# A Product Modeling Design Decision Model Based on PGA Genetic Algorithm

Authors: Licheng Zong; Nana Wang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

A Pareto-based genetic algorithm (PGA) product design decision model is proposed in this work to improve the efficiency of product design decisions and avoid the instability of individual decision differences. Based on the product modeling design decision constraint space, decision variables, and other factors, the model utilizes the PGA optimization algorithm to make an objective decision on a design scheme. Using the analytic hierarchy process, the design expectations, objectives, variables, and schemes are constructed into a hierarchical structure. The design decision problems are then mapped to a mathematical model, and a simulation of the design scheme decision process is performed. Finally, the feasibility of the proposed model is analyzed and verified by evaluating the design decisions of a brand electric scooter product to guide designers in making innovative design decisions.


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## Body

## 1. Introduction

Product modeling design integrates various factors, including art, technology, and engineering [1]. Product modeling characteristics can convey a brand’s cultural concept and are the most direct carrier of a product’s brand image [2]. The product modeling design process involves iteration and intersection [3] and the collision and integration of reason and emotion [4]. The design scheme evaluation process is also a multitask, multiobjective decision weighing method. In the process of product scheme design, decisions are a typical multiattribute, multiobjective comprehensive decision problem influenced by the diversity of design criteria and the ambiguity of evaluation [5].Currently, in the field of product modeling design research, research on product modeling design decisions is mainly focused on the following three areas:(1) experimental evaluation: by collecting physiological and psychological data from the evaluators on the product design scheme, a scheme preference is optimized. For example, Lin et al. [6] determined the visual effects of different camouflage design schemes through eye-movement experiments analysis. Guo et al. [7] constructed an accurate user perception measurement method via EEG experiments, analyzed the inner mechanism of product morphology and user preference and used the results as an indicator of product design. (2) Mathematical evaluation: the mathematical evaluation method is based on the establishment of an indicator and the construction of an evaluation algorithm, which is a quantitative method. Commonly-used evaluation algorithms include the analytic hierarchy process [8], neural network [9], Genetic Algorithm [10], and deep learning [11]. For example, Shieh and Yeh [9] used a neural network to build a system to predict design changes to the external form of running shoes and consumer emotion and to study how design factors influenced the consumers’ emotional responses. (3) Online evaluation: this method is a recently-developed network information evaluation technique, which uses data mining technology to obtain, cluster, and analyze online user data. Related research methods include big data [12], natural language processing [13], and text mining [14]. For example, Lai et al. [15] analyzed big data generated in a complex product design process using a deep neural network, predicted the design variables, and built a data-driven product design decision method. In the field of mathematical evaluation methods, combined with the Pareto solution set to improve the traditional genetic algorithm, the PGA algorithm will effectively improve the algorithm convergence speed and speed up the operation process [16]. Therefore, this paper is based on the PGA algorithm, proposes a product modeling design decision-making model, and researches the multiobjective decision-making method of product modeling design.


## 2. Theory

### 2.1. PGA Genetic Algorithm

Genetic algorithms are based on the bio-mimic optimization algorithm proposed by John Holland in 1975, which was inspired by natural selection [17]. The algorithm is based on the theory of biological evolution and chromosomal genetic variation and is characterized by large-scale global search capability, parallelism, simplicity, and strong robustness. Figure 1 shows the pseudocode of the classical genetic algorithm [18].Figure 1
Classical genetic algorithm (GA).Proposed by Pareto, the Pareto solution set was initially used for multiobjective optimization in the field of economics [19]. The Pareto solution set is defined as follows: if u′∈U (U is the feasible domain of multiobjective optimization) and there is no other feasible point u∈U such that fqu≤fqu′, q = 1, 2, …, n (n is the number of objectives) holds, then u′ is said to be a noninferior solution of multiobjective optimization. For multiobjective optimization, the Pareto optimized solution is a solution set instead of one single solution, and it is denoted as the Pareto optimized solution set.Multiobjective optimization is a design concept adopted to optimize of the overall performance of a design object according to multiple design objectives [20]. The Pareto-based genetic algorithm (PGA) is developed based on the standard genetic algorithm, in which the efficiency of the algorithm and the distribution status of the Pareto solution set are improved by introducing techniques such as floating-point coding, the hierarchical penalty function, and a Pareto solution set filter, it can effectively avoid problems such as local optimum and premature convergence and improve its global searchability and computational efficiency.In the specific genetic operation, the operator is selected using a roulette wheel, and the crossover probabilitypc and the variation probability pm of the genetic operator are dynamically adjusted according to the fitness value in the evolutionary process.(1)pc=k1fmax−fbigfmax−favefbig≥favek2fbig<fave,pm=k3fmax−ffmax−favef≥favek4f<fave,where f is the individual fitness value, fbig is the larger fitness value among individuals, fmax is the maximum fitness value in the current population, and fave is the average fitness value in the current population, 0≤ki≤1i=1,2,3,4.In order to make the population evolve in a benign direction, it is necessary to introduce a shared penalty function, which imposes a penalty on the individuals that are clustered into small pieces in the population so that their fitness value is reduced. The reduced individual fitness value is(2)FK|share=FK∑i=1MfshareK,Zi,fshareK,Q=0,σK,Q≥σshare1−σK,Qσshare,σK,Q<σshare,where M is the group size, K is any individual, Zi is an individual different from K, F(K) is the fitness value before and after imposing the shared function, σK,Q is the Euclidean distance between individuals, σshare is the distance parameter, and fshareK,Q is the shared function of K and Q.


### 2.2. Description of Product Modeling Design Decision Space

Product modeling design involves a product’s brand gene, function, ergonomics, commercial marketing, processing technology, and other factors [21]. For example, the modeling design of an automobile product can be divided into the front, side, and rear modeling, interior design, etc. Front modeling includes the design of the engine hood, air-inlet grille, air intake, headlights, and fog lights, while side modeling includes the side profile, waistline, side windows, front to rear overhang ratio, and overall vehicle length to height ratio design. Modeling design varies significantly across different car brands. Therefore, product modeling design has multiobjective, multitask properties [22]. Table 1 shows the factors of product modeling design.Table 1
Multiobjective factors of product modeling design.
FactorContentBrandBrand characteristics and brand gene are the first factors that must be considered and satisfied in product modeling design. A brand’s image and connotation will drive the style of product modeling design. The designer’s main responsibility is to convey the product’s brand connotations and culture through product modeling design so as to accurately and consistently stimulate user cognitionFunctionThe function is the core service provided by the product itself, which will determine the direction and orientation of product modeling design to a certain extent. The orientation of the product function has an important impact on product modeling designBusinessProduct modeling design will eventually reach consumers through commercial marketing, where the ultimate purpose of production is sales for profit. Product business positioning has a significant influence on product modeling design and is also an important constraint factorTechnologyDifferent processing requirements, materials, and production processes will directly affect the final shape of the product modeling designMaterialThe use of different materials involves factors, such as product brand positioning, function consideration, and commercial marketing, and the properties of the materials themselves directly affect the final shape of the product designHuman-machineProduct modeling design ultimately serves humans. Thus, the form, function, usage, and scenario of the product must be compatible with human posture and conform to the fixed range of values and movement of the human body. The stability, safety, comfort, and other human-machine factors of the final use of a product are also important constraints of product modeling designOthersIn the face of sustainable development, product design also needs to consider factors such as environmental protection and life cycle. Changing social, cultural, and fashion trends and consumption habits are also important constraint factorsIn product design, different design goals will produce completely different design schemes, and the fusion of various design tasks will further increase the complexity of the evaluation in styling design schemes. Therefore, by limiting the multiobjective decision space of modeling design, unnecessary iteration and output of design schemes can be avoided, shorten the design cycle, and improve design efficiency.


## 2.1. PGA Genetic Algorithm

Genetic algorithms are based on the bio-mimic optimization algorithm proposed by John Holland in 1975, which was inspired by natural selection [17]. The algorithm is based on the theory of biological evolution and chromosomal genetic variation and is characterized by large-scale global search capability, parallelism, simplicity, and strong robustness. Figure 1 shows the pseudocode of the classical genetic algorithm [18].Figure 1
Classical genetic algorithm (GA).Proposed by Pareto, the Pareto solution set was initially used for multiobjective optimization in the field of economics [19]. The Pareto solution set is defined as follows: if u′∈U (U is the feasible domain of multiobjective optimization) and there is no other feasible point u∈U such that fqu≤fqu′, q = 1, 2, …, n (n is the number of objectives) holds, then u′ is said to be a noninferior solution of multiobjective optimization. For multiobjective optimization, the Pareto optimized solution is a solution set instead of one single solution, and it is denoted as the Pareto optimized solution set.Multiobjective optimization is a design concept adopted to optimize of the overall performance of a design object according to multiple design objectives [20]. The Pareto-based genetic algorithm (PGA) is developed based on the standard genetic algorithm, in which the efficiency of the algorithm and the distribution status of the Pareto solution set are improved by introducing techniques such as floating-point coding, the hierarchical penalty function, and a Pareto solution set filter, it can effectively avoid problems such as local optimum and premature convergence and improve its global searchability and computational efficiency.In the specific genetic operation, the operator is selected using a roulette wheel, and the crossover probabilitypc and the variation probability pm of the genetic operator are dynamically adjusted according to the fitness value in the evolutionary process.(1)pc=k1fmax−fbigfmax−favefbig≥favek2fbig<fave,pm=k3fmax−ffmax−favef≥favek4f<fave,where f is the individual fitness value, fbig is the larger fitness value among individuals, fmax is the maximum fitness value in the current population, and fave is the average fitness value in the current population, 0≤ki≤1i=1,2,3,4.In order to make the population evolve in a benign direction, it is necessary to introduce a shared penalty function, which imposes a penalty on the individuals that are clustered into small pieces in the population so that their fitness value is reduced. The reduced individual fitness value is(2)FK|share=FK∑i=1MfshareK,Zi,fshareK,Q=0,σK,Q≥σshare1−σK,Qσshare,σK,Q<σshare,where M is the group size, K is any individual, Zi is an individual different from K, F(K) is the fitness value before and after imposing the shared function, σK,Q is the Euclidean distance between individuals, σshare is the distance parameter, and fshareK,Q is the shared function of K and Q.


## 2.2. Description of Product Modeling Design Decision Space

Product modeling design involves a product’s brand gene, function, ergonomics, commercial marketing, processing technology, and other factors [21]. For example, the modeling design of an automobile product can be divided into the front, side, and rear modeling, interior design, etc. Front modeling includes the design of the engine hood, air-inlet grille, air intake, headlights, and fog lights, while side modeling includes the side profile, waistline, side windows, front to rear overhang ratio, and overall vehicle length to height ratio design. Modeling design varies significantly across different car brands. Therefore, product modeling design has multiobjective, multitask properties [22]. Table 1 shows the factors of product modeling design.Table 1
Multiobjective factors of product modeling design.
FactorContentBrandBrand characteristics and brand gene are the first factors that must be considered and satisfied in product modeling design. A brand’s image and connotation will drive the style of product modeling design. The designer’s main responsibility is to convey the product’s brand connotations and culture through product modeling design so as to accurately and consistently stimulate user cognitionFunctionThe function is the core service provided by the product itself, which will determine the direction and orientation of product modeling design to a certain extent. The orientation of the product function has an important impact on product modeling designBusinessProduct modeling design will eventually reach consumers through commercial marketing, where the ultimate purpose of production is sales for profit. Product business positioning has a significant influence on product modeling design and is also an important constraint factorTechnologyDifferent processing requirements, materials, and production processes will directly affect the final shape of the product modeling designMaterialThe use of different materials involves factors, such as product brand positioning, function consideration, and commercial marketing, and the properties of the materials themselves directly affect the final shape of the product designHuman-machineProduct modeling design ultimately serves humans. Thus, the form, function, usage, and scenario of the product must be compatible with human posture and conform to the fixed range of values and movement of the human body. The stability, safety, comfort, and other human-machine factors of the final use of a product are also important constraints of product modeling designOthersIn the face of sustainable development, product design also needs to consider factors such as environmental protection and life cycle. Changing social, cultural, and fashion trends and consumption habits are also important constraint factorsIn product design, different design goals will produce completely different design schemes, and the fusion of various design tasks will further increase the complexity of the evaluation in styling design schemes. Therefore, by limiting the multiobjective decision space of modeling design, unnecessary iteration and output of design schemes can be avoided, shorten the design cycle, and improve design efficiency.


## 3. PGA-Based Product Modeling Design Decision Model

### 3.1. Model Description

During product design, the design scheme will go through multiple rounds of project analysis and selection in the process of locating an optimized solution to the design problem. The PGA-based product modeling design decision model works to describe and hierarchize the design decision objectives until a Pareto optimized solution is selected [23]. The design decision model includes a design decision function, variables, constraints, and a design evaluation model [24].The product modeling design multi-objective optimization design decision functionF(X), design decision problem description fn(x), and design variable x constitute the design constraint space model. In the product design process, the design assignment is analyzed and interpreted as design decision constraints and expectations for product modeling design, and the specific tasks are described as particular design problems, design variables, and optimized scheme parameters, forming the design decision space. The designer and their team then generate a design scheme in the design decision space. Table 2 shows the product modeling design constraint model.Table 2
Product modeling design constraint factors.
fn(x)xF(X)f1(x) brand geneBrand design characteristics, style, language, and other design genesf2(x) function parametersThe product’s main function, positioning, use, parameters, etcf3(x) business factorsProduct positioning, manufacturing cost, price, sales expectation, marketing mode, etcf4(x) technology factorsManufacturing and assembly process, forming method, process flow, process difficulty, etcf5(x) material factorsMaterial properties, technology, prices, ratios, etcf6(x) Human-machine relationshipSafety, comfort, stability, ease of use, human-computer interaction, etcf7(x) emotional semanticsFor example, modern, retro, simple, technology, humanities, gender, etcfn(x) other factorsFashion trends, consumption habits, aesthetic culture, technological innovation, product replacement, etcFigure2 shows the overall model structure. The process is described as follows:(1)
Initialize the product design decision space, set the group size, randomly assign the design scheme initial position, and assign the initial velocity to 0.(2)
In the design process, the target is located according to the objective function and design constraints. The design decision space is searched, the locally optimized solution is stored in the population poolV1, and the nonoptimal solution is stored in the population pool V2.(3)
After multiple searches, the selected optimized solutions are formed into a Pareto solution set, and an optimized design scheme library is constructed.(4)
In the Pareto solution set, based on the design evaluation model, the global optimized Pareto solution is selected, and the population poolV1 is updated. The design team will then refine the design based on the optimized design scheme and update the design decision constraint space.(5)
Using populationV1 as the initial population and the global optimized Pareto solution as the starting point, multiple iterations are performed in the design space until the output is satisfactory.(6)
The Pareto solution is output, the final scheme is selected, and the operation is ended.Figure 2
Overall model algorithm mechanism.


### 3.2. Decision Hierarchy in Product Modeling Design

Design evaluation is the main basis for product design decisions [25], and the design often undergoes multiple rounds of scheme selection. Thus, the design decision space is constantly converging in the design decision process, and design evaluation is the main basis for Pareto global optimized solution selection [26]. In the design evaluation process, the diversity of the design scheme and evaluation factors lead to complexity in design evaluation. In order to reduce the computational complexity of the system and make the comprehensive evaluation more reasonable, the analytic hierarchy process is used for expert weighting and to make the complex evaluation factors hierarchical [27]. The design expectations, objectives, variables, and scheme are built into a hierarchical structure, as shown in Figure 3.Figure 3
Product modeling design hierarchical evaluation model.When constructing the judgment matrix, experts employ the design decision constraints and expectations as the basis for judgment and finally derive the weight coefficient by comparing the design decision objectives and variables. The judgment scale is 1: equally important; 3: slightly important; 5: important; 7: much more important; 9: absolutely important. The judgment matrixO is expressed as follows:(3)O=o11o12⋯o1no21o22⋯o2n⋯⋯⋯⋯on1on2⋯onn.In the judgment matrix, the importance ratio of objectsi and j is aij,oij>0,oji=1/oij,oii=1. In the hierarchical structure, Bm and Cq are transitive. Thus, the judgment matrix is a consistency matrix, so the judgment matrix O=oijmxq. Meanwhile, using the row vector averaging method for hierarchical sorting, the weight vector Wi is obtained after normalizing the n column vectors:(4)Wi=1n∑j=1noij∑i=1noij,i,j=1,2,⋯,n.In the consistency index test of the weight vector, calculate the consistency vectorVi,(5)Vi=∑j=1nWjoijWi,i,j=1,2,⋯,n.The consistency index formula is as follows:(6)C.I.=λ−nn−1.It can be seen from (5) that,(7)λ=1n∑i=1nVi,i=1,2,⋯,n.TheC.I. value can be obtained by substituting (7) into (6), calculate the concordance ratio C.R., the formula is as follows:(8)C.R.=C.I.R.I..TheR.I. can be obtained by looking up the table, and the C.R. can be calculated. When C.R.<0.1, it means that the judgment has a better consistency.Here, Wi is the weight vector of a set of elements to an element in the upper level. Finally, the weight vector of each element can be obtained, and the weights of the elements at the bottom of the target are weighted. The total ranking weights can be synthesized from the top down under a single criterion. If Wk−1=w1k−1,w2k−1,⋯,wk−1k−1T denotes the ranking weight vector of the nk − 1th element on the k − 1th layer with respect to the total target, and Pjk=P1jk,P2jk,⋯,PnkjkT denotes the ranking weight vector of the nk-th element on the k-th layer with respect to the j-th element on the k − 1th layer as the criterion, then the total ranking W(k) of the elements on the k-th layer with respect to the total target is as follows:(9)Wk=w1k,w2k,⋯,wnk=Pk·Wk-1.


## 3.1. Model Description

During product design, the design scheme will go through multiple rounds of project analysis and selection in the process of locating an optimized solution to the design problem. The PGA-based product modeling design decision model works to describe and hierarchize the design decision objectives until a Pareto optimized solution is selected [23]. The design decision model includes a design decision function, variables, constraints, and a design evaluation model [24].The product modeling design multi-objective optimization design decision functionF(X), design decision problem description fn(x), and design variable x constitute the design constraint space model. In the product design process, the design assignment is analyzed and interpreted as design decision constraints and expectations for product modeling design, and the specific tasks are described as particular design problems, design variables, and optimized scheme parameters, forming the design decision space. The designer and their team then generate a design scheme in the design decision space. Table 2 shows the product modeling design constraint model.Table 2
Product modeling design constraint factors.
fn(x)xF(X)f1(x) brand geneBrand design characteristics, style, language, and other design genesf2(x) function parametersThe product’s main function, positioning, use, parameters, etcf3(x) business factorsProduct positioning, manufacturing cost, price, sales expectation, marketing mode, etcf4(x) technology factorsManufacturing and assembly process, forming method, process flow, process difficulty, etcf5(x) material factorsMaterial properties, technology, prices, ratios, etcf6(x) Human-machine relationshipSafety, comfort, stability, ease of use, human-computer interaction, etcf7(x) emotional semanticsFor example, modern, retro, simple, technology, humanities, gender, etcfn(x) other factorsFashion trends, consumption habits, aesthetic culture, technological innovation, product replacement, etcFigure2 shows the overall model structure. The process is described as follows:(1)
Initialize the product design decision space, set the group size, randomly assign the design scheme initial position, and assign the initial velocity to 0.(2)
In the design process, the target is located according to the objective function and design constraints. The design decision space is searched, the locally optimized solution is stored in the population poolV1, and the nonoptimal solution is stored in the population pool V2.(3)
After multiple searches, the selected optimized solutions are formed into a Pareto solution set, and an optimized design scheme library is constructed.(4)
In the Pareto solution set, based on the design evaluation model, the global optimized Pareto solution is selected, and the population poolV1 is updated. The design team will then refine the design based on the optimized design scheme and update the design decision constraint space.(5)
Using populationV1 as the initial population and the global optimized Pareto solution as the starting point, multiple iterations are performed in the design space until the output is satisfactory.(6)
The Pareto solution is output, the final scheme is selected, and the operation is ended.Figure 2
Overall model algorithm mechanism.


## 3.2. Decision Hierarchy in Product Modeling Design

Design evaluation is the main basis for product design decisions [25], and the design often undergoes multiple rounds of scheme selection. Thus, the design decision space is constantly converging in the design decision process, and design evaluation is the main basis for Pareto global optimized solution selection [26]. In the design evaluation process, the diversity of the design scheme and evaluation factors lead to complexity in design evaluation. In order to reduce the computational complexity of the system and make the comprehensive evaluation more reasonable, the analytic hierarchy process is used for expert weighting and to make the complex evaluation factors hierarchical [27]. The design expectations, objectives, variables, and scheme are built into a hierarchical structure, as shown in Figure 3.Figure 3
Product modeling design hierarchical evaluation model.When constructing the judgment matrix, experts employ the design decision constraints and expectations as the basis for judgment and finally derive the weight coefficient by comparing the design decision objectives and variables. The judgment scale is 1: equally important; 3: slightly important; 5: important; 7: much more important; 9: absolutely important. The judgment matrixO is expressed as follows:(3)O=o11o12⋯o1no21o22⋯o2n⋯⋯⋯⋯on1on2⋯onn.In the judgment matrix, the importance ratio of objectsi and j is aij,oij>0,oji=1/oij,oii=1. In the hierarchical structure, Bm and Cq are transitive. Thus, the judgment matrix is a consistency matrix, so the judgment matrix O=oijmxq. Meanwhile, using the row vector averaging method for hierarchical sorting, the weight vector Wi is obtained after normalizing the n column vectors:(4)Wi=1n∑j=1noij∑i=1noij,i,j=1,2,⋯,n.In the consistency index test of the weight vector, calculate the consistency vectorVi,(5)Vi=∑j=1nWjoijWi,i,j=1,2,⋯,n.The consistency index formula is as follows:(6)C.I.=λ−nn−1.It can be seen from (5) that,(7)λ=1n∑i=1nVi,i=1,2,⋯,n.TheC.I. value can be obtained by substituting (7) into (6), calculate the concordance ratio C.R., the formula is as follows:(8)C.R.=C.I.R.I..TheR.I. can be obtained by looking up the table, and the C.R. can be calculated. When C.R.<0.1, it means that the judgment has a better consistency.Here, Wi is the weight vector of a set of elements to an element in the upper level. Finally, the weight vector of each element can be obtained, and the weights of the elements at the bottom of the target are weighted. The total ranking weights can be synthesized from the top down under a single criterion. If Wk−1=w1k−1,w2k−1,⋯,wk−1k−1T denotes the ranking weight vector of the nk − 1th element on the k − 1th layer with respect to the total target, and Pjk=P1jk,P2jk,⋯,PnkjkT denotes the ranking weight vector of the nk-th element on the k-th layer with respect to the j-th element on the k − 1th layer as the criterion, then the total ranking W(k) of the elements on the k-th layer with respect to the total target is as follows:(9)Wk=w1k,w2k,⋯,wnk=Pk·Wk-1.


## 4. Case Study

The feasibility of the PGA product modeling design decision model is verified by using a fashionable electric scooter as an example. The project assignment requires this electric scooter modeling design to be stylish, simple, and popular as design objectives.


### 4.1. Modeling Design Decision Space Constraints

As shown in Table3, F(X) is the goal of the entire design project, corresponding to the goal expectation A. Each subfunction f(x) is a subobjective function under the corresponding decision constraint, corresponding to the decision goal layer B, and the specific constraint index is the C layer.Table 3
Description of product design constraint model.
Design problem descriptionfn(x)Design variablexF(X)Brand genef1(x)-B1Chassis:C1; color:C2Function parameter2(x)-B2Motor driven:C3; rear drive: C4Business factorf3(x)-B3Mid-range model:C5; daily transportation: C6Technology factorf4(x)-B4Module welding:C7; bolt fixing: C8; blow molding: C9Material factorf5(x)-B5Stainless steel:C10; plastic: C11Human-machine relationshipf6(x)-B6Safe:C12; stable: C13Emotional semanticsf7(x)-B7Modern:C14; fashion: C15; dynamic: C16Other factorsfn(x)-B8Low cost:C17; simple shell: C18


### 4.2. Realization of Target Scheme Design Decision

In the design process, the design group size was a team of five persons. The designers performed the scheme design in the framework of a clear design decision constraint and finally carried out scheme evaluation with the design scheme side view. This design scheme is shown in Figure4, where D0 is the design scheme reference model, and the first round of the design scheme populationincludesD1, D2, D3, D4, and D5.Figure 4
Design schemes in the first round.In the design process, according to the design objective and decision constraints, the optimized scheme was searched in the decision space, the local optimized solution was stored in the population poolU1, and the local nonoptimal solution was stored in the population pool U2. Table 4 lists the design scheme population in the first round.Table 4
Design scheme population in the first round.
U1U2D1D3D4D2D5Conforms to design constraints, overall modeling simplicity, fashionConforms to design constraints, overall modeling simplicity, popularityConforms to design constraints, overall modeling simplicity, fashionModeling slightly complex, body structure is not simple enoughModeling proportion is large, the design is not stylish and simpleThe experts compared the importance of the objective function and design variables ofD1, D3, and D4, with respect to the design constraints and design expectations, scored them, and constructed a judgment matrix. Table 5 shows the weights of indexes in A-B.Table 5
A-B weights.
W (A-B)B1B2B3B4B5B6B7B8A0.150.220.130.140.200.160.140.22The experts then scored theC layer, constructed a judgment matrix, and calculated the B-C weights using MATLAB. The weights are shown in Table 6.Table 6
B-C weights.
W (B-C)C1C2C3C4C5C6C7C8C9B10.310.30B20.410.28B30.610.34B40.360.210.33W (B-C)C10C11C12C13C14C15C16C17C18B50.320.41B60.430.46B70.650.410.32B80.650.33TheD layer was then scored, a judgment matrix was constructed, and the C-D weights were calculated by MATLAB. The weights are shown in Table 7.Table 7
C-D weights.
W (C-D)D1D3D4C10.320.310.32C20.330.320.32C30.210.470.33C40.200.420.32C50.340.460.22C60.240.460.25C70.300.350.31C80.310.300.27C90.330.260.41C100.330.340.25C110.300.300.31C120.320.320.31C130.190.380.34C140.210.400.22C150.270.440.29C160.280.320.36C170.330.300.31C180.310.310.32The final weight of layerD to layer A was obtained as WsumD1 = 0.2834, WsumD3 = 0.3921, and WsumD4 = 0.3127, where C.R. = 0.0082 < 0.1, which passed the consistency test. In the Pareto solution set, the global optimized Pareto solutions D3 and D4 were selected according to the design evaluation model, and the population poolU1 (D3, D4) was updated.


### 4.3. Realization and Analysis of Final Scheme Decision

Using the populationV1 as the initial population and the global optimized Pareto solution (D3, D4) as the design starting point, the designers completed five design schemes in the updated design decision space. The design schemes P1, P2, P3, P4, and P5 were selected after five iterations, a judgment matrix was constructed, and the weight list of criterion layer C for the five schemes was obtained (see Table 8).Table 8
C-P weights.
W (C-P)P1P2P3P4P5C10.140.210.140.250.23C20.130.220.170.240.22C30.150.170.190.250.22C40.160.180.210.220.20C50.170.150.180.230.21C60.160.150.220.240.22C70.110.150.210.180.31C80.210.150.200.210.20C90.170.180.190.210.22C100.210.200.180.190.20C110.150.220.180.210.24C120.210.180.160.210.24C130.230.160.180.250.21C140.180.170.180.280.17C150.210.140.210.220.19C160.220.180.210.200.17C170.230.210.170.200.17C180.210.170.220.180.18Finally,WsumP1 = 0.2931, WsumP2 = 0.2061, WsumP3 = 0.1945, WsumP4 = 0.2341, and WsumP5 = 0.2621 were obtained, where C.R. = 0.035482 < 0.1. After the consistency test, the scheme P1 was obtained as the final scheme. The overall design of scheme P1 is simple and elegant, the color of P1 is mainly gray, the shape design and color matching meet the expected design goals, and the design decision is effective.


## 4.1. Modeling Design Decision Space Constraints

As shown in Table3, F(X) is the goal of the entire design project, corresponding to the goal expectation A. Each subfunction f(x) is a subobjective function under the corresponding decision constraint, corresponding to the decision goal layer B, and the specific constraint index is the C layer.Table 3
Description of product design constraint model.
Design problem descriptionfn(x)Design variablexF(X)Brand genef1(x)-B1Chassis:C1; color:C2Function parameter2(x)-B2Motor driven:C3; rear drive: C4Business factorf3(x)-B3Mid-range model:C5; daily transportation: C6Technology factorf4(x)-B4Module welding:C7; bolt fixing: C8; blow molding: C9Material factorf5(x)-B5Stainless steel:C10; plastic: C11Human-machine relationshipf6(x)-B6Safe:C12; stable: C13Emotional semanticsf7(x)-B7Modern:C14; fashion: C15; dynamic: C16Other factorsfn(x)-B8Low cost:C17; simple shell: C18


## 4.2. Realization of Target Scheme Design Decision

In the design process, the design group size was a team of five persons. The designers performed the scheme design in the framework of a clear design decision constraint and finally carried out scheme evaluation with the design scheme side view. This design scheme is shown in Figure4, where D0 is the design scheme reference model, and the first round of the design scheme populationincludesD1, D2, D3, D4, and D5.Figure 4
Design schemes in the first round.In the design process, according to the design objective and decision constraints, the optimized scheme was searched in the decision space, the local optimized solution was stored in the population poolU1, and the local nonoptimal solution was stored in the population pool U2. Table 4 lists the design scheme population in the first round.Table 4
Design scheme population in the first round.
U1U2D1D3D4D2D5Conforms to design constraints, overall modeling simplicity, fashionConforms to design constraints, overall modeling simplicity, popularityConforms to design constraints, overall modeling simplicity, fashionModeling slightly complex, body structure is not simple enoughModeling proportion is large, the design is not stylish and simpleThe experts compared the importance of the objective function and design variables ofD1, D3, and D4, with respect to the design constraints and design expectations, scored them, and constructed a judgment matrix. Table 5 shows the weights of indexes in A-B.Table 5
A-B weights.
W (A-B)B1B2B3B4B5B6B7B8A0.150.220.130.140.200.160.140.22The experts then scored theC layer, constructed a judgment matrix, and calculated the B-C weights using MATLAB. The weights are shown in Table 6.Table 6
B-C weights.
W (B-C)C1C2C3C4C5C6C7C8C9B10.310.30B20.410.28B30.610.34B40.360.210.33W (B-C)C10C11C12C13C14C15C16C17C18B50.320.41B60.430.46B70.650.410.32B80.650.33TheD layer was then scored, a judgment matrix was constructed, and the C-D weights were calculated by MATLAB. The weights are shown in Table 7.Table 7
C-D weights.
W (C-D)D1D3D4C10.320.310.32C20.330.320.32C30.210.470.33C40.200.420.32C50.340.460.22C60.240.460.25C70.300.350.31C80.310.300.27C90.330.260.41C100.330.340.25C110.300.300.31C120.320.320.31C130.190.380.34C140.210.400.22C150.270.440.29C160.280.320.36C170.330.300.31C180.310.310.32The final weight of layerD to layer A was obtained as WsumD1 = 0.2834, WsumD3 = 0.3921, and WsumD4 = 0.3127, where C.R. = 0.0082 < 0.1, which passed the consistency test. In the Pareto solution set, the global optimized Pareto solutions D3 and D4 were selected according to the design evaluation model, and the population poolU1 (D3, D4) was updated.


## 4.3. Realization and Analysis of Final Scheme Decision

Using the populationV1 as the initial population and the global optimized Pareto solution (D3, D4) as the design starting point, the designers completed five design schemes in the updated design decision space. The design schemes P1, P2, P3, P4, and P5 were selected after five iterations, a judgment matrix was constructed, and the weight list of criterion layer C for the five schemes was obtained (see Table 8).Table 8
C-P weights.
W (C-P)P1P2P3P4P5C10.140.210.140.250.23C20.130.220.170.240.22C30.150.170.190.250.22C40.160.180.210.220.20C50.170.150.180.230.21C60.160.150.220.240.22C70.110.150.210.180.31C80.210.150.200.210.20C90.170.180.190.210.22C100.210.200.180.190.20C110.150.220.180.210.24C120.210.180.160.210.24C130.230.160.180.250.21C140.180.170.180.280.17C150.210.140.210.220.19C160.220.180.210.200.17C170.230.210.170.200.17C180.210.170.220.180.18Finally,WsumP1 = 0.2931, WsumP2 = 0.2061, WsumP3 = 0.1945, WsumP4 = 0.2341, and WsumP5 = 0.2621 were obtained, where C.R. = 0.035482 < 0.1. After the consistency test, the scheme P1 was obtained as the final scheme. The overall design of scheme P1 is simple and elegant, the color of P1 is mainly gray, the shape design and color matching meet the expected design goals, and the design decision is effective.


## 5. Discussion

To verify the validity and decision satisfaction of the PGA design decision model, the design entrusting party and four experts participated in six rounds of design scheme decision processes. The design scheme selected by the PGA-based decision model and the scheme selected by experts were scored according to the satisfaction of the design entrusting party, with a full score of 10 points. As shown in Figure5, the client satisfaction trend of the four experts and the PGA design decision model gradually increased as the design progress deepened. After six rounds of scheme evaluation, the client satisfaction with the PGA-based design scheme decision model was higher, and the decision results of the four experts were highly compatible with the PGA decision model. Meanwhile, during the PGA-based design decision model experiment, the design decision evaluations were more stable, the decision time was shorter, and the decision efficiency was higher after six rounds.Figure 5
PGA-based design decision model vs. expert decision satisfaction.The intelligent decision-making system is more rational and efficient than traditional manual decision-making. By comparison, it is found that the design decision model based on PGA can quickly optimize the design scheme without losing satisfaction, and it can be used as a rapid auxiliary evaluation tool for product design schemes.To further verify the validity of the PGA design decision model, based on the original data set, the classical GA [18] algorithm and the traditional DNN [28] deep learning algorithm were compared respectively (see Table 9), and the average decision satisfaction of the PGA design decision model is higher than the other algorithms. The PGA design decision model performed stably in 6 rounds of the design decision, and the design decision time was greatly shortened compared with the manual decision.Table 9
The comparison of design evaluation satisfaction.
MethodAverage satisfaction (%)Average recall (%)GA63.5 ± 4.151DNN57.8 ± 4.663PGA71.6 ± 5.364


## 6. Conclusions

As product modeling design decisions are characterized as multitask, multiobjective, and dynamic, the conventional expert evaluation method has low efficiency and stability in the decision-making process. This article proposed a PGA-based product design decision model and basic concepts based on the essential characteristics of design decision-making. During design, the design decision task index was decomposed, and the design expectation was transformed into the design decision constraint space using the analytic hierarchy process. By iterating the design evaluation process, the design scheme population was updated and a Pareto solution set satisfying the design expectation was obtained. A case study of electric scooter design decisions was then employed to verify the validity of the decision model. The experimental results showed that the PGA-based decision model had a high degree of fit with the conventional expert evaluation method, the decision stability and efficiency were greatly improved, and the design decision satisfaction was high. Future studies will further improve the PGA algorithm, improve the PGA-based design decision model, combine deep learning and big data theory, improve the accuracy of the design decisions, and build a product modeling design decision software system.



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*Source: 7794320-2022-08-29.xml*