Leslie A Sombersa

H Jacob Hanchara

Tom L Collivera

Nathan J Wittenberga

Ann-Sofie Cansc

Stéphane Arbaultd

Christian Amatored

Andrew G Ewinga

The modulation of vesicular volume and its effects on neurotransmitter secretion through the fusion

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The modulation of vesicular volume and its effects on neurotransmitter secretion through the fusion pore in PC12 Cells

Leslie Understanding vesicular exocytosis is fundamental to developing insight into the biology, chemistry and physics of neurotransmission. Through the direct 'presynaptic' observation of quantal release using amperometry it becomes strikingly evident that the exocytotic release event is regulated by multiple mechanisms1. For instance, many transients in amperometric records of exocytosis events exhibit a pre-spike feature, or foot, which represents a steadystate flux of neurotransmitter through a stable fusion pore connecting the vesicle lumen to the extracellular fluid2. This flux is thought to be driven by diffusion along a gradient of chemical potential. Recent work in our laboratory indicates that vesicular volume prior to secretion is strongly correlated with the characteristics of amperometric foot events, and furthermore, suggests that the protein dense core in many vesicles acts to pressurize the inner solution and drive catecholamine through the fusion pore3.

RESULTS AND DISCUSSION

In order to alter vesicular volume, we have used pharmacological manipulations that directly affect the VMATmediated transport of catecholamines into PC12 cell vesicles. Cells were incubated in 100 μM L-3,4-dihydroxyphenylalanine or 100 nM reserpine for 90 minutes in order to increase and decrease, respectively, the volume of single pheochromocytoma (PC12) cell vesicles4. Amperometry experiments utilizing a same-cell paradigm were used in conjunction with transmission electron microscopy to determine that as vesicle size is decreased the frequency with which foot events are observed increases. Consistent with this, fewer events with feet are observed as vesicle size is increased. Additionally, both the amount and duration of neurotransmitter released in the foot portion of the event decrease as vesicle size decreases, whereas both of these characteristics increase as vesicle size increases. Finally, smaller vesicles release a greater percentage of their total contents in the foot portion of the event. These trends provide evidence for a nanotube-like intermediate structure for the exocytotic fusion pore. This is shown in Figure 1B, where a model is presented to describe the effect of vesicle volume on membrane tension and fusion pore dynamics. A brief description of the mechanisms regulating neurotransmitter release via the fusion pore is presented in the figure legend. Treatment with reserpine diminishes the vesicular halo; however the volume of the dense core changes relatively little. In contrast, treatment with L-DOPA swells the vesicular halo, and again, the dense core volume remains relatively constant. B) Upon opening of the fusion pore, the dense core expands resulting in enhanced pressure-driven mass transport through the fusion pore and fluidic pressure on the interior vesicle walls. As the dense core to vesicular halo volume ratio is greatest for reserpine treated vesicles, it appears that the intravesicular pressure is greatest for these cells. An increase in intravesicular pressure increases vesicular membrane tension. If the fusion pore is of a nanotube geometry, this will lead to an immediate constriction of the fusion pore, as shown3. Subsequently, the increase in the difference in membrane tension from the cell to the vesicle should result in increased lipid flow through the fusion pore, decreasing its overall stability and resulting in an abrupt opening of the pore.

These studies are noteworthy because the dynamics of the exocytotic fusion pore have recently been proposed to play a role in synaptic plasticity5. Additionally, physiological6-8, genetic8 and pharmacological3,10 conditions can affect vesicle size, and in several instances vesicle size has been found to be inversely related to levels of synaptic activity9. This work provides new insight into the biological consequences of such vesicular volume modification. It 46 Cell Biology of the Chromaffin Cell provides evidence that cells may modulate the rate of neurotransmitter release, or the duration of that release, in the synaptic cleft by manipulating vesicle volume. This appears to be true in the case of release via the fusion pore that is formed in the early stages of exocytosis from PC12 cells.

  A Sombers, H. Jacob Hanchar, Tom L. Colliver, Nathan J Wittenberg, Ann-Sofie Cans, Stéphane Arbault, Christian Amatore, Andrew G Ewing To cite this version: Leslie A Sombers, H. Jacob Hanchar, Tom L. Colliver, Nathan J Wittenberg, Ann-Sofie Cans, et al.. The modulation of vesicular volume and its effects on neurotransmitter secretion through the fusion pore in PC12 Cells. 12th International Symposium on Chromaffin Cell Biology (ISCCB-12), Sep 2003, La Palma, Spain. hal-04467837

Figure 1 :

 1 Figure 1: A) Pharmacological manipulation of vesicle volume alters the dense core to vesicular halo volume ratio.Treatment with reserpine diminishes the vesicular halo; however the volume of the dense core changes relatively little. In contrast, treatment with L-DOPA swells the vesicular halo, and again, the dense core volume remains relatively constant. B) Upon opening of the fusion pore, the dense core expands resulting in enhanced pressure-driven mass transport through the fusion pore and fluidic pressure on the interior vesicle walls. As the dense core to vesicular halo volume ratio is greatest for reserpine treated vesicles, it appears that the intravesicular pressure is greatest for these cells. An increase in intravesicular pressure increases vesicular membrane tension. If the fusion pore is of a nanotube geometry, this will lead to an immediate constriction of the fusion pore, as shown3. Subsequently, the increase in the difference in membrane tension from the cell to the vesicle should result in increased lipid flow through the fusion pore, decreasing its overall stability and resulting in an abrupt opening of the pore.


Zhujun Wang

Xuyuan Tao

Xianyi Zeng

Yingmei Xing

Zhenzhen Xu

Pascal Bruniaux

Design of Customized Garments Towards Sustainable Fashion Using 3D Digital Simulation and Machine Learning-Supported Human-Product Interactions

Keywords: Interactive garment design, Machine learning, Sustainable fashion, Garment e-mass customization, Radial basis function artificial neural network, Genetic algorithm, Probabilistic neural network, Support vector regression

This paper put forward a new interactive design approach for customized garments towards sustainable fashion using machine learning techniques, including radial basis function artificial neural network (RBF ANN), genetic algorithms (GA), probabilistic neural network (PNN), and support vector regression (SVR). First, RBF ANNs were employed to estimate the detailed human body dimensions to fulfill consumers' ergonomics requirements. Next, the GA-based models were developed to generate the formalized design solutions following the consumer profiles (demands). Afterwards, the evaluation model was established to quantitatively characterize the relations between consumer profiles and garment profiles from the generated design solutions. The design solutions would be digitally demonstrated and recommended to the consumer following the evaluation results in descending order. Meanwhile, the PNN-based models were created to predict garment fitness based on virtual try-on. Moreover, the SVR-based self-adjustment mechanism was built to estimate and control garment design parameters according to the consumer's feedback. Based on these mathematical models, the approach enhances the interactions among digital garment demonstration, the designer's professional knowledge and the user's perception to find out the most relevant design solution. The effectiveness of the new approach was verified by a real application case of leisure pants customization. The results show that the proposed method can powerfully support the designers' quality personalized design solutions for consumers more accurately, fast, intelligently, and sustainably, compared with the existing approaches. More importantly, it also establishes an effective and reliable communication channel and mechanism among consumers, fashion designers, pattern designer, and garment producer.

Introduction

Over the past few decades, the fashion industry has been criticized to be one of the most polluting industries in the world [START_REF] Vătămănescu | Before and after the outbreak of Covid-19: Linking fashion companies' corporate social responsibility approach to consumers' demand for sustainable products[END_REF][START_REF] Charnley | Can digital technologies increase consumer acceptance of circular business models? The case of second hand fashion[END_REF][START_REF] Hofmann | Overcoming growth challenges of sustainable ventures in the fashion industry: a multinational exploration[END_REF][START_REF] Peleg Mizrachi | Sustainable fashion-rationale and policies[END_REF]. To change this situation, an innovation named sustainable fashion (SF) has occurred presently in the fashion industry [START_REF] Lee | Framing sustainable fashion concepts on social media. An analysis of #slowfashionaustralia Instagram Posts and Post-COVID visions of the future[END_REF]. The SF concentrates on the efforts to minimize the fashion industry's adverse environmental and social impacts [START_REF] Peleg Mizrachi | Sustainable fashion-rationale and policies[END_REF]. Hence, classical garment design and manufacturing should be innovated to satisfy the requirements of the SF in a more optimized manner [START_REF] Tao | A customized garment collaborative design process by using virtual reality and sensory evaluation on garment fit[END_REF]. For this purpose, garment e-mass customization (e-MC), aiming at enhancing the quality of products and their manufacturing to fulfil the consumer's personalized demands, has been adopted by many fashion companies [START_REF] Christensen | Enabling Mass Customization Life Cycle Assessment in Product Configurators[END_REF][START_REF] Martínez-Olvera | Towards the development of a digital twin for a sustainable mass customization 4.0 environment: a literature review of relevant concepts[END_REF][START_REF] Perret | Production scheduling of personalized fashion goods in a mass customization environment[END_REF]. Conventionally, quality customized garments are obtained by repeatedly performing the circle of "design-evaluation-adjustment" using physical prototypes. This design process is rather tedious and material wasting, leading to negative impacts on the environment [START_REF] Tao | Toward advanced three-dimensional modeling of garment prototype from draping technique[END_REF][START_REF] Chaw Hlaing | Garment prototyping based on scalable virtual female bodies[END_REF][START_REF] Harwood | JBlockCreator: an open source, pattern drafting framework to facilitate the automated manufacture of made-to-measure clothing[END_REF]. To overcome these shortcomings, cuttingedge digital technologies (i.e. 3D human body scanning and virtual reality) have been utilized for reshaping the entire garment customization process in a more sustainable way [START_REF] Kozlowski | Tools for sustainable fashion design: an analysis of their fitness for purpose[END_REF][START_REF] Li | Virtual reconstruction of 3D articulated human shapes applied to garment try-on in a virtual fitting room[END_REF][START_REF] Morotti | Exploiting fashion x-commerce through the empowerment of voice in the fashion virtual reality arena[END_REF][START_REF] Varadarajan | Digital product innovations for the greater good and digital marketing innovations in communications and channels: evolution, emerging issues, and future research directions[END_REF]. One of the most representative technologies is 3D digital simulation, also named virtual fitting, virtual try-on, etc. Since this technology can simulate the garment design process without making real garments [START_REF] Liu | An evaluation of garment fit to improve customer body fit of fashion design clothing[END_REF], the targets of material saving, environmental protection, and sustainability can be achieved. In the past few years, researchers have attempted to apply digital technologies for optimizing the quality of garment design. For example, Liu et al. suggested that a "what you see is what you get" way to design garment patterns efficiently [START_REF] Liu | 3D interactive garment pattern-making technology[END_REF]. Tao et al. originally put forward a customized 3D garment collaborative design process by integrating interactions between the designer and the specific consumer [START_REF] Tao | A customized garment collaborative design process by using virtual reality and sensory evaluation on garment fit[END_REF]. In Ref. [START_REF] Zhang | An integrated method of 3D garment design[END_REF], an intuitive method that seamlessly integrates the whole process of garment design including 3D modelling, pattern development, garment simulation, and grading was proposed by Zhang et al. Hong et al. present a virtual reality (VR)-based collaborative customized garment design methodology for disabled people with scoliosis [START_REF] Hong | Application of 3D-TO-2D garment design for atypical morphology: a design case for physically disabled people with scoliosis[END_REF]. Mulat et al. put forward a bra pattern design process for customizing female seamless soft armour based on innovative 3D reverse engineering approaches [START_REF] Abtew | Development of comfortable and well-fitted bra pattern for customized female soft body armor through 3D design process of adaptive bust on virtual mannequin[END_REF]. Han et al. proposed a 3D prototyping method and procedure for middle-aged women's swimsuit [START_REF] Han | Patternmaking for middle-aged women's swimsuit applying 3D scan pattern development[END_REF]. Yan et al. established a novel approach of virtual e-bespoke design permitting the ready completion of a well-fitted and balanced men's shirt [START_REF] Yan | A virtual e-bespoke men's shirt based on new body measurements and method of pattern drafting[END_REF]. A new 3D pattern-making approach based on graphic coding was put forth by Lei et al. in [START_REF] Lei | A new approach to 3D pattern-making for the apparel industry: graphic coding-based localization[END_REF], for generating garment patterns in any constructions intuitively, accurately, and quickly. These research results present fine prospects for the 3D digital simulation-based design process of customized garments, but the generality and accuracy of the techniques in the above-mentioned work still need further verification in real production scenarios using more cases.

Meanwhile, for realizing sustainable fashion by providing consumers with more accurate and personalized products, there has been a trend in that fashion companies wish to involve the consumer in the garment customization process and make him/her directly interact with the product [START_REF] Rincon-Guevara | Product design and manufacturing system operations: an integrated approach for product customization[END_REF]. Thus, efficient human-product interactions, aiming at offering decision support for designers by unveiling and applying the sophisticated quantified relationships between consumers' equivocal needs and product design parameters, have become a key to success in garment e-MC. Presently, diverse computational tools have been put forward to provide decision supports in key links of the personalized garment design process, such as design solution generation [START_REF] Dong | An interactive knowledge-based recommender system for fashion product design in the big data environment[END_REF][START_REF] Ling | Development of a dress design knowledge base (DDKB) based on sensory evaluation and fuzzy logic[END_REF][START_REF] Li | A model of an e-customized co-design system on garment design[END_REF], fabric selection [START_REF] Hong | Development of a new knowledge-based fabric recommendation system by integrating the collaborative design process and multi-criteria decision support[END_REF][START_REF] Takatera | Fabric retrieval system for apparel e-commerce considering Kansei information[END_REF], colour coordination [START_REF] Hong | CBCRS: an open case-based color recommendation system[END_REF][START_REF] Lu | A product design method for form and color matching based on aesthetic theory[END_REF][START_REF] Shamoi | Modeling aesthetic preferences: color coordination and fuzzy sets[END_REF], fashion sketch design [START_REF] Liu | Parametric design of garment flat based on body dimension[END_REF][START_REF] Mok | An IGA-based design support system for realistic and practical fashion designs[END_REF][START_REF] Xu | A web-based design support system for fashion technical sketches[END_REF], garment pattern design [START_REF] Abtew | Female seamless soft body armor pattern design system with innovative reverse engineering approaches[END_REF][START_REF] Abtew | A systematic pattern generation system for manufacturing customized seamless multi-layer female soft body armour through dome-formation (moulding) techniques using 3D warp interlock fabrics[END_REF][START_REF] Liu | Associate design of fashion sketch and pattern[END_REF][START_REF] Liu | Parametric design of garment pattern based on body dimensions[END_REF][START_REF] Sharma | Development of an intelligent data-driven system to recommend personalized fashion design solutions[END_REF][START_REF] Wang | A knowledge-supported approach for garment pattern design using fuzzy logic and artificial neural networks[END_REF], and so forth. For instance, in Ref. [START_REF] Li | A model of an e-customized co-design system on garment design[END_REF], an e-customized garment co-design system was developed by Li et al. based on the evolutionary algorithm and fuzzy logic theory, to optimize the size and affect the customized skirt with communication and expert evaluation. Takatera et al. created a fabric retrieval system for designers based on Kansei information that allows designers to find the most relevant fabric with the Kansei values and experience without technical knowledge of fabrics [START_REF] Takatera | Fabric retrieval system for apparel e-commerce considering Kansei information[END_REF]. Mok et al. set up a web-based design support system using interactive genetic algorithm that enables users to design realistic and interesting skirts in the form of technical sketches over the Internet [START_REF] Mok | An IGA-based design support system for realistic and practical fashion designs[END_REF][START_REF] Xu | A web-based design support system for fashion technical sketches[END_REF]. Shukla et al. originally developed an interactive fashion and garment design system for men's shirts by combining garment design recommendation, 3D virtual demonstration, design knowledge base, and design parameters adjustment [START_REF] Sharma | Development of an intelligent data-driven system to recommend personalized fashion design solutions[END_REF]. These proposed tools have facilitated the optimization of the garment e-MC process. However, there still exist several shortcomings as follows:

• The previous methods mainly focused on resolving the problems existing in a specific garment style, such as skirt, shirt, brassiere, and jeans. A generalized customization solution for a wide range of garment styles is still lacking. • The techniques mentioned above paid major attention to one or several concrete key links in the garment e-MC process, especially the fabric selection, fashion sketch design, and garment pattern design. However, from the perspectives of the whole design process, they still have weaknesses in systematicness and integrity. • Due to the expensive and time-consuming physical and sensory experiments, as well as the consumer's concern for personal privacy, sufficient modelling data (i.e. anthropometric data, user perception and experience data) can hardly be acquired, leading to the emergence of poor garment quality. How to conquer this technical bottleneck by reliable computational models has been rarely mentioned in the above-mentioned research.

In this context, we propose a knowledge-driven approach with an adaptive self-adjustment mechanism for generating personalized garment design solutions. Compared with the current techniques, our approach can predict and control the garment style and structural design parameters from a limited quantity of consumers' anthropometric and personalized demand data. It will enable to design and manufacture garments sustainably by promoting accuracy, fitting, and efficiency and mitigate the adverse impacts on the natural environment.

In practice, garment e-MC is regarded as a knowledgeintensive work dealing with implicit and complex relationships among multidisciplinary knowledge, such as the general design rules and specific adaptation rules characterizing the relations among design elements (fabrics, style, and human body shapes). Due to the outstanding merits in learning, generalizing, and handling uncertain and nonlinear relationships and solving optimization problems, machine learning (ML) techniques, such as artificial neural network (ANN), fuzzy logic (FL), and genetic algorithm (GA), have been introduced and broadly utilized in garment e-MC recently [START_REF] Thomassey | Artificial Intelligence for Fashion Industry in the Big Data Era[END_REF][START_REF] Giri | A detailed review of artificial intelligence applied in the fashion and apparel industry[END_REF][START_REF] Guo | Applications of artificial intelligence in the apparel industry: a review[END_REF]. Therefore, ML technologies integrated with 3D digital simulation, including radial basis function (RBF) ANN, probabilistic neural network (PNN), support vector regression (SVR) and GA, were employed to enhance the human-product interactions in this study.

The proposed design approach with the process for customized garments (See Fig. 1) is majorly supported by five design knowledge models. First, Model 1 is created to estimate the detailed human body dimensions, which were critical to garment pattern making and inconvenient to be acquired in a real garment e-MC scenario. The predictive data enable the formation of more complete and accurate consumer profiles constituted by personalized body dimensions and demands. Next, Model 2 generates a series of initial personalized garment design solutions following consumer profiles, to satisfy consumers' demands. Afterwards, Model 3 evaluates the generated design solutions following the quantified relationships between consumer profiles and garment profiles from the generated design solutions firstly. Then, the design solutions will be digitally demonstrated and recommended to the consumer following the evaluation results in descending order. Sequentially, Model 4 predicts the recommended garment fitness by fully taking the consumer's human body dimensions, fabric properties, and garment ease allowances (or digital pressures) into account. After that, the consumer is available to select the most preferred garment from the recommended solutions. If none of the recommended solutions is selected, Model 5 will be activated to adjust the most relevant design solution. The circle of "design solution generation-3D demonstration-evaluation-adjustment" will be performed repeatedly until a satisfactory design solution is achieved, in terms of garment style and fitness. In the end, the production patterns of the determined customization solution will be generated and delivered to the following department for manufacturing.

The major contributions of this study are in presenting:

• Resolving the critical technical bottleneck of providing high-quality garments to satisfy consumer's vague demands under the circumstances of a limited quantity of available data in garment e-MC.

• Proposing an applicable and potential solution for sustainable development in the fashion industry by designing more accurate garments through enhancing humanproduct interaction using ML technologies.

Fig. 1 The proposed ML-enhanced design approach and process for customized garments

• Providing reliable communication channels and interaction mechanisms among products, consumers, designers, and manufacturers based on more robust and intelligent computational tools. • Facilitating the creation of sustainable manufacturing mode in the fashion industry by combining the proposed garment design process with the advanced clothing assembly line; • Conveniently extending the general principles of the proposed method to establish a generalized fashion product e-MC framework or platform by systematically considering human aesthetic preferences, ergonomic requirements, and product parameters. • Supporting the formation of a new O2O (order online and receive services off-line) business model in the fashion industry by upgrading the level of e-MC.

The remainder of this article is structured as follows. Section 2 introduces the general formalization of this study. The construction of the design knowledge models is described in detail in Sect. 3. Section 4 elaborates the implementation of the proposed method using a real application case. The extensibilities of the proposed approach are discussed in Sect. 5. Lastly, Sect. 6 presents the conclusion and future research directions.

General Formalization

Let CP = SD FD be a vector of profiling the consumer's demands, where SD and FD refer to the demands of garment style and fitness, respectively.

Let SD = SD 1 , … , SD i , … , SD m be a set of normalized vectors representing the demands for m categories of style design elements. For a specific garment style, the SD can be constituted by various categories of style design elements. For example, pants' style can be constituted by the combination of various design elements, such as the silhouette, pant length, waist line position, darts, pleats, pockets, ornaments, and so on.

Let SD i = sd i 1 ⋯ sd i j ⋯ sd i u be an i u -dimensional normalized or one-hot vector expressing the demands for the i-th category style design element. The value of sd i j is defined as the nearness degree of the style demand to the i j -th style element. For example, if the pants' silhouette includes five types, namely H type, A type, T type, X type and S type, then it can be expressed by SD pants silhouette = {H type, A type, T type, Let FS = {extremly tight, tight, neutral, loose, extremely loose} be a semantic set for evaluating garment fitness.

X
Let FD = FD 1 , … , FD j , … , FD q be a set of q normal- ized vectors representing the demands for garment fitness at q feature positions.

Let Let S = S 1 , … , S k , … , S n be a set of n generated garment design solutions in this study.

Let GP = GP 1 , … , GP k , … , GP n be a set of n garment profiles corresponding to the set of garment design solutions S , where GP k is denoted as the k-th garment profile correspond- ing to the k-th garment design solution S k .

Let GP k = SF k FF k be a vector of profiling the features for garment profile GP k , where SF k and FF k represent the fea- tures of garment style and fitness, respectively. The elements of GP k have a one-to-one correspondence with those of CP.

Let

SF k = SF k 1 , … , SF k i , ⋯ , SF k
m be a set of formalized vectors expressing the style features of the k-th garment from the aspects of the m categories style design elements, repre- sented by normalized vectors or one-hot vectors.

Let

SF i = sf i 1 ⋯ sf i j ⋯ sf i u be an i u -dimensional vec-
tor expressing the concrete style feature of a specific garment in the i-th category style design element. The structure of SF m has a one-to-one correspondence with that of SD m . Further- more, the value of sf i j is defined by using the same method as sd i j mentioned above.

Let FF k = FF k 1 , … , FF k i , … , FF k
n be a set of normalized vectors expressing the features of garment fitness of the k-th garment. The elements of FF k have a one-to-one correspondence with those of FD . The definition of FF k i is the same as that of FD i .

Construction of Design Knowledge Models for Customized Garments

The general principles of the present method can be easily spread to other garment styles. For simplicity, we expound it using a real case of males' leisure pants from the companies involved in our projects in this study.

Estimation Model for Human Body Dimensions (Model 1)

In practice, the acquisition of precise human body dimensions has become a challenging issue in real garment e-MC scenarios, due to either the lack of necessary anthropometric instruments and knowledge or the worry of privacy protection. To address this issue, we proposed an estimation model for human body dimensions. The inputs of the model are the easy-to-measure feature body dimensions, such as stature, waist girth, and hip girth. The outputs are defined as the difficult-to-measure detailed body dimensions corresponding to the garment style.

Contributing to its advantages of simple topological structure, fast convergence, and acceptable predictive accuracy [START_REF] Olabanjo | A machine learning prediction of academic performance of secondary school students using radial basis function neural network[END_REF], RBF ANN was employed in our study. The concrete modelling procedure is described below:

Step 1: To obtain the data quickly and precisely [START_REF] Lunscher | Deep learning whole body point cloud scans from a single depth map[END_REF], we collected the anthropometric measurements of 500 Chinese adult males by the Vitus Bodyscan. Considering the garment type, ten relevant anthropometric measurements were chosen (see Fig. 2), including stature, waist height, hip height, crotch height, knee height, waist girth, hip girth, thigh girth, knee girth, and ankle girth.

Step 2: We set up seven RBF ANN models for human body estimation, respectively, corresponding to waist height, hip height, crotch height, knee height, thigh girth, knee girth, and ankle girth.

Generation Model of Design Solution (Model 2)

The garment design solution generation model (see Fig. 3) is constituted by two parts, namely the GA model and linear model supported by a garment design knowledge base. The garment ease allowances corresponding to the standard design solutions were predefined by professional and experienced garment pattern makers based on the real cases from the fashion brand companies involved in our study. The inputs of the solution generation model are the style demands (SD) and the garment fitness demands (FD) for the feature positions. The outputs of the model are the garment ease allowances, which are denoted as an indicator expressing the extra space difference between the human body and the garment to present the diverse features of the garment style and fitness [START_REF] Wang | A knowledge-supported approach for garment pattern design using fuzzy logic and artificial neural networks[END_REF].

In the application process, we can utilize the GA-based model to generate the normalized design solution corresponding to a new garment style and fitness firstly. Next, the garment design solutions (garment ease allowances) can be calculated by combining the outputs of the GA model with the standard design solutions from the garment design knowledge base in a linear combination way. In the end, the obtained ease data are utilized for garment pattern making.

The creation of the garment design solution generation model is given below:

Let the fitness value f fitness SD j for the garment style demand SD j be denoted in Eq. ( 1) and the fitness value f fitness FD j for the garment fitness demand FD j be denoted in Eq. ( 2).

where SF new j represents the generated new garment style features corresponding to the garment style demand SD j .

where FF new j represents the generated new garment fitness features corresponding to the garment fitness demand FD j .

From Eqs. ( 1) and ( 2), a smaller value of the f f itness

SD j or f f itness FD j
indicates a more optimal degree of fitness.

The execution process of the GA-based model is as follows. The termination criteria of the GA-based model were as follows: (1) the preset maximum iterations achieved; (2) the average variation in the fitness function values with a specific number of generations less than a predefined tolerance; (3) reaching the consumer's demands. For each SD j or FD j , the consumer's demand can be denoted by two sets SD constraint j and FD constraint j . If the terminal criteria were not reached, the process of "selection-crossover-mutation-calculation-evaluation" would be repeatedly performed till the terminal criteria were satisfied. The objective functions of GA are defined in Eqs. ( 3) and ( 4).

(1) The new garment ease allowance is computed following Eq. ( 5):

f fitness SD j = | | | SF new j -SD j | | | SD j ∈ SD , (2)
f fitness FD j = | | | FF new j -FD j | | | FD j ∈ FD , (3) argmin
SF new j f fitness SD j SD j ∈ SD, SF new j ∈ SF constraint j , (4) argmin
where GE new i is defined as the new garment ease allowance of the new garment design solution at i feature position; OP i represents the i output of the GA-based model, which could be SF new i or FF new i ; GE std i refers to a standard garment ease (5) , then the new garment ease for the fitness of hip girth GE new hip girth can be computed by GE new hip girth = 0 × gf 1 + 0 × gf 2 +0.55 × gf 3 + 0.45 × gf 4 + +0 × gf 5 .

GE new i = OP i • GE std i , OP i isSF new i orFF new i ,

Evaluation Model of Design Solution (Model 3)

In the garment design solution evaluation model, we defined a similarity degree indicator r CP, GP k to express the quan- titative relationships between the consumer profile (CP) and the garment profile GP k . In this study, r CP, GP k is defined and calculated by Eq. ( 6).

(6) r CP, GP k = × r SD, SF k + β × r FD, FF k ,
where and β represent the weights of garment style and fitness, respectively. The weights, varying between 0 and 1, can be set by the designer or consumer following the specific scenario. r SD, SF k is denoted as the indicator for charac- terizing the similarity degrees between the style demands (SD) and the style features SF k of a garment profile GP k . r SD, SF k is defined by Eq. (7).

From Eq. ( 7), we can find that the values of r SD, SF k vary between 0 and 1. If all style elements of SD and SF k are close to each other, the value of r SD, SF k is close to 1. Otherwise, it tends to 0.

r FD, FF k refers to the indicator for representing the sim- ilarity degrees between the global garment fitness demands (FD) and the global fitness features FF k of a garment profile GP k . r FD, FF k is defined and computed with Eq. ( 8) and ( 9). ( 7) where r FD i , FF k i is defined as the indicator for evaluating the similarity degrees between the local garment fitness demands FD i and the local fitness features FF k i of a garment profile GP k at the i-th feature position.

r � SD, SF k � = ∑ j ∑ i min � sd i , sf i � ∑ j ∑ i max � sd i , sf i � , � sd i ∈ SD j ∈ SD, sf i ∈ SF j ∈ SF k � .
Both the values of r FD i , FF k i and r FD, FF k are between 0 and 1. From Eq. ( 8), if the local fitness features FF k i is close to the fitness demands FD i , the value of r FD i , FF k i is close to 1. Otherwise, it tends to 0. Similarly, following Eq. ( 9), if the value of r FD, FF k is close to 1, (8)

r FD i , FF k i = min et d i , et f i + min ti d i , ti f i + min nl d i , nl f i + min lo d i , lo f i + min el d i , tl f i max et d i , et f i + max ti d i , ti f i + max nl d i , nl f i + max lo d i , lo f i + max el d i , tl f i , (9)
r FD, FF k = avg r FD i , FF k i , FF k i ∈ FF k , FD i ∈ FD ,
it means that the global fitness features FF k is close to the fitness demands (FD) and vice versa.

Prediction Model of Garment Fitness (Model 4)

Thanks to its powerful performance in dealing with pattern recognition and classification problems in the textile and apparel industry [START_REF] Mohebali | Chapter 14-Probabilistic neural networks: a brief overview of theory, implementation, and application[END_REF], PNN was applied to build the garment fitness prediction models in this study. A series of PNN-based models were created to predict garment fitness Fig. 4 The general scheme of the garment fitness prediction model for feature position at various feature positions, such as waist, hip, thigh, knee, ankle, and so on. Each model had an identical fourlayer structure, with thirteen inputs and one output (see Fig. 4). The inputs were constituted by the body dimension at feature position, fabric properties, and garment ease allowance (for loose-fit garments) or digital pressure (for tight-fitted garments) measured in a 3D digital design environment. The output was the predicted real garment fitness.

The detailed procedure for creating the garment fitness prediction model is presented as follows:

Step 1: A series of real try-on-based sensory experiments were conducted to collect the real garment fitness data on various feature positions. Considering the target markets of the fashion companies involved in our study, [START_REF] Li | Virtual reconstruction of 3D articulated human shapes applied to garment try-on in a virtual fitting room[END_REF] [START_REF] Samui | Standard Sizing Systems for Garments-Men, in GB/T 1335.1-2008[END_REF]. Meanwhile, we invited an expert with over 20 years of experience in sizing systems to join our research. With her indepth knowledge and rich experience, we can guarantee the recruited subjects were in line with the China National Standard.

Step 2: Every subject performed his try-on with the experimental garments in static and dynamic scenarios.

Meanwhile, they recorded the garment fitness data represented by {1, 2, 3, 4, 5} , corresponding to the semantics {εextremelytight(1)ε, εtight(2)ε, εneutral(3)ε, εloose(4)ε, ε extremelyloose(5)ε} . These data were used to form the out- put dataset to construct the proposed models.

Step 3: 25 pieces of real experimental garments (leisure pants) of five sizes with five types of fabrics were selected in this research (see Tables 1 and2). The inputs for creating the proposed models were procured using the software CLO 3D, thanks to its cutting-edge simulation techniques. First, 14 mannequins corresponding to the subjects were modelled. Next, we created 25 pieces of digital garments corresponding to the real experimental garments. Then, these digital garments were tried on the 14 digital mannequins one by one. For each virtual try-on, the garment ease allowances at each feature position were measured. Finally, all the collected ease data were aggregated to form the input dataset. Additionally, 11 indicators for characterizing the mechanical properties of the digital fabric were measured by the Fabric Kit of CLO 3D, including thickness (TH) , stretch weft (SWT) , stretch warp (SWP) , shear (SH) , bending weft (BWT) , bending warp (BWP) , bending ratio-weft (BRT) , bending ratio-warp (BRP) , buckling stiffness-weft (BST) , buckling stiffness-warp (BSP) , and density (DE).

Step 4: For each feature position, 350 records of data were collected to form the learning dataset in total. The PNN-based models were determined using the k-fold ( k = 10 ) cross-validation approach.

Adjustment Model of Design Solution (Model 5)

Step 1: The garment patterns for a specific style were divided into the main panel and the associated panels based on the knowledge of experienced and skillful pattern makers. For leisure pants in this study, the front panel was selected as the main panel with other panels as the associated panels.

Step 2: Since its excellent advantages of tackling the problems of function approximation [START_REF] Anand | A class of new support vector regression models[END_REF][START_REF] Wang | Construction of garment pattern design knowledge base using sensory analysis, ontology and support vector regression modeling[END_REF], SVR was employed to model the relationships between the length variation of the structural line and the movements of its corresponding controlling points. Initially, we set up five SVR-based adaptation models for each structural line (see Fig. 5). Meanwhile, we utilized the Bayesian optimization approach to determine the parameters of the SVR-based models. Afterwards, all the SVR-based models were aggregated to form a complete adaptation model for the main panel.

Fig. 5 The SVR-based adaptation models for the structural line sl i Step 3: The associate adjustment rules of other panels (see Table 3) were defined following the correspondence between the associated panels and the main panel. For example, Fp 1 and Bp 1 (see Fig. 5) belong to the outside seam of the front panel and back panel respectively. They have one-to-one correspondence. Therefore, the adjustment parameter of Fp 1 in the front panel (the main panel) is determined, the adjustment parameter of Bp 1 in the back panel (the associated panel) will be obtained simultaneously.

Application and Implementation

In this section, the application and implementation of our proposed method will be elaborated on using a real case of men's leisure pants customization for a specific consumer.

The key body dimensions of the consumer, namely stature, waist girth, and hip girth, were 170.8 cm, 69.8 cm, and 88.6, respectively. The detailed human body dimensions were estimated by the proposed RBF ANN-based models, as follows:

Creation of Consumer Profile

In this study, the consumer profile is defined by the combination of the demands on garment style and fitness. The style of leisure pants was constituted by ten categories of style elements, involving silhouette, length, waist line position, waist band, leg opening, dart, pleat, yoke, ornament, and pocket. Each category of style can be further divided into several types (see Table 4). The consumer's demands on the 22.3 .

style and fitness are expressed by vectors in Tables 5 and6. The value of the vector element refers to the nearness degree to the corresponding type of style design element and fitness.

Generation of Design Solutions

It was assumed that all the other style elements met the consumer's demands except the leisure pants' style and fitness. Hence, we first set up six GA-based models to generate new normalized pants' style and fitness feature vectors based on the method as presented in Sect. 3.2. In this article, the population size of the individuals was set to 50. To eliminate the effects of the raw fit scores returned by the fit function, rank scaling was utilized. Next, the roulette method was employed to choose the individuals. Additionally, we used the single-point crossover method to generate new individuals. The constraint-dependent method was utilized to execute the mutation. According to the consumer profile defined in Sect. 4.1, we randomly generated 100 normalized design solutions for further research. Afterwards, the ease allowances of the new design solution can be calculated by linearly combining the outputs of the GA-based models with the standard ease allowances, as follows:

GE std l = mini length -0.8WH

Evaluation and Recommendation of the Generated Design Solutions

First, the weights and in Eq. ( 6) were set to 0.5 and 0.5 based on the analytic hierarchy process. Next, according to Eq. ( 7), we obtained the relationships r SD, SF k between the pants style demands and the style features from generated design solutions. After that, according to Eq. ( 8) and ( 9), we obtained the relationships r FD, FF k between the pants fitness demands and the fitness features of the pants from the generated design solutions. Sequentially, the relationships r CP, GP k between the consumer profile and the generated pants profiles were calculated by Eq. ( 6). Finally, the generated design solutions were sorted by r CP, GP k in descending order, and then recommended to the consumer. The top-5 design solutions are shown in Table 7.

Prediction of Garment Fitness from the Recommended Design Solutions

For each recommended design solution, we predicted the garment fitness at various feature positions using the created PNN-based models. We take the fitness prediction of waist girth in design solution 1 S 1 for instance. The inputting vector was denoted as follows:

The predicted garment fitness output S 1 wg = f itness S 1 wg = 3.468, indicating that the predictive garment fitness at waist girth was between neutral and loose in general, but a little close to neutral. For the prediction of garment fitness at other feature positions, we only replaced waist girth and its ease allowance with other feature body dimensions with their corresponding ease allowance. Finally, the complete leisure pants design solution, which consisted of 3D digital garments and predicted garment fitness, was demonstrated to the consumer to support his further decision-making.

Adaptation of Garment Design Solutions

If the consumer is not satisfied with the recommended design solutions, the adaptation mechanism will be activated, for example, if the consumer is satisfied with most of the parts of the design solution 1 S 1 , but prefers the hip girth of the solution p (S p ) and the length of the solution q (S q ) . Meanwhile, FF SF q l = 0 0 0 0 0.563 0.437 . The adaptation process is described concretely below:

Step 1: The overall adaptation requirements were computed and distributed to each panel. For the main panel (front panel), the adaptation requirement of waist girth and pants length was determined to be -0.71 cm and 1.80 cm, respectively.

Step 2: We adjusted the front from the structural line l 1 (see Fig. 6). First, the movement of the point Fp 2 was calculated; next, the length deviation of the adjacent line l 2 under the condition of the movement of Fp 2 . If the length deviation dll 2 is less than a predefined threshold , then we will continue to check the adaptation results of the whole panel; otherwise, we will compute the movement of the point Fp 3 . Afterwards, if all the adaptation demands of the front panel are satisfied, then the adaptation of the main panel terminates; otherwise, the adaptation of the structure line l 3 will be activated. The process of "check- ing-adaptation" will be repeatedly performed until all the adjustment targets are approached.

Step 3: According to the relationships defined in Table 3, we determined the movements of the controlling points of the back panel (see 8).

Step 4: The movements of other controlling points were furtherly determined by modelling the relationships between them and the key points in the panel (i.e. Fp 1 , Fp 2 , Fp 3 , etc.). We take the movements of the pleat points pl 1 and pl 2 (see Fig. 5) in the main panel for example. The movements of pl 1 can be calculated by the following relationships: dx pl 1 = dx Fp 8 +dx Fp 9 2 , dy pl 1 = dy Fp 8 = dy Fp 9 . Then, the movements of pl 2 can be computed by the relation- ships: dx pl 2 = dx pl 1 , dy pl 2 = dy pl 1 . Finally, the movements of all the controlling points are obtained.

Discussion

Extensibility in the Design of the Production Patterns

Garment production patterns play pivotal roles by linking fashion design with garment manufacturing. They can x Fp 9 -1 y Bp 9 + 1 be designed by the relationships between the controlling points in the production panels and the original panels. For instance, if the final coordinates of the Fp 8 in the original panel (see Fig. 7) were x Fp 8 and y Fp 8 , then the coordinates of Fp ′ 8 will be x Fp � 8 = x Fp 8 -1 and y Fp � 8 = y Fp 8 + 1 . Table 9 shows the design rules of the production panels.

Extensibility in the Associate Adaptation of the Production Patterns

Based on the relationships of the controlling points in the original and production panels, the associate adaptation rules of the production patterns can be further defined (see Table 9). For example, when the movements of the Fp 2 in the original panel (see Fig. 6) are dx Fp 2 = -1.0457 and dy Fp 2 = -0.9000 , the movements of Fp ′ 2 in the production panel are set to dx Fp � 2 = dx Fp 2 = -1.0457 and dy Fp � 2 = dy Fp 2 = -0.9000 . Finally, the associated adaptation rules of the production patterns are presented in Table 10.

Extensibility in the Development of Interactive Garment Pattern Recommendation System

We further developed an interactive pants pattern recommendation system 2022 (IPPRS 2022) using MATLAB computer language. In the system, the user (consumer or designer) can intuitively input the feature body dimensions and determine the pants style and fitness demands using the interactive interfaces (see Fig. 8). The output of the system is a set of personalized pants production patterns.

With the help of IPPRS 2022, the consumer can conveniently express his/her personalized demands that usually cannot be presented in words accurately. More than that, the proposed system can support the pattern designer (especially the novice) to put forward accurate design solutions quickly and intelligently, to fulfil consumers' personalized demands. Figure 9 shows a case of the pants production patterns generated by IPPRS 2022, corresponding to the design solutions S 1 presented in Table 6. The proposed system is feasible to generate various pants production patterns according to the input parameters.

Compared with the existing garment pattern design methods, the IPPRS 2022 has the advantages below. First, it helps the consumer express their demands more intuitively and exactly, so that the communication gap between consumer and designer can be greatly narrowed. Second, it enables the designers to make patterns easier, more rapid and more accurate by integrating the machine learning models into the conventional design process. Third, it facilitates fashion companies to form a sustainable garment design and development process based on 3D digital simulation and machine learning-supported human-product interactions.

Conclusions

In this paper, we put forward a new design approach for customized garments towards sustainable fashion. It was based on 3D digital simulation and a series of machine learning techniques, involving radial basis function artificial neural network, probabilistic neural network, genetic algorithms, and support vector regression. The proposed approach is available to be applied in various classical 3D garment software, promoting the implementation level of garment e-MC for different fashion brand companies. The proposed design method as well as the process for customized garments are mainly supported by five design knowledge models. It can generate and recommend the most relevant design solution for consumers. Meanwhile, the proposed associate adjustment mechanism for garment patterns can dramatically reduce the difficulties of garment pattern-making without reducing the quality of garment patterns. More importantly, it is also able to generate personalized garment production patterns that can effectively enhance the linkage of fashion design and garment manufacturing which is quite critical in garment e-MC towards sustainable fashion. The contributions of this research can be mainly summarized as follows: (1) providing a feasible solution to resolve the critical technical bottleneck of offering quality products to satisfy consumer's personalized demands under the circumstances of a limited quantity of available data in garment e-MC;

(2) presenting potential prospects for sustainable fashion by designing quality customized products using 3D simulation and machine learning-based interaction technology; (3) offering reliable communication channels and mechanisms among products, consumers, and designers using more robust and intelligent computational tools; (4) facilitating the formation of sustainable manufacturing mode in the fashion industry by integrating the proposed approach into the advanced clothing assembly line; [START_REF] Lee | Framing sustainable fashion concepts on social media. An analysis of #slowfashionaustralia Instagram Posts and Post-COVID visions of the future[END_REF] supporting the form of a new generalized fashion product e-MC framework or platform by fully and systematically taking human aesthetic preferences, ergonomic demands, and product parameters into account; [START_REF] Tao | A customized garment collaborative design process by using virtual reality and sensory evaluation on garment fit[END_REF] boosting the emergence of a new O2O (order online and receive services off-line) business model in the fashion industry under the scenario of sustainable development.

Due to the length limitation of the paper, the proposed approach was verified using a real case of leisure pants customization only. Nonetheless, the general principles can be suitable for various garment styles. The validation of the proposed approach in other garment styles has become one of our future research works. Meanwhile, as the interactions among products, consumers, and designers are rather complicated and influenced by multiple factors (e.g. sociocultural backgrounds and human emotions), more affecting factors as well as their coupling effects should be taken into consideration in the future. Moreover, the performance promotion of the proposed approach through more advanced intelligent technologies constitutes one of our crucial future research directions.

  normalized vector representing the demands on garment fitness at the j-th feature position. The value of fd j p (p ∈ {1, 2, 3, 4, 5}) is defined as the nearness degree of the garment fitness demand to a certain fitness evaluation semantics at the j-th feature position. For example, if FD waist girth = demanded garment fitness for waist girth is close to neutral by 55% and loose by 45%.

  FF new j f fitness FD j FD j ∈ FD, FF new j ∈ FF constraint j .

3 T

 3 allowance vector at i feature position in the garment design knowledge base. For instance, if OP i = SF new waist line = new waist line was close to the normal waist line by 65% and the high waist line by 35% GE std waist line = lower waist line ge 1 normal waist line ge 2 high waist line ge , then the new garment ease for the waist line position GE new waist line can be computed by GE new waist line = 0 × ge 1 + 0.65 × ge 2 + 0.35 × ge 3 .

Fig. 2

 2 Fig. 2 The general structure of the proposed estimation model for detailed human body dimensions

Fig. 3

 3 Fig.3The general scheme of garment design solution generation model

Table 5

 5 Consumer's demands on leisure pants style elements SD Close to normal waist line by 80% and lower waist line by 20% Front straight inserted pocket and back inserted pocket

Fig. 6

 6 Fig. 6 General adaptation flowchart for the main panel

Fig. 7

 7 Fig.7The original and production panels

Fig. 8

 8 Fig. 8 Parts of the interfaces of interactive pants pattern recommendation system 2022. a The interactive interface of anthropometric data acquisition. b The interactive interface of collecting style

  type, S type} . If SD pants silhouette = H type demand for silhouette is H type. If the pants' length includes five types, such as mini length, thigh length, knee length, ankle length, and full length, then it can be represented bySD pants length = {mini length, thigh length, knee length, ankle length, andfull length} . I f SD pants length

			1	A type 0	T type 0	X type 0	S type 0 , it
	means that the = mini length 0 thigh length 0	knee length 0	ankle length 0.7	full length 0.3 , it indi-
	cates that the demand for the length is close to ankle length
	by 70% and full length by 30%.

  male subjects with various figure types in China were recruited to participate in the experiments. The involved figure types included 160/80A, 160/84A, 160/88A, 165/84A, 165/88A, 165/92A, 170/84A, 170/88A, 170/92A, 175/84A, 175/88A, 175/92A, 180/88A, and 185/92A. They were selected according to the accommodation rate demonstrated in the China National Standard (GB/T 1335.1-2008)

Table 1

 1 Feature dimensions of the involved experimental garment (unit: cm)

	Size Garment	Waist girth Hip girth Knee girth Ankle girth
		length
	XS 103	70	91	45	43
	S	104.5	74	95	46	44
	M	106	78	99	47	45
	L	107.5	82	103	48	46
	XL 109	86	107	49	47
	Table 2 Fabric properties of the involved experimental garment	No. Composition		Structure	Weight (g/m 2 )	Thickness (cm)	Bending resistance B
								(1e-6N.m)
								Warp	Weft
				1	100% cotton		Woven	153	0.03	40.63	13.82
				2	75% polyester, 25% cotton	Woven	210	0.03	23.56	15.96
				3	100% wool		Woven	268	0.07	17.66	11.77
				4	100% polyester	Knit	125	0.06	1.03	0.25
				5	90% polyamide 10% elasthane	Knit	200	0.05	0.66	0.63

Table 3

 3

	The relationships of movements of controlling points in the front and back panels	Controlling points of the front panel	Movement Horizontal	Vertical	Controlling points of the back panel	Movement Horizontal	Vertical
			direction	direction		direction	direction
		Fp 1	dx Fp 1	dy Fp 1	Bp 1	-dx Fp 1	dy Fp 1
		Fp 2	dx Fp 2	dy Fp 2	Bp 2	-dx Fp 2	dy Fp 2
		Fp 3	dx Fp 3	dy Fp 3	Bp 3	-dx Fp 3	dy Fp 3
		Fp 4	dx Fp 4	dy Fp 4	Bp 4	-dx Fp 4	dy Fp 4
		Fp 5	dx Fp 5	dy Fp 5	Bp 5	-dx Fp 5	dy Fp 5
		Fp 6	dx Fp 6	dy Fp 6	Bp 6	-dx Fp 6	dy Fp 6
		Fp 7	dx Fp 7	dy Fp 7	Bp 7	-dx Fp 7	dy Fp 7
		Fp 8	dx Fp 8	dy Fp 8	Bp 8	-dx Fp 8	dy Fp 8
		Fp 9	dx Fp 9	dy Fp 9	Bp 9	-dx Fp 9	dy Fp 9

Table 4

 4

	The classification of leisure pants style elements	Category	Type
		Silhouette SD 1	H type; A type; X type; T type; S type
		Length SD 2	Mini length; thigh length; knee length; ankle length; full length
		Waist line position SD 3	High waist line; normal waist line; lower waist line
		Waist band SD 4	No waist band; straight waist band; curved waist band
		Leg opening SD 5	Tapered opening; straight opening; flared opening
		Dart SD 6	No front dart; single front dart; double front darts; multiple front darts; No back dart; single back dart
		Pleat SD 7	No front pleat; single front pleat; double front pleats; multiple front pleats
		Yoke SD 8	No yoke; straight yoke; curved yoke; special yoke
		Ornament SD 9	Embroidery; printing; riveting; quilting; hollow cut; no ornament
		Pocket SD 10

No front pocket; front straight inserted pocket; front diagonal inserted pocket; front curved inserted pocket; front curved inserted pocket with coin pocket; front patched pocket; no back pocket; back inserted pocket; back inserted pocket with flap; back patched pocket; back patched pocket with flap Page 12 of 20

Table 6

 6 Consumer's demands on leisure pants fitness FD

	S.N	Feature position	Normalized fitness demands	Fitness demands
	1	Waist girth	FD 1 = 0 0 0.5 0.5 0	Close to neutral by 50% and loose by 50%
	2	Hip girth	FD 2 = 0 0 0.2 0.8 0	Close to neutral by 20% and loose by 80%
	3	Knee girth	FD 3 = 0 0 0.8 0.2 0	Close to neutral by 80% and loose by 20%
	4	Ankle girth	FD 4 = 0 0 0.65 0.35 0	Close to neutral by 65% and loose by 35%

Table 7

 7

	Top-5 leisure pants design solutions	Solution Feature position	Normalized design solutions	r SD, SF k r FD, FF k r CP, GP k
		S 1	Length	SF 1 l = 0 0 0 0 0.726 0.274	0.9942	0.9871	0.9907
			Waist line position SF 1 wl = 0.189 0.811 0
			Waist girth	FF 1 wg = 0 0 0.512 0.488 0
			Hip girth	FF 1 hg = 0 0 0.207 0.793 0
			Knee girth	FF 1 kg = 0 0 0.802 0.198 0
			Ankle girth	FF 1 ag = 0 0 0.645 0.355 0
		S 2	Length	SF 2 l = 0 0 0 0 0.761 0.239	0.9975	0.9818	0.9897
			Waist line position SF 2 wl = 0.196 0.804 0
			Waist girth	FF 2 wg = 0 0 0.501 0.499 0
			Hip girth	FF 2 hg = 0 0 0.211 0.789 0
			Knee girth	FF 2 kg = 0 0 0.823 0.177 0
			Ankle girth	FF 2 ag = 0 0 0.652 0.348 0
		S 3	Length	SF 3 l = 0 0 0 0 0.777 0.223	0.9950	0.9827	0.9889
			Waist line position SF 3 wl = 0.203 0.797 0
			Waist girth	FF 3 wg = 0 0 0.488 0.512 0
			Hip girth	FF 3 hg = 0 0 0.197 0.803 0
			Knee girth	FF 3 kg = 0 0 0.791 0.209 0
			Ankle girth	FF 3 ag = 0 0 0.661 0.339 0
		S 4	Length	SF 4 l = 0 0 0 0 0.758 0.242	0.9955	0.9701	0.9828
			Waist line position SF 4 wl = 0.219 0.781 0
			Waist girth	FF 4 wg = 0 0 0.493 0.507 0
			Hip girth	FF 4 hg = 0 0 0.188 0.812 0
			Knee girth	FF 4 kg = 0 0 0.831 0.169 0
			Ankle girth	FF 4 ag = 0 0 0.639 0.361 0
		S 5	Length	SF 5 l = 0 0 0 0 0.733 0.267	0.9942	0.9658	0.9800
			Waist line position SF 5 wl = 0.182 0.818 0
			Waist girth	FF 5 wg = 0 0 0.467 0.533 0
			Hip girth	FF 5 hg = 0 0 0.191 0.809 0
			Knee girth	FF 5 kg = 0 0 0.811 0.189 0
			Ankle girth	FF 5 ag = 0 0 0.633 0.367 0

Table 8

 8 The movements of controlling points in the front and back panels

	Controlling points of the	Movement		Controlling points of the	Movement
	front panel	Horizontal direction	Vertical direction	back panel	Horizontal	Vertical direction
					direction
	Fp 1	-0.7100	0	Bp 1	0.7100	0
	Fp 2	-1.0457	-0.9000	Bp 2	1.0457	0.9000
	Fp 3	-1.4710	-1.8000	Bp 3	1.4710	1.8000
	Fp 4	-1.4702	-1.8000	Bp 4	1.4702	1.8000
	Fp 5	-1.5663	-0.9000	Bp 5	1.5663	0.9000
	Fp 6	-1.8070	0	Bp 6	1.8070	0
	Fp 7	0	-0.2564	Bp 7	0	-0.2564
	Fp 8	0	-0.2521	Bp 8	0	-0.2521
	Fp 9	0	-0.2517	Bp 9	0	-0.2517

Table 9

 9 The design rules of the production patterns (unit: cm)

		Controlling points of	Coordinates		Controlling points of the	Coordinates
		the original panel	Horizontal	Vertical	production panel	Horizontal direction	Vertical direction
			direction	direction
	Front panel	Fp 1	x Fp 1	y Fp 1	Fp ′ 1	x Fp 1 + 1	y Fp 1
		Fp 2	x Fp 2	y Fp 2	Fp ′ 2	x Fp 2 + 1	y Fp 2
		Fp 3	x Fp 3	y Fp 3	Fp ′ 3	x Fp 3 + 1	y Fp 3 -3.5
		Fp 4	x Fp 4	y Fp 4	Fp ′ 4	x Fp 4 -1	y Fp 4 -3.5
		Fp 5	x Fp 5	y Fp 5	Fp ′ 5	x Fp 5 -1	y Fp 5
		Fp 6	x Fp 6	y Fp 6	Fp ′ 6	x Fp 6 -1	y Fp 6
		Fp 7	x Fp 7	y Fp 7	Fp ′ 7	x Fp 7 -1	y Fp 7
		Fp 8	x Fp 8	y Fp 8	Fp ′ 1	x Fp 8 -1	y Fp 8 + 1
		Fp 9	x Fp 9	y Fp 9	Fp ′ 1	x Fp 9 + 1	y Fp 9 + 1
		Controlling points of	Coordinates		Controlling points of the	Coordinates
		the original panel	Horizontal	Vertical	production panel	Horizontal direction	Vertical direction
			direction	direction
	Back panel	Bp 1	x Bp 1	y Bp 1	Bp	′ 1	x Bp 1 -1	y Bp 1
		Bp 2	x Bp 2	y Bp 2	Bp	′ 2	x Bp 2 -1	y Bp 2
		Bp 3	x Bp 3	y Bp 3	Bp	′ 3	x Bp 3 -1	y Bp 3 -3.5
		Bp 4	x Bp 4	y Bp 4	Bp	′ 4	x Bp 4 + 1	y Bp 4 -3.5
		Bp 5	x Bp 5	y Bp 5	Bp	′ 5	x Bp 5 + 1	y Bp 5
		Bp 6	x Bp 6	y Bp 6	Bp	′ 6	x Bp 6 + 1	y Bp 6
		Bp 7	x Bp 7	y Bp 7	Bp	′ 7	x Bp 7 + 1	y Bp 7
		Bp 8	x Bp 8	y Bp 8	Bp
		Bp 9	x Bp 9	y Bp 9	Bp

′ 8 x Bp 8 + 1 y Bp 8 + 1 ′ 9

Table 10

 10 The associate adjustment rules of the production patterns

	Front panel	Controlling points of the	Movements		Controlling points of the	Movements
		original panel	Horizontal direc-	Vertical direc-	production panel	Horizontal direc-	Vertical
			tion	tion			tion	direction
		Fp 1	dx Fp 1	dy Fp 1	Fp ′ 1	dx Fp 1	dy Fp 1
		Fp 2	dx Fp 2	dy Fp 2	Fp ′ 2	dx Fp 2	dy Fp 2
		Fp 3	dx Fp 3	dy Fp 3	Fp ′ 3	dx Fp 3	dy Fp 3
		Fp 4	dx Fp 4	dy Fp 4	Fp ′ 4	dx Fp 4	dy Fp 4
		Fp 5	dx Fp 5	dy Fp 5	Fp ′ 5	dx Fp 5	dy Fp 5
		Fp 6	dx Fp 6	dy Fp 6	Fp ′ 6	dx Fp 6	dy Fp 6
		Fp 7	dx Fp 7	dy Fp 7	Fp ′ 7	dx Fp 7	dy Fp 7
		Fp 8	dx Fp 8	dy Fp 8	Fp ′ 8	dx Fp 8	dy Fp 8
		Fp 9	dx Fp 9	dy Fp 9	Fp ′ 9	dx Fp 9	dy Fp 9
	Back panel	Controlling points of the	Movements		Controlling points of the	Movements
		original panel	Horizontal direc-	Vertical direc-	production panel	Horizontal direc-	Vertical
			tion	tion			tion	direction
		Bp 1	dx Bp 1	dy Bp 1	Bp	′ 1	dx Bp 1	dy Bp 1
		Bp 2	dx Bp 2	dy Bp 2	Bp	′ 2	dx Bp 2	dy Bp 2
		Bp 3	dx Bp 3	dy Bp 3	Bp	′ 3	dx Bp 3	dy Bp 3
		Bp 4	dx Bp 4	dy Bp 4	Bp	′ 4	dx Bp 4	dy Bp 4
		Bp 5	dx Bp 5	dy Bp 5	Bp	′ 5	dx Bp 5	dy Bp 5
		Bp 6	dx Bp 6	dy Bp 6	Bp	′ 6	dx Bp 6	dy Bp 6
		Bp 7	dx Bp 7	dy Bp 7	Bp	′ 7	dx Bp 7	dy Bp 7
		Bp 8	dx Bp 8	dy Bp 8	Bp	′ 8	dx Bp 8	dy Bp 8
		Bp 9	dx Bp 9	dy Bp 9	Bp	′ 9	dx Bp 9	dy Bp 9

Acknowledgements

The authors thank Francois Dassonville for his software guidance and experimental supports.

Availability of Data and Material

Since the data and materials are business secrets for the enterprises involved in this study, the authors are very sorry to declare that the data are not applicable and cannot be presented in public.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.

Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.