apparel style learning and recommendation system that can recognize the deep design-associated features of clothes and learn the connotative meanings conveyed by these features as they relate to style and the body [14]. Dong et al. put forth a new interactive designer-oriented, knowledge-based recommender system, permitting the generation and optimization of a fashion design scheme for a specific consumer accurately and quickly [10]. These research results provide good tools for advanced computational decision support to the fashion industry. However, for dealing with the particular challenges in garment design in terms of garment fit accuracy and efficiency, as well as garment appearances [36], the techniques mentioned above still showed some drawbacks, which are summarized as follows:

• The techniques mentioned above are mainly oriented to consumers and are concentrated on fashion aesthetics, such as styles and colors. However, the garment recommendation systems integrating design elements for simultaneously dealing with fashion aesthetics and garment fit are still limited. Both garment fit and fashion style are the most crucial elements constituting the whole textile/apparel value chain [10].
• The previous works are limited to some specific garment styles, such as shirts and jeans. They lack generalized recommendation solutions for supporting designers’ work.

In this context, we propose a knowledge-based approach (see Figure 1) for garment design recommendation, with a self-adjustment mechanism for predicting and controlling the style design and garment structural parameters from the consumers’ personalized body measurements and requirements (consumer profile). Compared with the current systems, our approach will enable the recommendation and design of new garments in terms of accuracy, fit, and efficiency, fully taking colors, fabrics, style, and patterns into account.

As one of the current computational tools for dealing with the uncertainties and ambiguities related to human factors, fuzzy techniques have been widely applied to fashion design. The concerned work includes design knowledge-based creation [10,21,22], fashion recommendation [8,9,11], human body classification [37], pattern design [25,38,39,40], product evaluation [24,28,41,42], garment size selection [43], and so forth. Meanwhile, genetic algorithms (GAs) have been regarded as a powerful tool for dealing with complex optimization problems due to their fast convergence and simple encoding, including human body clustering [44,45], clothing pressure prediction [46], thermal and moisture comfort estimation [47], production planning optimization [48], and design process optimization [26,49], and so on. Moreover, due to its easy implementation, simple network topology, and high generalized capability, support vector regression (SVR) has gained much success in the textile and fashion industry, especially in the predictions of textile dyeing process parameters [50], yarn characteristics [51,52], fabric qualities [53], fabric contents [54,55], and human body dimensions [56]. Therefore, the fuzzy technique, GA, and SVR were employed to construct the study’s personalized garment design recommendation system.

The proposed design recommendation system (see Figure 1) is mainly supported by a formalized, professional garment design knowledge base and a garment adaptation model. The knowledge base in the system (see Figure 2) is composed of a series of basic databases (style, color, fabric, and pattern) and relational models on style, color, fabric, and garment fit. The major function of these relational models is to quantitatively characterize the relations between the formalized consumer profile provided by the user and the formalized garment profile generated from combinations of the basic databases. According to the results of the relational models, if no existing garment meets the consumer profile, a self-adjustment mechanism for design parameters will be activated by using an automatic garment adaptation model (see Figure 1) until the consumer’s or designer’s satisfaction is reached. A satisfactory design solution will be recommended to the consumer by a 3D virtual demonstration. Meanwhile, the design knowledge base and adaptation model will be continuously updated by successful recommendation solutions recommended by the system. Finally, the performance of the proposed system will be improved progressively by generating personalized design solutions and learning the design knowledge for different business cases.

The significant contributions of our work are summarized as follows:

• Providing a feasible and efficient solution to realize accurate and efficient garment design recommendation and optimization towards garment e-MC;
• Supplying a friendly human–machine interactive framework for representing, recommending, controlling, and optimizing fashion design dynamically and precisely;
• Providing efficient support to general consumers who have no professional design knowledge for designing their own products according to their personalized preferences;
• Dramatically promoting design quality by constructing an effective communication channel between the consumers and fashion designers;
• Effectively decreasing high recall rates and risks for fashion companies by offering more consumer-oriented fashion design solutions;
• Facilitating the creation of new collaborative garment design processes by integrating the proposed recommendation system into a commercial 3D clothing design software, which can effectively upgrade the level of e-MC;
• Easily spreading the general principles of the proposed approach to other human-centered product design. A generalized human-centered product design platform can be constructed by modelling complex relations between human aesthetic preferences, body dimensions, and product parameters to provide the relevant decision support to designers.

The general principles of the proposed recommendation system can be applied to various garment styles (e.g., pants, skirts, coats, shirt, etc.). However, for simplicity, we make it explicit using the specific case of pants design. The involved pants samples, along with the corresponding patterns, were supported by a cooperative enterprise of our projects. Although the design solutions in this paper were demonstrated and validated using a commercial 3D garment CAD software named Clo 3D, the proposed approach and system can be generalized in other commercial garment CAD software and platforms.

In the clothing industry, a basic garment pattern (also named garment block) is broadly employed as a kind of pattern template, based on which various styles with different design elements can be further developed [24,28,30,51,57,58]. Therefore, we first take the sports leggings pattern as the representative of the pants basic pattern to expound on the proposed approach. Then, we further explain the realization of the associated design of various pants with complex structures and detailed design elements (e.g., darts, pleats, split lines, pockets, etc.) by modelling the quantitative relationships between the design elements and the pants basic pattern (leggings pattern).

The following sections of this paper are organized as follows. In Section 2, the general concept and data involved in this study are formalized. Section 3 elaborates the general scheme to create the garment design knowledge base. The effectiveness and implementation of the proposed knowledge-based system are described in Section 4. Section 5 gives a discussion on the performance of the proposed system. A conclusion and the future research work are presented in Section 6.

2. General Formalization

Let $CP=\left[\begin{array}{cccc}SR& CR& MR& FR\end{array}\right]$ be a vector for profiling the consumer’s requirements, where $SR$, $CR$, $MR$, and $FR$ refer to the requirements of style, color, fabric, and garment fit, respectively.

Let $GP=\left\{G{P}^1,\cdots G{P}^k,\cdots ,G{P}^n\right\}$ be a set of $n$ garment profiles in the database.

Let $G{P}^k=\left[\begin{array}{cccc}S{C}^k& C{C}^k& M{C}^k& F{C}^k\end{array}\right]$ be a vector for profiling the characteristics for garment profile $G{P}^k$ in the system database, where $S{C}^k$, $C{C}^k$, $M{C}^k$, and $F{C}^k$ represent the characteristics of style, color, fabric, and garment fit, respectively. The elements of $G{P}^k$ have a one-to-one correspondence with those of $CP$.

A complete garment style is composed of $m$ categories of style design elements, such as the garment silhouette, length, pockets, and ornaments. In addition, each of the $i$-th category style elements can be further divided into $u_i$ values. For example, the garment silhouette can be classified into the following types: H, X, T, O, and S according to the outline shapes [59]. All the values of the style design element amount to $v$ in total. Thus, the related symbols are defined as follows:

Let $SR=\left\{S{R}_1,\cdots ,S{R}_i,\cdots ,S{R}_m\right\}$ be a set of formalized vectors representing the requirements for $m$ categories of style design elements, where $S{R}_i=\left[\begin{array}{cccc}s{r}_{i_1}& \cdots s{r}_{i_j}& \cdots & s{r}_{i_u}\end{array}\right]$ is an $i_u$-dimensional normalized or one-hot vector expressing the requirements for the $i$-th category style design element. The $s{r}_{i_j}$ is denoted as the nearness degree of the style requirement to the $i_j$-th style element.

We take the pants design, for example. The requirements for the pants silhouettes can be defined as a $5$-dimensional one-hot vector, expressed by $S{R}_{silhouette}=\left[\begin{array}{ccccc}s{r}_H& s{r}_A& s{r}_X& s{r}_O& s{r}_T\end{array}\right]$. If $S{R}_{silhouette}=\left[\begin{array}{ccccc}\stackrel{H}{1}& \stackrel{A}{0}& \stackrel{X}{0}& \stackrel{T}{0}& \stackrel{O}{0}\end{array}\right]$, it means the silhouette of the required pants is an H type. Meanwhile, the waistline position requirements can be defined as a $3$-dimensional normalized vector, expressed by $S{R}_{waist-line}=\left[\begin{array}{ccc}s{r}_{lw}& s{r}_{nw}& s{r}_{hw}\end{array}\right]$. The $lw$, $nw$, and $hw$ refer to the lower, normal, and high waistline, respectively. If $S{R}_{waist-line}=\left[\begin{array}{ccc}\stackrel{lw}{0.3}& \stackrel{nw}{0.7}& \stackrel{hw}{0}\end{array}\right]$, which can be defined by the consumer using a graphic interface, it indicates that the required pants waistline is close to the normal waistline by 70% and the lower waistline by 30%.

Let $S{C}^k=\left\{S{C}_1^k,\cdots , S{C}_i^k,\cdots ,S{C}_m^k\right\}$ be a set of formalized vectors representing the style characteristics of the garment $G^k$ from the aspects of the $m$ categories of style design elements, represented by the normalized vectors and the one-hot vectors; $S{C}_1^k=\left[\begin{array}{cccc}s{c}_{i_1}& \cdots s{c}_{i_j}& \cdots & s{c}_{i_u}\end{array}\right]$ is an $i_u$-dimensional vector expressing the concrete style characteristics of a specific garment in the $i$-th category style design element. The structure of $S{C}_m$ has a one-to-one correspondence with those of $S{R}_m$. Furthermore, the value of $s{c}_{i_j}$ is defined by using the same method as that of $s{r}_{i_j}$ mentioned above.

Considering the generalizability of the proposed approach and system, we introduced the RGB color space to describe the color characteristics as it can be intelligible for both consumers and fashion designers.

Let $CR=\left[\begin{array}{ccc}c{r}_{red}& c{r}_{green}& c{r}_{blue}\end{array}\right]$ be a vector expressing the color requirements for the target garment. The value in $CR$ is from 0 to 255. For example, if $CR=\left[\begin{array}{ccc}\stackrel{red}{125}& \stackrel{green}{125}& \stackrel{blue}{125}\end{array}\right]$, it means that the values corresponding to the characteristics of red, green, and blue for a specific color required by the consumer are 125, 125, and 125, respectively.

Let $C{C}^k=\left[\begin{array}{ccc}c{c}_{red}& c{c}_{green}& c{c}_{blue}\end{array}\right]$ be a vector expressing the color characteristics of a specific garment in the proposed system. The value in $C{C}^k$ is from 0 to 255.

Let $MR=\left[\begin{array}{ccc}s{m}^r& s{f}^r& w{m}^r\end{array}\right]$ be a normalized vector expressing the fabric property requirements for the target garment, where $sm$, $sf$, and $wm$ represent, respectively, the smoothness, softness, and warmth. The element value in $MR$ is between 0 and 1. For the smoothness, the sensory descriptor $\left\{too smooth, smooth, neutral, rough, too rough\right\}$ corresponds to the scores of $\left\{0.1, 0.3, 0.5,0.7,0.9\right\}$. For the softness, the sensory descriptor $\left\{too soft, soft, neutral, stiff, too stiff\right\}$ corresponds to the scores of $\left\{0.1, 0.3, 0.5,0.7,0.9\right\}$. For the warmth, the sensory descriptor $\left\{too cool, cool, neutral, warm, too warm\right\}$ corresponds to the scores of $\left\{0.1, 0.3, 0.5,0.7,0.9\right\}$.

Let $M{C}^k=\left[\begin{array}{ccc}s{m}^c& s{f}^c& w{m}^c\end{array}\right]$ be a vector expressing the fabric properties of a specific garment in the proposed system.

We suppose that there are $n$ feature positions in a specific garment. The garment fit can be divided into five levels at each feature position, including too tight $\left(tt\right)$, tight $\left(ti\right)$, neutral $\left(nl\right)$, loose $\left(lo\right)$, and too loose $\left(tl\right)$.

Let $FR=\left\{F{R}_1,\cdots ,F{R}_i,\cdots ,F{R}_n\right\}$ be a set of normalized vectors representing the requirements for various garment fit levels at $n$ feature positions, where $F{R}_i=\left[\begin{array}{ccccc}t{t}_i^r& t{i}_i^r& n{l}_i^r& l{o}_i^r& t{l}_i^r\end{array}\right]$ is a $5$-dimensional normalized vector representing the requirements for five garment fit levels at the $i$ feature position.

We take the pants, for example. The requirements for the fit level for the waist girth $\left(wg\right)$ can be denoted as a $5$-dimensional normalized vector $F{R}_{wg}=\left[\begin{array}{ccccc}t{t}_{wg}^r& t{i}_{wg}^r& n{l}_{wg}^r& l{o}_{wg}^r& t{l}_{wg}^r\end{array}\right]$. For instance, $F{R}_{wg}=\left[\begin{array}{ccccc}\stackrel{tt}{0}& \stackrel{ti}{0}& \stackrel{nl}{0.8}& \stackrel{lo}{0.2}& \stackrel{tl}{0}\end{array}\right]$ represents the fact that the required fit level for the waist girth is close to the neutral level by 80% and the loose level by 20%.

Let $F{C}^k=\left\{F{C}_1^k,\cdots , F{C}_i^k,\cdots ,F{C}_n^k\right\}$ be a set of normalized vectors representing the garment fit levels of a specific garment in the proposed system. The elements of $F{C}^k$ are in a one-to-one correspondence with those of $FR$. The definition of $F{C}_i^k$ is the same as that of $F{R}_i$.

Let $BD=\left\{B{D}_1,\cdots ,B{D}_i,\cdots ,B{D}_p\right\}$ be a set of human body dimension vectors for the $p$ feature positions.

Let $G{D}^k=\left\{G{D}_1^k,\cdots ,G{D}_i^k,\cdots ,G{D}_p^k\right\}$ be a set of garment dimension vectors corresponding to the $p$ feature positions for garment $k$ in the database.

Let $G{E}^k=\left\{G{E}_1^k,\cdots ,G{E}_i^k,\cdots ,G{E}_p^k\right\}$ be a set of garment ease allowance vectors to the $p$ feature positions for garment $k$ in the database, where $G{E}_i^k=G{D}_i^k-B{D}_i$.

For one feature position, let $G{E}_i^k=\left[\begin{array}{cccc}g{e}_1& g{e}_2& \cdots & g{e}_{i_u}\end{array}\right]$ be an $i_u$-dimensional garment ease vector for $i_u$ types of style characteristics. Take the waistline position for example. The garment ease for garment $k$ in the waistline position can be defined by $G{E}_{waist-line}^k=\left[\begin{array}{ccc}\stackrel{lw}{g{e}_1}& \stackrel{nw}{g{e}_2}& \stackrel{hw}{g{e}_3}\end{array}\right]$.

For the garment fit levels, let $G{F}_i^k=\left[\begin{array}{ccccc}\stackrel{tt}{g{f}_1}& \stackrel{ti}{g{f}_2}& \stackrel{nl}{g{f}_3}& \stackrel{lo}{g{f}_4}& \stackrel{tl}{g{f}_5}\end{array}\right]$ be a $5$-dimensional garment ease vector corresponding to $5$ types of garment fit levels at $i$ feature positions for garment $k$ in the database.

3. General Scheme of the Design Knowledge Base Construction

3.1. Construction of the Garment Relational Model

In the garment relational model, we quantitatively define the similarity degree between $r\left(CP,G{P}^k\right)$ and the consumer profile $\left(CP\right)$ and the garment profile $\left(G{P}^k\right)$. During the recommendation, the system selects the most relevant garment profile from the garment database and then adapts its design to meet the consumer’s personalized requirements.

Formally, the $r\left(CP,G{P}^k\right)$ is defined as a linear combination of the similarity degrees of style $r\left(SR,S{C}^k\right)$, color $r\left(CR,C{C}^k\right)$, fabric $r\left(MR,M{C}^k\right),$ and garment fit $r\left(FR,F{C}^k\right)$ between the garment profile and the consumer profile (See Equation (1)), i.e.,

$$r\left(CP,G{P}^k\right)={\alpha }_1\times r\left(SR,S{C}^k\right)+{\alpha }_2\times r\left(CR,C{C}^k\right)+{\alpha }_3\times r\left(MR,M{C}^k\right)+{\alpha }_4\times r\left(FR,F{C}^k\right)$$

(1)

where ${\alpha }_1$, ${\alpha }_2$, ${\alpha }_3$, and ${\alpha }_4$ refer to the weights of style, color, fabric, and garment fit, respectively. These weights, varying between 0 and 1, are selected by the user (designer or consumer) according to the importance of each component in its specific scenario.

Let $\rho$ be a predefined threshold for evaluating the similarity degree $r\left(CP,G{P}^k\right)$ between the consumer profile $\left(CP\right)$ and the garment profile $\left(G{P}^k\right)$. Thus, we define the recommendation rules as follows:

(1)

Calculate a list of $r\left(CP,G{P}^k\right)$ for all the garment profiles in $G$ and sort them in descending order;

(2)

Recommend the garment profiles with $r\left(CP,G{P}^k\right)\ge \rho$ to the consumer or designer;

(3)

If $r\left(CP,G{P}^k\right)$ of all the garment profiles $GP$ is less than $\rho$, it means that all the existing garments cannot meet the requirements. Next, the self-adaptation mechanism will be activated based on the garment adaptation model.

3.1.1. Construction of the Style Relational Model

The main function of the style relational model was to evaluate the similarity degree $r\left(SR,S{C}^k\right)$ between the style requirements $\left(SR\right)$ of the consumer and the style characteristics $\left(S{C}^k\right)$ of a garment profile $G{P}^k$. Based on the classical similarity measurement approach [60,61], the $r\left(SR,S{C}^k\right)$ is defined by Equation (2):

$$r\left(SR,S{C}^k\right)=\frac{{{\displaystyle \sum }}_j{{\displaystyle \sum }}_{i}min\left(s{r}_i,s{c}_i\right)}{{{\displaystyle \sum }}_j{{\displaystyle \sum }}_{i}max\left(s{r}_i,s{c}_i\right)}\left(s{r}_i\in S{R}_j\in SR,s{c}_i\in S{C}_j\in S{C}^k\right)$$

(2)

From Equation (2), we can find that values of $r\left(SR,S{C}^k\right)$ vary between 0 and 1. If all style elements of $SR$ and $S{C}^k$ are close to each other, the value of $r\left(SR,S{C}^k\right)$ is close to 1. Otherwise, it tends to 0.

3.1.2. Construction of the Color Relational Model

The color relational model is mainly built to represent the similarity degree $r\left(CR,C{C}^k\right)$ between the color requirements $\left(CR\right)$ of the consumer and the color characteristics $\left(C{C}^k\right)$ in the proposed system. Based on the Euclidean distance, to keep the consistency with the function monotonicity of Equation (2), the $r\left(CR,C{C}^k\right)$ is defined by Equation (3).

$$r\left(CR,C{C}^k\right)=1-\frac{\sqrt{\left({\left(c{r}_{red}-c{c}_{red}\right)}^2+{\left(c{r}_{green}-c{c}_{green}\right)}^2+{\left(c{r}_{blue}-c{c}_{blue}\right)}^2\right)/3}}{255}$$

(3)

Equation (3) shows that the larger the value is, the nearer the color requirements $\left(CR\right)$ and the color characteristics $\left(C{C}^k\right)$ could be.

3.1.3. Construction of the Fabric Relational Model

The fabric relational model was created to recommend the most relevant fabric in the proposed system. The relationship $r\left(MR,M{C}^k\right)$ between the fabric requirements $\left(MR\right)$ of the consumer and the fabric characteristics $\left(M{C}^k\right)$ in the system is computed by Equation (4) using the same modeling method as Equation (2).

$$r\left(MR,M{C}^k\right)=\frac{min\left(s{m}^r,s{m}^c\right)+min\left(s{f}^r,s{f}^c\right)+min\left(w{m}^r,w{m}^c\right)}{max\left(s{m}^r,s{m}^c\right)+max\left(s{f}^r,s{f}^c\right)+max\left(w{m}^r,w{m}^c\right)}$$

(4)

According to Equation (4), the values of $r\left(MR,M{C}^k\right)$ are between 0 and 1. The larger value would indicate that the fabric characteristics $\left(M{C}^k\right)$ are closer to the fabric requirements $\left(MR\right)$.

3.1.4. Construction of the Garment Fit Relational Model

The main objective of the garment fit relational model was established to express the relationship $r\left(FR,F{C}^k\right)$ between the garment fit requirements $\left(FR\right)$ of the consumer and the characteristics of the garment fit in the system $\left(F{C}^k\right)$.

According to the same modeling method of $r\left(SR,S{C}^k\right)$ and $r\left(MR,M{C}^k\right)$, for each of the $j$ feature positions of the garment, the local garment fit relational model $r\left(F{R}_i,F{C}_i\right)$ is denoted by Equation (5):

$$r\left(F{R}_i,F{C}_i^k\right)=\frac{min\left(t{t}_i^r,t{t}_i^c\right)+min\left(t{i}_i^r,t{i}_i^c\right)+min\left(n{l}_i^r,n{l}_i^c\right)+min\left(l{o}_i^r,l{o}_i^c\right)+min\left(t{l}_i^r,t{l}_i^c\right)}{max\left(t{t}_i^r,t{t}_i^c\right)+max\left(t{i}_i^r,t{i}_i^c\right)+max\left(n{l}_i^r,n{l}_i^c\right)+max\left(l{o}_i^r,l{o}_i^c\right)+max\left(t{l}_i^r,t{l}_i^c\right)}$$

(5)

Then, the global garment fit relational model $r\left(FR,F{C}^k\right)$ is calculated as an average value by Equation (6).

$$r\left(FR,F{C}^k\right)=\mathrm{avg}\left(r\left(F{R}_i,F{C}_i^k\right)\right)\left(F{C}_i^k\in F{C}^k,F{R}_i\in FR\right)$$

(6)

Both the values of $r\left(F{R}_i,F{C}_i^k\right)$ and $r\left(FR, F{C}^k\right)$ are between 0 and 1. From Equation (5), if the local fit characteristics $\left(F{C}_i^k\right)$ are close to the fit requirements $\left(F{R}_i\right)$, the value of $r\left(F{R}_i, F{C}_i^k\right)$ is close to 1. Otherwise, it tends to 0. Similarly, following Equation (6), if the value of $r\left(FR, F{C}^k\right)$ is close to 1, it means that the global fit characteristics $\left(F{C}^k\right)$ are close to the fit requirements $\left(FR\right)$ and vice versa.

3.2. Construction of Garment Design Adaptation Model

3.2.1. General Framework and Process of the Garment Design Adaptation Model

As shown in Figure 3, the complete garment design adaptation model is composed of three sequential linked parts, including the GA-based design solution generation model (sub-model 1), the linear model (sub-model 2) supported by a knowledge-based design database, and the SVR-based adaptation rule model (sub-model 3). The inputs of the adaptation model are the requirements for the style design elements $\left(SR\right)$ expressed by the normalized vectors and the garment fit requirements $\left(FR\right)$ for the feature positions. The outputs of the model are the movements of the controlling points on the garment patterns.

Concretely, the computation process of the adaptation model is composed of three sequential steps (see Figure 3). First, a new and normalized design solution with new style and garment fit levels is generated by the design solution generation model using a genetic algorithm (GA). Next, the general garment adaptation requirements are obtained by combining the outputs of the design solution generation model with the standard design and fitting solution from the knowledge-based design database. Eventually, the movements of the controlling points on the garment patterns are determined by a supported vector regression (SVR)-based adaptation rule model, following the adaptation requirements.

3.2.2. Construction of the Garment Design Solution Generation Model

As the genetic algorithm (GA) has the advantages of fast convergence and simple encoding, it was employed in this study to rapidly generate multiple new solutions to meet the uncertain and vague requirements of the consumer.

Let the fit value $f_{S{R}_j}^{fitness}$ for the style design requirement $S{R}_j$ be denoted as Equation (7), and the fit value $f_{F{R}_j}^{fitness}$ for the fit requirement $F{R}_j$ be denoted as Equation (8).

$$f_{S{R}_j}^{fitness}=\left|S{C}_j^{new}-S{R}_j\right|\left(S{R}_j\in SR\right)$$

(7)

where $S{C}_j^{new}$ represents the new style characteristics.

$$f_{F{R}_j}^{fitness}=\left|F{C}_j^{new}-F{R}_j\right|\left(F{R}_j\in FR\right)$$

(8)

where $F{C}_j^{new}$ represents the new fit characteristics.

From Equations (7) and (8), a smaller value of the $f_{S{R}_j}^{fitness}$ or $f_{F{R}_j}^{fitness}$ indicates a more optimal fit degree.

The implementation process of the GA-based sub-model is described below. The termination criteria of the GA-based sub-model were determined as: (1) the predefined maximum iteration is reached; (2) the average variation in the fit function values with a specific number of generations is less than a pre-designed tolerance; (3) the consumer’s requirements are satisfied. For each $S{R}_j$ or $F{R}_j$, the consumer’s requirement can be defined as two sets, $S{R}_j^{constraint}$ and $F{R}_j^{constraint}$. If the terminal criteria were not satisfied, the process of “selection-crossover-mutation-calculation-evaluation” would be implemented repeatedly until the terminal criteria were reached. The objective functions of GA are denoted as Equations (9) and (10).

$$\underset{S{C}_j^{new}}{\mathrm{argmin}}\left(f_{S{R}_j}^{fitness}\right)\left(S{R}_j\in SR,S{C}_j^{new}\in S{R}_j^{constraint}\right)$$

(9)

$$\underset{F{C}_j^{new}}{\mathrm{argmin}}\left(f_{F{R}_j}^{fitness}\right)\left(F{R}_j\in FR,F{C}_j^{new}\in F{R}_j^{constraint}\right)$$

(10)

3.2.3. Calculation of the New Garment Ease Allowances

The ease allowance is denoted as a metric indicating the extra space difference between the human body and the garment to express the various characteristics of the style design elements and the garment fit levels [39,62,63].

The new garment ease allowance in this study is calculated by Equation (11):

$$G{E}_i^{new}=\left\{\begin{array}{c}O{P}_i·G{E}_i^{std} O{P}_{i}isS{C}_i^{new}\\ O{P}_i·G{F}_i^{std} O{P}_i is F{C}_i^{new} \end{array}\right.$$

(11)

where $G{E}_i^{new}$ refers to the new garment ease allowance of the new garment design solution at the $i$ feature position; $O{P}_i$ represents the $i$-th output of the design solution generation model, which could be $S{C}_i^{new}$ or $F{C}_i^{new}$; $G{E}_i^{std}$ is denoted as a knowledge-based standard garment ease allowance vector at the $i$ feature position; $G{F}_i^{std}$ is denoted as a knowledge-based standard garment fitting vector at the $i$ feature position (see Figure 3).

For example, if $O{P}_i=S{C}_{waistline}^{new}=\left[\begin{array}{ccc}\stackrel{lw}{0.3}& \stackrel{nw}{0.7}& \stackrel{hw}{0}\end{array}\right]$, indicating that the new waistline was close to the normal waistline by 70% and the lower waistline by 30%, $G{E}_{waistline}^{std}={\left[\begin{array}{ccc}\stackrel{lw}{g{e}_1}& \stackrel{nw}{g{e}_2}& \stackrel{hw}{g{e}_3}\end{array}\right]}^T$, then the new garment ease for the waistline position $G{E}_{waistline}^{new}$ can be computed by $G{E}_{waistline}^{new}=0.3\times g{e}_1+0.7\times g{e}_2+0\times g{e}_3$.

If $O{P}_i=F{C}_{waistgirth}^{new}=\left[\begin{array}{ccccc}\stackrel{tt}{0}& \stackrel{ti}{0}& \stackrel{nl}{0.65}& \stackrel{lo}{0.35}& \stackrel{tl}{0}\end{array}\right]$, meaning that the new garment fit level of the waist girth was close to the neutral fit by 65% and the loose fit by 35%, and $G{F}_i^{std}={\left[\begin{array}{ccccc}\stackrel{tt}{g{f}_1}& \stackrel{ti}{g{f}_2}& \stackrel{nl}{g{f}_3}& \stackrel{lo}{g{f}_4}& \stackrel{tl}{g{f}_5}\end{array}\right]}^T$, then the new garment ease for the fit level of waist girth $G{E}_{waistgirth}^{new}$ can be calculated by $G{E}_{waistgirth}^{new}=0\times g{f}_1+0\times g{f}_2+0.65\times g{f}_3+0.35\times g{f}_4+0\times g{f}_5$.

3.2.4. Determination of the General Garment Adaptation Requirements

The general garment adaptation requirements are defined by $AR=\left\{A{R}_1,A{R}_2,\cdots ,A{R}_i\right\}$, where $A{R}_i$ is computed following Equation (12):

$$A{R}_i=G{E}_i^{new}-G{E}_i^k$$

(12)

where $G{E}_i^k$ expresses the garment ease allowance of the most relevant existing garment in the proposed system corresponding to the $G{E}_i^{new}$. For instance, if the $G{E}_i^{new}$ represented the new ease allowance of the waistline position, then $G{E}_i^k$ would express the ease allowance of the waistline position for the most relevant existing garment in the system.

3.2.5. Construction of the Garment Design Adaptation Model

Due to its easy implementation, simple network topology, and high generalized capability, for each structural line $s{l}_i$, the relations between the length variation of the line $\left(dl\text{\_}s{l}_i\right)$ and the movements of the corresponding points $\left(dx\text{\_}c{p}_i^{start},dy\text{\_}c{p}_i^{start},dx\text{\_}c{p}_i^{end},dy\text{\_}c{p}_i^{end}\right)$ are modeled using support vector regression (SVR), as shown in Figure 4. The Bayesian approach presented by Jonas Mockus is a sequential design strategy for the global optimization of “black-box” functions [64]. In this study, Bayesian optimization was utilized to determine the parameters of the SVR models in our work. Meanwhile, a 10-fold cross-validation approach was introduced to train the SVR models. The complete garment design adaptation model is composed of the SVR models of all the structural lines.

4. Implementation and Application

Due to its simple structure with basic and necessary structure lines (e.g., waistline, outside seam, hemline, inseam, crotch line, etc.), the patterns of sports leggings were employed as the representative of the basic pattern of pants in this study. Therefore, in this section, to explicate our present approach with clarity, we implemented the proposed system to design personalized pants (represented by sports legging) for a specific male consumer. In the sequential section (Section 5), the design of other styles of pants with more complicated structures and detailed design elements will be discussed.

As shown in Figure 5, the style design elements of the pants in the proposed system were classified into ten categories (i.e., silhouette, length, waistline position, and waistband, etc.) and 50 types (i.e., H type, A type, O type, T type, X type, etc.). The requirements and characteristics corresponding to the length and waistline position were defined by the normalized vectors, while those of the remaining style elements were defined by the one-hot vectors.

4.1. Determination of the Consumer Profile

The consumer profile was constituted by the requirements for the style, color, fabric, and garment fit level. The requirements for the pants style elements and garment fit levels were shown in

Table 1. The requirements for the pants style elements $SR$.

S.N.	Category	Type	Style Requirements
1	Silhouette	$S{R}_1=\left[\begin{array}{ccccc}0& 0& 0& 0& 1\end{array}\right]$	Skinny type
2	Length	$S{R}_2=\left[\begin{array}{cccccc}0& 0& 0& 0& 0.2& 0.8\end{array}\right]$	Close to ankle length by 80% and full length by 20%
3	Waistline position	$S{R}_3=\left[\begin{array}{ccc}0.25& 0.75& 0\end{array}\right]$	Close to normal waistline by 75% and lower waistline by 25%
4	Waistband	$S{R}_4=\left[\begin{array}{ccc}0& 1& 0\end{array}\right]$	Straight waistband
5	Leg opening	$S{R}_5=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]$	Tapered leg opening
6	Dart	$S{R}_6=\left[\begin{array}{cccccc}1& 0& 0& 0& 1& 0\end{array}\right]$	No front and back dart
7	Pleat	$S{R}_7=\left[\begin{array}{cccc}1& 0& 0& 0\end{array}\right]$	No front pleat
8	Yoke	$S{R}_8=\left[\begin{array}{cccc}1& 0& 0& 0\end{array}\right]$	No yoke
9	Ornament	$S{R}_9=\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 1\end{array}\right]$	No ornament
10	Pocket	$S{R}_{10}=\left[\begin{array}{ccccccccccc}1& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0\end{array}\right]$	No front and no back pocket

;

Table 2. The requirements of garment fit levels at feature positions $FR$.

S.N.	Feature Position	Normalized Garment Fit Level Requirements	Garment Fit Level Requirements
1	Waist girth	$F{R}_1=\left[\begin{array}{ccccc}0& 1& 0& 0& 0\end{array}\right]$	Tight
2	Hip girth	$F{R}_2=\left[\begin{array}{ccccc}0& 1& 0& 0& 0\end{array}\right]$	Tight
3	Knee girth	$F{R}_3=\left[\begin{array}{ccccc}0& 1& 0& 0& 0\end{array}\right]$	Tight
4	Ankle girth	$F{R}_4=\left[\begin{array}{ccccc}0& 1& 0& 0& 0\end{array}\right]$	Tight

. The color requirements were expressed by $CR=\left[\begin{array}{ccc}77& 73& 72\end{array}\right]$, meaning that the required value of red, green, and blue were 77, 73, and 72, respectively. The fabric requirements were represented by $MR=\left[\begin{array}{ccc}0.4& 0.45& 0.4\end{array}\right]$, indicating that the required values of fabric smoothness, softness, and warmth were 0.4, 0.45, and 0.4, respectively.

4.2. Determination of the Garment Profile

The garment profile was constituted by the characteristics of the style, color, fabric, and garment fit level. It is assumed that there are five kinds of leggings patterns, five kinds of fabrics, and five kinds of colors in the proposed system.

These were the two approaches for determining the style characteristics. For the style elements, whose requirements and characteristics were defined by one-hot vectors, including the silhouette ($S{R}_1$), the waistband ($S{R}_4$), the leg opening ($S{R}_5$), the dart ($S{R}_6$), the pleat ($S{R}_7$), the yoke ($S{R}_8$), the ornament ($S{R}_9$), and the pocket ($S{R}_{10}$).

For the remaining elements, involving the length ($S{R}_2$) and the waistline position ($S{R}_3$), their characteristics (see

Table 3. The characteristics of the length and waistline position.

Garment	Category	Type	Style Characteristics
$G^1$	Length	$S{C}_{length}^1=\left[\begin{array}{cccccc}0& 0& 0& 0.58& 0.42& 0\end{array}\right]$	Close to calf length by 58% and ankle length by 42%
	Waistline position	$S{C}_{waist-line}^1=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]$	Lower waistline
$G^2$	Length	$S{C}_{length}^2=\left[\begin{array}{cccccc}0& 0& 0& 0.47& 0.53& 0\end{array}\right]$	Close to calf length by 47% and ankle length by 53%
	Waistline position	$S{C}_{waist-line}^2=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]$	Lower waistline
$G^3$	Length	$S{C}_{length}^3=\left[\begin{array}{cccccc}0& 0& 0& 0.4& 0.6& 0\end{array}\right]$	Close to calf length by 40% and ankle length by 60%
	Waistline position	$S{C}_{waist-line}^3=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]$	Lower waistline
$G^4$	Length	$S{C}_{length}^4=\left[\begin{array}{cccccc}0& 0& 0& 0.33& 0.67& 0\end{array}\right]$	Close to calf length by 33% and ankle length by 67%
	Waistline position	$S{C}_{waist-line}^4=\left[\begin{array}{ccc}0.77& 0.23& 0\end{array}\right]$	Close to lower waistline by 77% and normal waistline by 23%
$G^5$	Length	$S{C}_{length}^5=\left[\begin{array}{cccccc}0& 0& 0& 0.26& 0.74& 0\end{array}\right]$	Close to calf length by 26% and ankle length by 74%
	Waistline position	$S{C}_{waist-line}^6=\left[\begin{array}{ccc}0.5& 0.5& 0\end{array}\right]$	Close to lower waistline by 50% and normal waistline by 50%

) were calculated based on fuzzy classification. We take the calculation of the characteristics of the waistline position as an example by which to expound on the proposed method. The concrete procedures were as follows:

Step 1: The waistline position’s fuzzy membership functions $M{F}_{S{C}_{wl}}$ are defined as below:

$$M{F}_{lowerwaistline}\left(g{e}^{wl}\right)=\left\{\begin{array}{cc}1,& g{e}^{wl}\in \left[-\infty ,-3\right]\\ -\frac{g{e}^{wl}}{3},& g{e}^{wl}\in \left[-3,0\right]\\ 0,& otherwise\end{array}\right.$$

(13)

$$M{F}_{normalwaistline}\left(g{e}^{wl}\right)=\left\{\begin{array}{cc}\frac{g{e}^{wl}}{3}+1,& g{e}^{wl}\in \left[-3,0\right]\\ -\frac{g{e}^{wl}}{3}+1,& g{e}^{wl}\in \left[0,3\right]\\ 0,& otherwise\end{array}\right.$$

(14)

$$M{F}_{highwaistline}\left(g{e}^{wl}\right)=\left\{\begin{array}{cc}\frac{g{e}^{wl}}{3},& g{e}^{wl}\in \left[0,3\right]\\ 1,& g{e}^{wl}\in \left[3,+\infty \right]\\ 0,& otherwise\end{array}\right.$$

(15)

where $g{e}^{wl}$ refers to the garment ease allowance of the waistline position.

Step 2: For each pattern, we calculated the $g{e}^{wl}$, following the computation method illustrated and expounded in Figure 6.

Meanwhile, the characteristics of the garment fit levels (see

Table 4. The characteristics of the garment fit levels.

	Feature Position	Formalized Garment Fit Level Characteristics	Garment Fit Level Characteristics
$G^1$	Waist girth	$F{C}_{waist-girth}^1=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
	Hip girth	$F{C}_{hip-girth}^1=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
	Knee girth	$F{C}_{knee-girth}^1=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
	Ankle girth	$F{C}_{ankle-girth}^1=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
$G^2$	Waist girth	$F{C}_{waist-girth}^2=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
	Hip girth	$F{C}_{hip-girth}^2=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
	Knee girth	$F{C}_{knee-girth}^2=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
	Ankle girth	$F{C}_{ankle-girth}^2=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
$G^3$	Waist girth	$F{C}_{waist-girth}^3=\left[\begin{array}{ccccc}0& 0.45& 0.55& 0& 0\end{array}\right]$	Close to tight by 45% and neutral by 55%
	Hip girth	$F{C}_{hip-girth}^3=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
	Knee girth	$F{C}_{knee-girth}^3=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
	Ankle girth	$F{C}_{ankle-girth}^3=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
$G^4$	Waist girth	$F{C}_{waist-girth}^4=\left[\begin{array}{ccccc}0& 0& 0& 0.45& 0.55\end{array}\right]$	Close to loose by 45% and too loose by 55%
	Hip girth	$F{C}_{hip-girth}^4=\left[\begin{array}{ccccc}0.22& 0.78& 0& 0& 0\end{array}\right]$	Close to too tight by 22% and tight by 78%
	Knee girth	$F{C}_{knee-girth}^4=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
	Ankle girth	$F{C}_{ankle-girth}^4=\left[\begin{array}{ccccc}0.82& 0.18& 0& 0& 0\end{array}\right]$	Close to too tight by 82% and tight by 18%
$G^5$	Waist girth	$F{C}_{waist-girth}^5=\left[\begin{array}{ccccc}0& 0& 0& 0& 1\end{array}\right]$	Too loose
	Hip girth	$F{C}_{hip-girth}^5=\left[\begin{array}{ccccc}0& 0.22& 0.78& 0& 0\end{array}\right]$	Close to tight by 22% and neutral by 78%
	Knee girth	$F{C}_{knee-girth}^5=\left[\begin{array}{ccccc}1& 0& 0& 0& 0\end{array}\right]$	Too tight
	Ankle girth	$F{C}_{ankle-girth}^5=\left[\begin{array}{ccccc}0& 0& 0& 0.42& 0.58\end{array}\right]$	Close to loose by 42% and too loose by 58%

) were also determined by the fuzzy classification approach.

Additionally, the characteristics of the color and fabric are shown in

Table 5. The characteristics of the color and fabric.

Fabric No.	Formalized Fabric Property	Fabric Property	Color No.	Formalized Color Characteristics	Color Characteristics
1	$M{C}^1=\left[\begin{array}{ccc}0.12& 0.12& 0.15\end{array}\right]$	Smoothness: 0.12 Softness: 0.12 Warmth: 0.25	1	$C{C}^1=\left[\begin{array}{ccc}26& 24& 19\end{array}\right]$	Red: 26 Green: 24 Blue: 19
2	$M{C}^2=\left[\begin{array}{ccc}0.1& 0.1& 0.25\end{array}\right]$	Smoothness: 0.1 Softness: 0.1 Warmth: 0.25	2	$C{C}^2=\left[\begin{array}{ccc}24& 27& 38\end{array}\right]$	Red: 24 Green: 27 Blue: 38
$3$	$M{C}^3=\left[\begin{array}{ccc}0.9& 0.1& 0.45\end{array}\right]$	Smoothness: 0.9 Softness: 0.1 Warmth: 0.45	3	$C{C}^3=\left[\begin{array}{ccc}46& 42& 33\end{array}\right]$	Red: 46 Green: 42 Blue: 33
4	$M{C}^4=\left[\begin{array}{ccc}0.85& 0.65& 0.15\end{array}\right]$	Smoothness: 0.85 Softness: 0.65 Warmth: 0.15	4	$C{C}^4=\left[\begin{array}{ccc}51& 47& 36\end{array}\right]$	Red: 51 Green: 47 Blue: 36
5	$M{C}^5=\left[\begin{array}{ccc}0.7& 0.2& 0.55\end{array}\right]$	Smoothness: 0.7 Softness: 0.2 Warmth: 0.55	5	$C{C}^5=\left[\begin{array}{ccc}64& 54& 43\end{array}\right]$	Red: 64 Green: 54 Blue: 43

.

4.3. Evaluation of the Relationship between Consumer Profile and Garment Profile

According to Equation (1), ${\alpha }_1$, ${\alpha }_2$, ${\alpha }_3$, and ${\alpha }_4$, corresponding to the weights of the style, color, fabric, and garment fit, were set to 0.45, 0.05, 0.05, and 0.45, using the analytic hierarchy process (AHP). According to Equation (2), we obtained the relationships between the style requirements and the style characteristics of the five patterns: $r\left(SR,S{C}^1\right)=0.6721$, $r\left(SR,S{C}^2\right)=0.6727$, $r\left(SR,S{C}^3\right)=0.6730$, $r\left(SR,S{C}^4\right)=0.7148$, and $r\left(SR,S{C}^5\right)=0.7665$.

According to Equation (3), we obtained the relationships between the color requirements and the five color characteristics in the system:$r\left(CR,C{C}^1\right)=0.011,r\left(CR,C{C}^2\right)=0.013,r\left(CR,C{C}^3\right)=0.017,$ $r\left(CR,C{C}^4\right)=0.019$, and $r\left(CR,C{C}^5\right)=0.027$.

According to Equation (4), we obtained the relationships between the fabric requirements and the three fabrics in the system: $r\left(MR,M{C}^1\right)=0.312$, $r\left(MR,M{C}^2\right)=0.36$, $r\left(MR,M{C}^3\right)=0.50$, $r\left(MR,M{C}^4\right)=0.53$, and $r\left(MR,M{C}^5\right)=0.59$.

According to Equations (5) and (6), we obtained the relationships between the garment fit requirements and the garment fit characteristics of the pants in the system: $r\left(FR,F{C}^1\right)=0$, $r\left(FR,F{C}^2\right)=0$, $r\left(FR,F{C}^3\right)=0.0726$, $r\left(FR,F{C}^4\right)=0.1330$, and $r\left(FR,F{C}^5\right)=0.1846$.

Then, with the combinations of the five fabrics, five colors, and five size patterns, we created 125 pants profiles and evaluated them based on Equation (1).

Table 6. The combinations of color, fabric, and patterns with the top 5 $r\left(CP,G{P}^k\right)$ .

No.	$\mathit{r}\left(\mathit{S}\mathit{R},\mathit{S}{\mathit{C}}^{\mathit{k}}\right)$	$\mathit{r}\left(\mathit{C}\mathit{R},\mathit{C}{\mathit{C}}^{\mathit{k}}\right)$	$\mathit{r}\left(\mathit{M}\mathit{R},\mathit{M}{\mathit{C}}^{\mathit{k}}\right)$	$\mathit{r}\left(\mathit{F}\mathit{R},\mathit{F}{\mathit{C}}^{\mathit{k}}\right)$	$\mathit{r}\left(\mathit{C}\mathit{P},\mathit{G}{\mathit{P}}^{\mathit{k}}\right)$
1	0.7665	0.027	0.59	0.1846	0.4588
2	0.7665	0.019	0.59	0.1846	0.4584
3	0.7665	0.017	0.59	0.1846	0.4583
4	0.7665	0.013	0.59	0.1846	0.4581
5	0.7665	0.011	0.59	0.1846	0.4580

shows the top five $r\left(CP,G{P}^k\right)$ in our database $GP$.

If the tolerance $\rho$ was set to 0.40, all the top five pants combinations (see Table 6) would be recommended to the consumer based on the 3D virtual try-on technology. Additionally, combination one would be recommended first due to the highest $r\left(CP,G{P}^k\right)$ value. If the tolerance $\rho$ was set to 0.80, none of the combinations at present would meet the requirements. A self-adaptation mechanism will be active until $r\left(CP,G{P}^k\right)\ge \rho$.

4.4. Adaptation of the Pants Style and Fit Level

According to $r\left(CP,GP\right)$, the combination of pattern 5, color $1$, and fabric $1$ was selected as the most relevant style and pattern for further adaptation. Furthermore, the six parts, including the pants length, waistline position, waist girth, hip girth, knee girth, and ankle girth, were chosen for further adjustment until $r\left(CP,G{P}^{new}\right)\ge \rho$ ($G{P}^{new}$ refers to the new pants profile.).

According to the modeling method described in Section 3.2.2, we constructed six varied GA-based models to generate new normalized style and garment fit level characteristics vectors (see

Table 7. New normalized style and garment fit level characteristics.

Style Element	Normalized Characteristics Vector
Length	$S{C}_{pl}^{new}=\left[\begin{array}{ccc}0& 0& 0\end{array}\begin{array}{ccc}0.196& 0.804& 0\end{array}\right]$
Waistline position	$S{C}_{wl}^{new}=\left[\begin{array}{ccc}0.282& 0.734& 0\end{array}\right]$
Waist girth	$F{C}_{wg}^{new}=\left[\begin{array}{ccc}0& 0.963& 0.037\end{array}\begin{array}{cc}0& 0\end{array}\right]$
Hip girth	$F{C}_{hg}^{new}=\left[\begin{array}{ccc}0& 0.977& 0.023\end{array}\begin{array}{cc}0& 0\end{array}\right]$
Knee girth	$F{C}_{kg}^{new}=\left[\begin{array}{ccc}0& 0.983& 0.017\end{array}\begin{array}{cc}0& 0\end{array}\right]$
Ankle girth	$F{C}_{ag}^{new}=\left[\begin{array}{ccc}0& 0.991& 0.009\end{array}\begin{array}{cc}0& 0\end{array}\right]$

), which were used as the inputs of the garment ease allowance database to generate the new ease allowances of the new garment design solution. In this study, the population sizes of the individuals were set to 50. To remove the effects of the raw fit scores returned by the fit function, rank scaling is employed. Then, we applied the roulette method to realize the selection of the individuals. In addition, the single-point crossover method was utilized to generate new individuals. The constraint-dependent approach was used to perform the mutation.

Then, according to Equations (1)–(6), we obtained the $R\left(CP,G{P}^{new}\right)=0.837>\rho \left(=0.80\right)$, meaning that the objective of the adaptation was reached.

4.5. Adaptation of the Pants Patterns

Step 1: The new garment ease allowance for the six parts was calculated based on Equation (9).

Table 8. The garment ease in the garment ease allowance database (Unit: cm).

No.	Design Elements	Garment Ease Corresponding to Various Style and Garment Fit Characteristics
1	Waistline position	$G{E}_{wl}^{std}={\left[\begin{array}{ccc}\stackrel{lw}{-3}& \stackrel{nw}{0}& \stackrel{hw}{0}\end{array}\right]}^T$
2	Pants length	$G{E}_{pl}^{std}={\left[\begin{array}{cccccc}\stackrel{ml}{-0.8WH}& \stackrel{tl}{-0.7WH}& \stackrel{kl}{-0.5WH}& \stackrel{cl}{-0.3WH}& \stackrel{al}{-0.1WH}& \stackrel{fl}{0}\end{array}\right]}^T$
3	Waist girth	$G{E}_{wg}^{std}={\left[\begin{array}{ccccc}\stackrel{tt}{-2}& \stackrel{ti}{0}& \stackrel{nl}{2}& \stackrel{lo}{4}& \stackrel{tl}{6}\end{array}\right]}^T$
4	Hip girth	$G{E}_{hg}^{std}={\left[\begin{array}{ccccc}\stackrel{tt}{0}& \stackrel{ti}{4}& \stackrel{nl}{8}& \stackrel{lo}{12}& \stackrel{tl}{16}\end{array}\right]}^T$
5	Knee girth	$G{E}_{kg}^{std}={\left[\begin{array}{ccccc}\stackrel{tt}{0}& \stackrel{ti}{3}& \stackrel{nl}{6}& \stackrel{lo}{9}& \stackrel{tl}{12}\end{array}\right]}^T$
6	Ankle girth	$G{E}_{ag}^{std}={\left[\begin{array}{ccccc}\stackrel{tt}{0}& \stackrel{ti}{4}& \stackrel{nl}{8}& \stackrel{lo}{12}& \stackrel{tl}{16}\end{array}\right]}^T$

Where $WH$ is denoted as the waist height of the human body.

shows the standard garment ease corresponding to the various style and garment fit characteristics.

Step 2: Through comparing with the ease data of pattern five, we obtained the general adaption requirements for each feature position (see

Table 9. The adaptation requirements of the pattern (unit: cm).

Human Body		Pattern 5			Target Patterns		Adaptation Requirements
Position 1	Dimension 1	Position 2	Dimension 2	Ease I	Position 3	Ease II
$W{G}_h$	68.9	$W{G}_{P5}$	78	9.1	$W{G}_{TG}$	0	−9.1
$H{G}_h$	88.9	$H{G}_{P5}$	96	7.1	$H{G}_{TG}$	3.908	−3.192
$K{G}_h$	35.2	$K{G}_{P5}$	32	−3.2	$K{G}_{TG}$	2.949	6.149
$A{G}_h$	23.3	$O{G}_{P5}$	25	1.7	$O{G}_{TG}$	3.964	2.264
$C{L}_h$	28.4	$C{L}_{P5}$	26.9	−1.5	$C{L}_{TG}$	−0.846	0.636
$W{H}_h$	106	$P{L}_{P5}$	90	−16	$P{L}_{TG}$	−14.755	1.245

Where $W{G}_h$, $H{G}_h$,$K{G}_h$,$A{G}_h$,$C{L}_h$, and $W{H}_h$ are denoted as the waist girth, hip girth, knee girth, ankle girth, crotch length, and waist height of the human body, respectively; $W{G}_{P5}$, $H{G}_{P5}$,$K{G}_{P5}$,$A{G}_{P5}$,$C{L}_{P5}$, and $P{L}_{P5}$ refer to the waist girth, hip girth, knee girth, ankle girth, crotch length, and pants length of pattern 5, respectively; $W{G}_{TG}$, $H{G}_{TG}$,$K{G}_{TG}$,$A{G}_{TG}$,$C{L}_{TG}$, and $P{L}_{TG}$ refer to the waist girth, hip girth, knee girth, ankle girth, crotch length, and pants length of the target pattern, respectively.

). Furthermore, the adaptation requirements were distributed for each pattern element at feature position.

Step 3: Adaptation of the front panel (see Figure 7).

(1)

Calculation of the movement of the controlling point $c{p}_2$ of the structure line $s{l}_1$;

(2)

Calculation of the length deviation of the adjacent structure line $s{l}_2$ under the condition of the movement of the controlling point $c{p}_2$;

(3)

Checking of the length deviation of the structure line $s{l}_2$;

If the length deviation $dls{l}_2$ is less than a predefined threshold value $ϵ$, then we will check the adaptation results of the whole front pattern; otherwise, we will calculate the movement of the controlling point $c{p}_3$ of the structure line $s{l}_2$;

(4)

Checking the adaptation results of the whole front panel

If all the adaptation requirements of the front panel are satisfied, then the adaptation of the front panel terminates; otherwise, the adaptation of the structure line $s{l}_3$ will be activated;

(5)

The process of “checking-adaptation” will be executed repeatedly until all the remaining adaptation requirements are met.

Step 4: Adaptation of the back panel following the general principle described in Step 4. The final adaptation effects were illustrated in Figure 8. The hip part turned red from green for the adjusted pattern, meaning that the hip became tighter. Meanwhile, the knee part became blue, indicating that the part was looser than before.

5. Discussion

As mentioned in Section 4, the proposed system can be implemented in a personalized pants design with a simple structure, such as sports leggings. More significantly, it can be extended to realize the personalized design of the pants with more complicated structures and detailed design elements (e.g., darts, pleats, split lines, pockets, etc.) by creating associated design rules.

The method and procedures of the associated design of the detailed design elements will be concretely expounded in this section.

5.1. Associated Adaptation of the Darts/Pleats

Darts and pleats are considered as the critical style design elements to promote the garment appearance and fit. After adapting the outline of the pants patterns, the associated adaptation of the darts/pleats can be realized by defining the relationships between the darts/pleats and the corresponding structure lines and controlling points. Take, for instance, the realization of the associated adaptation of the front waist dart. The dart was positioned as shown in Figure 9. Then, the adaptation rules can be defined as follows:

(1)

The length of the dart $d{l}_{dp23}$ was set to a constant;

(2)

$d{x}_{dp0}=\left(d{x}_{cp1}-d{x}_{cp2}\right)/2$, $d{y}_{dp0}=\left(d{y}_{cp2}-d{y}_{cp3}\right)/2$;

(3)

$d{x}_{dp1}=d{x}_{dp0}$, $d{y}_{dp1}=d{y}_{cp1}=d{y}_{cp2};$

(4)

$d{x}_{dp2}=d{x}_{dp3}=d{x}_{dp0}$, $d{y}_{dp2}=d{y}_{dp3}=d{y}_{cp1}=d{y}_{cp2}$.

For the case described in Section 4, if the consumer selected a leggings style with a front waist dart, then the dart can be adjusted by the rules in Figure 9.

5.2. Associated Design of the Split Lines

The split lines are the common design elements in fashion design. After the dart adaptation, the pattern can be further developed to meet the users’ requirements on the split lines. Figure 10 shows a case of the development of the yoke pattern. From this case, it can be easily observed that the adjusted patterns based on the proposed system in this study can be very convenient in realizing the design of any types of split lines by combining it with the traditional pattern design knowledge.

5.3. Associated Adaptation of the Pockets

The pockets are also one of the key design elements of the pants. Take the adaptation of the patch pocket for example. The definition of the associated adaptation rules is given below.

(1)

$d{x}_{po1}=d{x}_{po4}-d_{open}/2$,$d{y}_{po1}=d{y}_{cp1}=d{y}_{cp2}$;

(2)

$d{x}_{po2}=d{x}_{po1}+d_{open}$, $d{y}_{po2}=d{y}_{po1}$;

(3)

$d{x}_{po3}=d{x}_{po2}$, $d{y}_{po3}=d{y}_{po1}+d_{length}$;

(4)

$d{x}_{po4}=\left(d{x}_{cp1}-d{x}_{cp2}\right)/2$, $d{y}_{po4}=d{y}_{po3}$;

(5)

$d{x}_{po5}=d{x}_{po1}$, $d{y}_{po5}=d{y}_{po4}=d{y}_{po3}$;

where $d_{open}$ and $d_{length}$ refer to the deviation rules of the pocket defined by the pattern designers. In this case, $d_{open}=d_{length}=0$.

Figure 11 shows a case of the adaptation of the patch pocket. From this case, it can be found that the associated adaptation of the pockets can be easily performed by modeling the relationships of the controlling points between the pockets and the outlines of the patterns.

5.4. Adaptation Effects Comparison

The fitting effects were compared between two kinds of patterns. Pants A were developed based on the proposed system, and pants B were designed by a professional pattern designer. As shown in Figure 12a, the shapes of the two kinds of patterns are rather similar. Moreover, from Figure 12b, the garment pressure distribution of the two pants was also very closed. It indicates that the garment fit of the two kinds of patterns is also similar. From the perspectives of the pattern shape and the garment fit, the conclusion can be drawn that the performance of the patterns developed by the proposed system in this paper is close to that of the patterns designed by the expert. Hence, it indicates that the proposed system offers a feasible solution for garment pattern makers to realize an automatic and intelligent design and adaptation of the garment patterns, particularly for the novices without sufficient expertise and experience.

6. Conclusions

In this research, we put forth a new interactive, personalized garment design recommendation approach based on a series of intelligent techniques, including fuzzy logic, genetic algorithms, and support vector regression. This system can be easily combined with classical 3D clothing design software (e.g., Lectra Modaris 3D, Clo 3D, Vstitcher, etc.) to form a new, interactive, personalized garment design process, enhancing the level of mass customization for various fashion brand companies. The proposed personalized design recommendation system is composed of a formalized garment design knowledge base (databases and relational models) and a garment design adaptation model. It can effectively characterize relations between consumer profiles and garment profiles to find the most relevant garment design solution. It can also be used for the estimation of the garment design technical parameters. More significantly, the self-adjusting adaptation mechanism for the garment patterns provided in the proposed system is critical in garment mass customization. The main contributions of this study can be summarized as follows: (1) the proposed approach can supply personalized garments with high accuracy and velocity, facilitating the implementation of mass customization; (2) the model proposed can not only help general consumers without a mastery of professional design knowledge to select proper personalized garments, but can also make the enterprises to control the design qualities precisely; (3) a new collaborative garment design process can be formed by combining the proposed knowledge-based system with a commercial 3D garment design software to satisfy the individualized demands of the consumer more intuitively, accurately, and promptly. Moreover, the performance of the knowledge bases and the system put forward can be enhanced progressively by supplementing new successful recommendation and design cases from the continuous implementation.

Due to the length limitation of the article, the implementation of the proposed system was validated in a personalized pants design only. The performance of the proposed system should be verified further by various garment styles, such as shirts, skirts, coats, dresses, and so on. Apart from the garment styles, the factors affecting the decision making in the garment recommendation processes, such as socio-cultural backgrounds and the user’s emotions, should also be fully taken into account in future research. Furthermore, the development of a personalized garment design recommendation system using more advanced intelligent techniques for higher quality recommendations constitutes one of our future research focuses.