A second-generation fast Non-dominated Sorting Genetic Algorithm product shape multi-objective imagery optimization model based on degradation (DNSGA-II) strategy is proposed to make the product appearance optimization scheme meet the complex emotional needs of users for the product. First, the semantic differential method and K-Means cluster analysis are applied to extract the multi-objective imagery of users; then, the product multidimensional scale analysis is applied to classify the research objects, and again the reference samples are screened by the semantic differential method, and the samples are parametrized in two dimensions by using elliptic Fourier analysis; finally, the fuzzy dynamic evaluation function is used as the objective function of the algorithm, and the coordinates of key points of product contours Finally, with the fuzzy dynamic evaluation function as the objective function of the algorithm and the coordinates of key points of the product profile as the decision variables, the optimal product profile solution set is solved by DNSGA-Ⅱ. The validity of the model is verified by taking the optimization of the shape scheme of the hospital connection site as an example. For comparison with DNSGA-II, other multi-objective optimization algorithms are also presented. To evaluate the performance of each algorithm, the performance evaluation index values of the five multi-objective optimization algorithms are calculated in this paper. The results show that DNSGA-II is superior in improving individual diversity and has better overall performance.

The consumption pattern in today’s product-consuming market has moved from a rational desire for product function to a psychological demand for emotional expression [

The emotional experience effect of a product becomes an essential factor in determining its popularity among consumers. Thus, the production of pleasant emotional experiences in consumers via perceptual image design has increasingly become the focal point of product form conceptualdesign [

Relevant Kansei Engineering [

Ren et al. [

In the literature mentioned above, the mapping connection between product appearance and perceptual image, as well as the prediction of the perceptual image of product appearance, are examined in depth, effectively guiding the expression of the product appearance’s perceptual image. However, the study mentioned above still has the following limitations: the expression of users’ perceptual images is diverse; for items of the same appearance, the expression of users’ image preferences is complex. Users will express their subjective sentiments from numerous dimensions [

Kansei Engineering is a broad field that combines design, psychology, ergonomics, and other fields. Users’ perceptual needs for products are recessive, imprecise, and fuzzy; consequently, in product design based on perceptual image, accurately measuring, positioning, and capturing users’ perceptual cognition of product appearance is the primary problem to be solved and the focus of product perceptual design research [

The objective function of perceptual imagery optimization is actually to establish a mapping relationship between product form elements and product imagery vocabulary. The manifestation of this mapping relationship can be divided into linear and nonlinear objective functions. Multiple regression analysis [

Fuzzy theory is based on the acceptance of the existence of objective phenomena that are vague. Its research goal is to deal with fuzzy uncertainties and quantify them into computer-identifiable data [

As discussed in

This paper’s selection of multi-target perceptual imagery required experiments using the semantic differential twice. First, a preliminary set of imagery words was obtained by reviewing a large amount of relevant product information and collecting imagery words related to the research object; second, a first set of questionnaires was created to compare the similarity of the two sets of words in the range [0, 1] with a step size of 0.2. If the two words are identical, the similarity is 1; if they are very similar, the similarity is 0.8; if they are relatively similar, the similarity is 0.6; if they are different, the similarity is 0.4; and if they are not similar at all, the similarity is 0, and the semantic similarity matrix of the imagery words can be obtained. Then, the K-Means clustering method [

Initial prime selection:

Calculating the distance from the remaining perceptual vocabulary to the original center of mass and arranging them into the closest distance group.

Recalculation of the obtained centers of mass for each categorization.

Repeat steps (2) and (3) until the output criteria are fulfilled.

The concept of K-Means clustering is to vectorize all imagery words, whose center of mass is the vector center of

_{k}

Product images are taken from a company’s current product instance collection, and the samples are first integrated using product morphology analysis, which groups samples with similar profiles into one category. Although the morphological differences between samples are large enough to enable the diversification of gene characteristics in the gene pool. However, it can lead to effects such as instability of genetic traits and uncontrolled offspring characteristics. Therefore, it is only necessary to select a certain class of example samples and then apply the multidimensional scale analysis to classify these samples in terms of shape similarity. Next, a 5-point Likert scale questionnaire was developed using the imagery vocabulary. Users were invited to rate these categorized samples. Based on the combined ranking of the sample imagery scores, the most representative sample was selected from each sample category. This approach efficiently categorized the samples while guaranteeing a more comprehensive genetic profile. The example sample maps were then pre-processed using image processing applications such as CorelDRAW and Adobe Illustrator to provide the groundwork for sample parameterization, the specific steps are shown in

The process of digitally describing a product instance sample through the application of a suitable method that takes into account the characteristics of the product’s form is known as sample instance parameterization. Methods such as morphological analysis [

In the process of extracting product contours using MATLAB, sometimes some of the contours are missing. The key points of the missing part of the product contour can be extracted using elliptic Fourier analysis by inserting new points into the original contour coordinates. Then the two-dimensional coordinates of these points are calculated, and finally, the missing part of the key points are replaced by the average of the coordinates of these new points. The steps are as follows:

Image pre-processing: The initial product contour points are extracted using MATLAB 2022a to obtain a two-dimensional contour point consisting of the

Insert new coordinate points: assume that the number of points to be inserted is

Assuming that

The objective function of product modeling imagery optimization in the multi-objective optimization algorithm, the fitness function can be transformed into an objective function [

Compute the absolute value of the difference between the coordinates of the reference sample and the sample to be optimized.

where:

Fuzzy dynamic scores [

where: _{k}

According to

In

1. In the eye-tracking experiment,

2. Defining

The weights of the product profile’s main points may be calculated as follows based on the preceding definition:

The mathematical formulation of the multi-objective optimization issue to be addressed in this study is as follows:

As there are no globally optimum individuals in multi-objective optimization, the connection between optimal individuals may be represented mathematically as follows: if the solution vector

The NSGA-II method [

The various steps of the NSGA-II tournament approach are as follows:

1. Set the number of comparisons to 2 [

2. The individual with the smaller non-dominance rank joins the crossover pool; if the two individuals have the same non-dominance rank, they are filtered according to their crowding distance, and the person with the greater crowding distance enters the crossover pool.

3. Continue the procedure until the crossover pool size is reached.

To maintain the genes of high-quality individuals, the tournament approach prioritizes those with a lower non-dominance rank and a greater crowding distance, as described above. However, this has a significant impact on the diversity of offspring during product shape optimization.

The tournament selection approach is based on a descending strategy to solve the issue of recurrent selection of the parent individuals. The particular procedure is described as follows: A rapid non-dominated ranking is done on the parent population

If individual

This strategy effectively reduces the likelihood of an individual

Input: Non-dominance class |

1: For |

Input: Primary population key point coordinates |

1: |

This paper introduces the proposed multi-objective optimization method for composite image product shape, taking the appearance optimization of medical transceiver stations as an example. A library of enterprise product examples provides a sample of research. Hospital shuttle stations can be divided into single-level stations and double-level stations according to their exterior structure. To ensure the stability of the genetic characteristics of the offspring, this study illustrates the application of the method in this paper by using the lateral map of the two-level site provided by the company as an example.

Initially, discussions with medical professionals, industrial design students, and site design engineers were used to compile an initial list of 50 image-related terms. A comparison analysis was conducted to exclude terms that were improper for the research as well as those with similar or repeating meanings, resulting in 30 imagery words. A questionnaire was subsequently created based on the semantic differential approach to quantify the semantics of the imagery vocabulary by comparing the semantic similarity of any two imagery terms. There were 50 questionnaires issued in all, but 46 were ultimately collected. The data findings were compiled to produce the vocabulary similarity matrix for images. The similarity matrix was input into Statistical Product and Service Solutions (SPSS) for K-Means clustering analysis, with the number of clusters set to 3. The mean squared errors of the K-Means clustering analysis are all less than 0.08, as shown in

Clustering | Inaccuracy | F | Sig. | |||
---|---|---|---|---|---|---|

Mean square | df | Mean square | df | |||

Jawless | 0.394 | 2 | 0.043 | 27 | 9.087 | 0.000 |

Safe | 0.381 | 2 | 0.063 | 27 | 6.083 | 0.000 |

Gentle | 0.340 | 2 | 0.059 | 27 | 5.797 | 0.000 |

Lightweight | 0.379 | 2 | 0.046 | 27 | 8.183 | 0.000 |

Rational | 0.539 | 2 | 0.058 | 27 | 9.321 | 0.000 |

Comfortable | 0.582 | 2 | 0.034 | 27 | 17.030 | 0.000 |

… | … | … | … | … | … | … |

Simple | 0.632 | 2 | 0.036 | 27 | 17.451 | 0.000 |

Lightsome | 0.536 | 2 | 0.054 | 27 | 9.964 | 0.000 |

Stable | 0.356 | 2 | 0.055 | 27 | 6.517 | 0.000 |

Soft | 0.605 | 2 | 0.052 | 27 | 11.707 | 0.000 |

Concise | 0.354 | 2 | 0.036 | 27 | 17.451 | 0.000 |

Steady | 0.498 | 2 | 0.023 | 27 | 21.634 | 0.000 |

Clustering | 1 | 2 | 3 |
---|---|---|---|

1 | 2.131 | 2.087 | |

2 | 2.131 | 2.677 | |

3 | 2.087 | 2.677 |

Classification | Category 1 | Category 2 | Category 3 |
---|---|---|---|

Lightsome | Mature | Soft | |

Simple | Reposeful | Amiable | |

Crisp | Traditional | Harmonious | |

Concise | Steady | Streamlined | |

Vocabulary | Handy | Popular | Consecutive |

Smooth | Stable | Humanistic | |

Succinct | Burly | Rounded | |

Geometrical | Sturdy | Comfortable | |

Regular | Jarless | Gentle | |

Rational | Safe | ||

Lightweight |

Using a side profile of a hospital shift station, respondents were asked to select three words with high similarity from each category of imagery vocabulary. A total of 60 questionnaires were sent out, of which 60 were valid. As shown in

An initial sample of 30 cases was retrieved from the double-decker medical transport site instance library; however, after removing samples with nearly identical profiles and those with entirely distinct profile components, a final sample of 22 instances was produced. The similarity matrix of any two samples was assessed for shape similarity by four experts, and the similarity matrix of four sets of lower triangular matrix data was produced. The similarity matrix was entered into the SPSS software for multidimensional scale analysis, and the rubble diagram was created, as seen in _{20} is far distant, perhaps as a result of the variation in individual ratings. Therefore, sample P_{20} is excluded.

Classification | Category 1 | Category 2 | Category 3 | Category 4 |
---|---|---|---|---|

Sample | P_{4}、P_{11}、P_{12} |
P_{2}、P_{3}、P_{6}、P_{8}、P_{13}、P_{18}、P_{21} |
P_{1}、P_{5}、P_{16}、P_{19}、P_{22} |
P_{7}、P_{9}、P_{10}、P_{14}、P_{15}、P_{17} |

Using the semantic differential method to design the questionnaire, respondents combined the five-point Likert scale to evaluate the imagery of the example sample according to the target imagery, and the semantic evaluation scale is shown in

Side view of the sample | Imagery vocabulary | Evaluation scale | Imagery vocabulary |
---|---|---|---|

Shaky | 1 2 3 4 5 | Stable | |

Complex | 1 2 3 4 5 | Concise | |

Hard | 1 2 3 4 5 | Soft |

Objective imagery | |||
---|---|---|---|

Stable | Concise | Soft | |

Mean | Mean | Mean | |

Sample 3 | 4.75 | 3.25 | 4.95 |

Sample 5 | 3.26 | 4.36 | 3.02 |

Sample 12 | 4.68 | 3.98 | 3.14 |

Sample 19 | 4.25 | 4.55 | 4.45 |

The procedure is as follows: 1) Preprocessing: The size of the sample side view is reduced to 200 * 200 dpi and converted to grayscale. 2) Contour line extraction Pepper noise is applied to the image and binarized, then the morphological opening and closing of the binarized noise image are calculated to generate a sample contour consisting of multiple points. The coordinates of key points are extracted. The points that are most similar to the sample contour line are selected and then the coordinate values of the key points are extracted using MATLAB’s coordinate display tool, see

Variables | Sample 3 | Sample 5 | Sample 12 | Sample 19 |
---|---|---|---|---|

X_{1} |
12.42 | 20.00 | 10.00 | 10.00 |

Y_{1} |
0.00 | 0.00 | 0.00 | 0.00 |

X_{2} |
12.42 | 20.00 | 10.00 | 10.00 |

Y_{2} |
0.00 | 5.00 | 0.00 | 3.00 |

X_{3} |
164.76 | 180.00 | 174.71 | 175.00 |

Y_{3} |
0.49 | 5.00 | 0.29 | 3.00 |

… | … | … | … | … |

X_{20} |
11.44 | 20.00 | 10.00 | 9.92 |

Y_{20} |
147.50 | 150.00 | 144.00 | 141.90 |

X_{21} |
7.11 | 20.00 | 4.00 | 6.97 |

Y_{21} |
150.00 | 150.00 | 150.00 | 144.90 |

X_{22} |
0.00 | 0.00 | 0.00 | 0.00 |

Y_{22} |
150.00 | 150.00 | 150.00 | 145.00 |

In

Sample 3 | Sample 5 | Sample 12 | Sample 19 | |
---|---|---|---|---|

1 | 0.36 | 0.31 | 0.07 | 0.38 |

2 | 0.31 | 0.36 | 0.16 | 0.57 |

3 | 0.29 | 0.40 | 0.45 | 0.33 |

4 | 0.70 | 0.47 | 0.45 | 0.82 |

5 | 0.63 | 0.71 | 0.48 | 0.81 |

… | … | … | … | … |

18 | 0.43 | 0.12 | 0.27 | 0.24 |

19 | 0.41 | 0.10 | 0.32 | 0.27 |

20 | 0.39 | 0.59 | 0.57 | 0.60 |

21 | 0.39 | 0.48 | 0.57 | 0.59 |

22 | 0.02 | 0.03 | 0.26 | 0.03 |

In the product modeling imagery optimization of this paper, since the real Pareto frontier cannot be obtained precisely, this paper combines

Objective function of stable imagery

Objective function of concise imagery

Objective function of soft imagery

The expression of the combined multi-objective optimization function is as follows:

The decision variables of the objective function are the coordinates of the key points of the product profile, and the range of the decision variables is determined by the coordinates of the four reference samples, specifically, the coordinate values of the four reference samples are compared horizontally, and the maximum and minimum values of each coordinate are taken as the range of the decision variables, as shown in

Decision variables | Minimum value | Maximum value | Step length |
---|---|---|---|

10.00 | 20.00 | 2.00 | |

0.00 | 0.00 | 0.00 | |

10.00 | 20.00 | 20.00 | |

3.00 | 5.00 | 1.00 | |

164.76 | 180.00 | 50.00 | |

0.49 | 5.00 | 1.00 | |

… | … | … | … |

9.92 | 20.00 | 1.00 | |

141.90 | 150.00 | 1.00 | |

4.00 | 20.00 | 2.00 | |

144.90 | 150.00 | 1.00 | |

0.00 | 0.00 | 0.00 | |

145.00 | 150.00 | 1.00 |

According to

As can be seen from

To verify the performance of the proposed DNSGA-II multi-imagery objective optimization algorithm, four other sets of experiments were conducted in the same environment to introduce the traditional NSGA-II, Strength Pareto Evolutionary Algorithm-II (SPEA-II), Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) and Non-dominated Sorting Genetic AlgorithmIII (NSGA-III) to compare the algorithm performance with DNSGA-II, and the advantages of each algorithm are shown in

The algorithms | Advantages |
---|---|

NSGA-II | The use of local search and elite retention strategies can retain high-quality individuals and effectively improve the search capability of the algorithm. |

SPEA-Ⅱ | The density estimation operator enables the maintenance of global and local searches, effectively improving the search capability of the algorithm. |

MOEA/D | It can effectively deal with high-dimensional problems; the idea of decomposition is adopted to facilitate the handling of multi-objective optimization problems with complexity constraints. |

NSGA-III | Using reference points and polynomial transformation, the solution space of non-convex multi-objective problems can be searched effectively; supporting parallel computing, the solution space of large-scale can be searched quickly. |

To further validate the performance of the algorithm, it was further evaluated using Inverted Generational Distance (IGD), Hypervolume (HV), Generational Distance (GD), Spacing Metric (Spacing) and Convergence and Preservation Factor (CPF) [

Number of runs | DNSGA-II | NSGA-II | SPEA-II | MOEA/D | NSGA-III | |
---|---|---|---|---|---|---|

IGD | 50 | 9.780 5e−1 | 7.880 6e−1 | 5.627 6e−1 | 5.228 8e−1 | |

HV | 50 | 4.023 6e−1 | 4.560 4e−1 | 7.520 4e−1 | 9.814 6e−1 | |

GD | 50 | 6.214 5e−1 | 7.325 1e−1 | 6.853 2e−1 | 5.496 2e−1 | |

Spacing | 50 | 3.278 4e−1 | 4.965 1e−1 | 5.621 4e−1 | 6.325 4e−1 | |

CPF | 50 | 5.278 9e−1 | 1.765 6e−1 | 4.169 8e−1 | 3.389 1e−1 |

The product appearance optimization methodology developed in this research may successfully improve current product form ideas based on the user’s perceptual image. 1) A user perceptual image cognition experiment was performed using a perceptual engineering research approach, and three objective imageries of stable, concise, and soft were generated by K-means clustering analysis. 2) The objective function of product shape imagery optimization is constructed according to the fuzzy evaluation method, and an eye-movement experiment was created to estimate the imagery weight value of each set of coordinates of the research samples. 3) The NSGA-II method based on the degradation strategy was suggested, and the coordinates of the outer contour of the samples to be assessed were utilized as the decision variables for optimizing the form of the medical feeder station, as an example. Twenty sets of optimum Pareto solution sets were obtained through experiments. The ultimate solution of the product profile must be assessed based on consumption environment, manufacturing cost, production time, and other criteria. Compared to conventional NSGA-II, SPEA-II, MOEA/D and NSGA-III, DNSGA-II has a broader range of Pareto fronts, a more uniform distribution, and a higher overall performance. It successfully overcomes the issue of people being regularly picked many times, resulting in decreased population variety, assures the diversity of individuals in the ideal solution set, and gives a larger search space. The model is also relevant to other multi-objective product appearance optimization challenges.

It is important to note that in this research, the model is based on two-dimensional product outlines, and other factors that impact the perceptual imaging of product forms, such as product material and color, are omitted. In the future study, the use of 3D products in the multi-objective imagery optimization of the form will be further investigated, and the materials and colors of the goods will be integrated to discover more precise ways of product shape parameterization.

The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

This research project was supported by National Natural Science Foundation Grant 52065010; the Science and Technology Project supported by Guizhou Province of China ZK [2021]341 and [2021]397; the transformation Project of Scientific and Technological Achievements in Guiyang, Guizhou Province, China [2021]7-3.

Study conception and design: Yinxue Ao, Jian Lv; data collection: Jian Lv, Zhengming Zhang; analysis and interpretation of results: Yinxue Ao; draft manuscript preparation: Yinxue Ao; Jian Lv and Qingsheng Xie reviewed the results and approved the final version of the manuscript.

The data used in this paper can be requested from the corresponding author upon request.

The authors declare that they have no conflicts of interest to report regarding the present study.