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ArticlesAn Interactive Genetic Algorithm with an Alternation Ranking Method and Its Application to Product Customization
• Dong Zeng1,2, Mao-en He1,*, Zhuan Zhou3, and Chaogang Tang4

Human-centric Computing and Information Sciences volume 11, Article number: 15 (2021)
https://doi.org/10.22967/HCIS.2021.11.015

Abstract

Product customization can not only meet customers’ needs but also increase the market competitiveness of corporations and businesses. Effective product customization requires customers’ participation during the product design process. As such, the interactive genetic algorithm could be an effective approach to integrating customers into the product design process. However, due to inappropriate individual evaluation, the interactive genetic algorithm cannot be applied to product customization very effectively. To simplify the evaluation process in the algorithm, this paper presents an interactive genetic algorithm with an alternation ranking method. First, the alternation ranking method is used to evaluate individuals and obtain their rankings. Second, to express user preferences more accurately, this study proposes a method of transforming individuals’ rankings to their respective fuzzy fitness values, and then adopts an existing method of comparing and selecting individuals’ fuzzy fitness values. The proposed method is then applied to the customization system of sneaker colors, andcompared with the traditional interactive genetic algorithm. The experimental results show that the proposed method outperforms the traditional algorithm in four aspects. Therefore, itis considered to be effective not only in improving the user evaluation process and accelerating the convergence of the algorithm, but also in enhancing the applicability of the interactive genetic algorithm to product customization.

Keywords

Interactive Genetic Algorithm, Alternation Ranking Method, Product Customization, Fuzzy Fitness

Introduction

As customer behavior changes, there is an increasing need for product customization [1]. From the perspective of customers, product customization could meet their needs and improve their experience, whereas, from the perspective of companies, product customization could beeffectivein enhancing their market competitiveness [2]. As such, product customization has become an important business service model in the era of Industry 4.0 [3].
Traditional product customization relies mainly on the user surveys conducted by designers. Designers learn about customer preferences through surveys of users and then provide a personalized design scheme. However, it is difficult to obtain exact information about customer preferences through such surveys. Furthermore, this kind of product customization also consumes large amounts of the human and material resources of companies [4]. To solve these problems, researchers aim to combine user preferences with computer intelligence so as to present the idea of human-computer collaborative design. With the assistance of computers, customers can become directly involved in the product design process. The interactive genetic algorithm (IGA) is a suitable method for human-computer collaborative design.
The IGA is a genetic algorithm that utilizes users’ subjective evaluation as a fitness function to implement the evolution process [5]. Since human intelligence is incorporated into the IGA to solve optimization problems, it is widely used in many fields related to human intuitions and preferences, such as fashion design [6], pattern design [79], book cover design [10], image retrieval [11, 12], product design [1316], and product customization [17, 18]. However, the IGA still has some issues that need to be addressed in terms of its practical applications, such as the random initial population [19] and the inappropriate evaluation method [20].
The inappropriate evaluation method increases the users’ operational and psychological burden, and alsoaffects the application of the IGA in actual customization. First, the inappropriate evaluation method consumes more cognitive resources, increases the users’ physical and psychological workload, and then leads to an evaluation that is inconsistent with their preferences [21]. Second, the inappropriate evaluation method cannot comprehensively and accurately obtain users’ preferences [22], which then leads to a deviation in the direction of algorithm optimization. In addition, the user evaluation is an essential factor for actual product customization (such as fashion, souvenirs, and etc.). Therefore, the improvement of evaluation methods will help to alleviate the physical and psychological load, and improve the algorithm’s performance, which will in turn ensure the validation of the IGA in actual product customization.
This paper adopts a novel method of individual evaluationand proposes an interactive genetic algorithm with the alternation ranking method (AR-IGA). In the AR-IGA, users evaluate individuals by the alternation ranking method. Then, a fuzzy number is used to transform individuals’ rankings into their individual fitness, and a method is proposed to calculate the center and width of individual fuzzy fitness. Finally, the proposed algorithm employs an existing method to compare the individuals’ fuzzy fitness and identify superior individuals.
The major contributions in this paper are as follows:
First, from the perspective of user evaluation, this paper adopts the alternation ranking method to conduct an individual evaluation, which simplifies the evaluation operation and reduces the psychological load.
Second, from the perspective of algorithm performance, the proposed method transforms individuals' rankings to fuzzy fitness, which accelerates the convergence of the algorithm.
Third, in terms of application needs, the proposed method is consistent with users' behavior habits in actual product customization (such as fashion, souvenirs, etc.), which increases the usability of the IGA-based systems of product customization.
The remaining sections of this paper proceed as follows: Section 2 describes the evaluation problems in the IGA,compares existing research on individual evaluation, and briefly illustrates the alternation ranking method;Section 3 presents the research framework;Section 4 provides a detailed description of the AR-IGA;Section 5 applies the proposed algorithm to the customization system of sneakers, and compares it with the TIGA;Section 6 presents the experimental results and analysis;andSection7 presents the conclusions and recommendsa direction for further research in the future.

Related Work

Interactive Genetic Algorithm
First proposed in 1986 by Dawkins[23], the IGAis effective in solving optimization problems with implicit indices. The IGA utilizes the user evaluation as the individuals’ fitness to guide the population evolution; and it has been widely used in many fields involving human preferences.
As mentioned earlier, there are still some problems with the IGA.For example, inappropriate methods of individual evaluation are used, leading to a physical andpsychological load on the users, and reducing the efficiency of evolution. In the TIGA, the users evaluate an individual by assigning an accurate number to represent the individual’s fitness. However, assigning an accurate number requires mapping many feelings to a precise value [24], which causes psychological stress for the users. Furthermore, it is difficult to correctly distinguish slight differences among individuals [25]. Some methods of solving this problem have been proposed, largely falling into two categories, i.e. (1) methods aimed at improving the fitness expression, and (2) methods of adopting the non-assigned evaluation. The following introduces specific methods. Analysis and comparison wereperformed based on the following three indicators: evaluation operation, psychological load, and algorithm performance (Table 1).
The first category includes discrete fitness, interval fitness and fuzzy fitness:
(1) Discrete fitness: Ohsaki et al. [25] utilized discrete fitness values instead of continuous fitness values to evaluate individuals. Their study proposed that the evaluation operation of the TIGA required users to correctly distinguish slight differences among individuals. Users expressed these differences in terms of accurate fitness values; however, the quantitative levels of fitness usually exceeded actual human cognition ability. This method utilized a few levels only to rate individuals, such as a three-point or five-point scale. The experiments were conducted to clarify the relationship between the number of levels and quantization noise.
(2) Interval fitness: Gong et al. [24] employed interval fitness to evaluate an individual. In the proposed method, each individual’s fitness was expressed as an interval, and users assigned two numbers as the upper and lower limits of the interval fitness. Considering the complexity of the evaluation operation, Dou et al. [26] proposed an interactive genetic algorithm with interval fitness based on user hesitancy. In this algorithm, users only assigned a number as the midpoint of the interval fitness, and the evaluation time was utilized to calculate the width of the interval fitness. Compared with the previous algorithms involving interval fitness, users only assigned a number for each individual evaluation and were not required to assign the upper and lower limits of the interval. This method simplified the evaluation process for users. Then, Wang and Zhou [27] combined the fuzzy Kano model with interval fitness based on hesitancy. The fuzzy Kano model was introduced to analyze whethera product image was consistent with users' perceptual needs, and five relevant factors were extracted as evaluation indicators, on the basis of which users then evaluated individuals.
(3) Fuzzy fitness: Gong et al. [28] adopted a fuzzy number described with a Gaussian membership function to express an individual’s fitness. With this method,users firstly assigned a number as the center of an individual’s fuzzy fitness, andthenhad to select a modifying word as the width of the individual’s fuzzy fitness, such as “about,” “close to,” or “very close to.” Compared with interval fitness, fuzzy fitness cost users less time in finding a satisfactory solution. Then, Guo et al. [29] attempted to utilize the evaluation time to calculate the width of an individual’s fuzzy fitness. With this method, users were not required to select a modifying word. The system calculated the degree of ambiguity of the results of the evaluation based on the evaluation time. Lv et al. [7] proposed a novel method of calculating an individual’s fuzzy fitness. With this method, the center of fuzzy fitness was not only dependent on users’ evaluation, but was also related to basic color theory and formal esthetic principles. In addition, a back propagation (BP) neural network was used to simulate users' characteristics and predict individual fitness, which provided a reference for evaluating users. Yang and Tian [15] summarized the cognitive noise of the IGA into three stages (cognitive stage, intermediate stage, and fatigue stage). Based on these three stages, a trapezoidal fuzzy number was adopted as an individual’s fitness to describe the uncertainty of a user evaluation. Users evaluated individuals based on the seven-pointLikert scale from two perceptual dimensions.

Table 1. Analysis and comparison of existing research on individual evaluation
Category Author, year Method Evaluation operation Psychological load Algorithm performance
Improving the fitness expression Ohsaki et al. [25], 1998 Discrete fitness There is no obvious improvement compared with the TIGA. It requires users to make a rough evaluation, which reduces their psychological load. The evaluation results are inaccurate, which reduces the convergence speed.
Gong et al. [24], 2008 Interval fitness Two numbers (the upper and lower limits) are assigned for each evaluation, which complicates the operation. Users assign a range as individual fitness, which reduces the psychological load. It is consistent with the users' cognitive characteristics and can obtain accurate user preferences.
Dou et al. [26], 2016 Interval fitness based on hesitancy Compared with [24], it simplifies the evaluation operation; compared with the TIGA, the operation is more complicated. Compared with [24], it increases the psychological load; compared with the TIGA, there is no obvious improvement. Compared with [24], the evaluation time is used as the width of interval fitness, which ensures that the evolution direction accords with user preferences.
Wang and Zhou[27], 2020 Interval fitness based on hesitancyand thefuzzy Kano model Compared with other studies related to interval fitness, the evaluation operation is complicated. Users are under a heavy mental burden, and it is difficult to evaluateindividualseffectively for a long time. Compared with [24, 26], users' perceptual image is fully and accurately obtained.
Gong et al. [28], 2011 Fuzzy fitness is described with a Gaussian membership function. In addition to assigning a number, a modal word needs to be selected, which is slightly complicated. It is consistent with users' cognitive characteristics, andreduce users' cognitive load. It accords with users' fuzzy and gradual cognition, reflects user preferences accurately, and improves the algorithm’s performance.
Guo et al. [29], 2018 Fuzzy fitness is described with a Gaussian membership function based on evaluation time. Compared with [28], it simplifies the evaluation operation. Compared with [24], it increases the psychological load; compared with the TIGA, there is no obvious improvement. Compared with [24], the evaluation time is utilized as the width of fuzzy fitness to improve the efficiency of algorithm convergence.
Lv et al. [7], 2019 Fuzzy fitness is described with a Gaussian membership function based on hesitancy and the principle of formal aesthetics, BP neural network. A number is typed to evaluate an individual, which complicates the evaluation operation. It provides users with a reference value of individual fitness to help users recognize individuals and reduce the cognitive load. It incorporates basic aesthetic standards to tunethe user evaluation results, and improve the quality of output schemes.
Yang and Tian [15], 2019 Fuzzy fitness is described with a Trapezoidal membership function. A seven-point Likert scale is adopted to evaluate individuals, which slightly simplifies the operation. Users need to evaluate an individual from two dimensions, which consumes their cognitive resources. Based on the cognition noise of the evolution process, the corresponding noise reduction is conducted to ensure convergence of the algorithm.
Adopting the non-assigned evaluation Cheng and Liu [30], 2012 Users' eye movement data are obtained, and user preferences are inferred. Users only observe the individuals based on intuition. The operation is extremely simple. Users are not required to deliberately evaluate the pros and cons of individuals, which greatly reduces the psychological load. It is difficult to obtain accurate user preferences in complex design tasks.
Takenouchiand Tokumaru [31], 2019 Multiple users' gaze information is used. The user operation of this method is similar to that of [30]. Compared with [30], the number of individuals observed is two each time, which reduces the psychological load. It can obtain the preference characteristics of the group.
Watanabe et al. [32], 2007 Paired comparison and fitness inference Compared with the first category and the TIGA, user operation is simple; Compared with [30, 31], user operation is a little inconvenient. Use of the paired comparison can reduce the psychological load. When the population is large, a large number of comparisons is performed, which decreases the optimization speed.
Sun et al. [33], 2010 Boolean evaluation The user operation is a little complicated compared with [32], but it is simple compared with the first category and the TIGA. Users select satisfied individuals without distinguishing between specific differences, which reduces the users’ psychological load. It can increase the population size and expand the search space, but convergence is slow in complex problems.
Leelathakuland Rimcharoen[9], 2020 Multi-stage evaluation, combination of partial and overall evaluation, judgement The operation process is simplified, but it is inconvenient compared with others of the second category. For users without design experience, the judgement operation increases psychological hesitation. It weakens the genetic and evolution mechanism of the IGA, and limits the performance in exploring unknown domains.
The first half of Table 1 shows the analysis and comparison of the first category research. First, interval fitness and fuzzy fitness contribute to reflecting the ambiguity and gradualness of user cognition, which helps to ensure correct evolution and accelerate convergence. However, these methods pay little attention to the evaluation operation, and some of them add additional steps which only serve to complicate the operation (such as [24, 27, 28]). In addition, the above methods have difficulty balancing simplification of the operation with reduction of the psychological load (such as [26, 29]).
The second category research aims to utilize a non-assigned evaluation method. Cheng and Liu [30] utilized an eye-tracking system to evaluate individuals. Withthe method, users observed the individuals on a screen, without assigning any numbers. Then, the system calculated individual fitness based on the eye-movement data of users. Then, Takenouchiand Tokumaru[31] conducted more detailed research on the application of the interactive genetic algorithm based on the gaze information of multiple users. The method adopted a Human Vision Component, B5T-007001, to collect the gaze information of group users, and inferred the overall preferences of the group. Watanabe et al. [32] adopted a paired comparison method for individual evaluation. With this method, users were required to compare two individuals and select the better one. Because the users only paid attention to two individuals at a time, the amount of information to be processed was greatly reduced. Sun et al. [33] proposed a Boolean method of evaluation to replace the assignment operation. Users selected satisfactory individuals from a population without rating. The algorithm calculated the individual fitness according to the order in which individuals were selected. Leelathakuland Rimcharoen[9] redesigned an evaluation mechanism based on the specific application. The main operation for users included the following three steps: randomization for an individual at any generation, maintenance and reorganization, and fixation. This method paidparticular attention to users' judgment and choice.
The second half of Table 1 shows the analysis and comparison of the second category research. These methods do not require users to assign a number, which simplifies the operation process and reduces the psychological load. However, most methods obtain only rough evaluations of users’ preferences, weakening the convergence of the algorithm. Therefore, these methods are not suitable for dealing with complex design problems.

Alternation Ranking Method
The alternation ranking method was first introduced at Standard Oil of New Jersey in the 1950s [34], and isnow mainly applied to performance appraisal [35]. The alternation ranking method requires appraisers to first select the best n(n≥1) objects and the worst n objects from all objects being evaluated, and then tocontinue selecting the best n objects and the worst n objects from the remaining objects. This process continues until all objects have been evaluated, after which the rankings of all individuals can be obtained.
For this study, the alternation ranking method was adoptedin order to evaluate individuals in the IGA because of following three primary factors. (1) Users are not required to assign a number to express their preferences, which can simplify the evaluation operation for them. (2) Users only select the best n individuals and the worst n individuals each time. The evaluation tasks are thus effectively divided into several subtasks, and users only need to focus on one task each time. Thus, the method helps to reduce the psychological load. (3) The individuals that have been evaluated are hidden in the interface. Therefore, a decreasing number of individuals will be presented to the users, which facilitates the evaluation process.
However, simplifying the operation leads to inaccurate evaluation results. To obtain accurate results, the proposed method transforms individuals' rankings into fuzzy fitness based on evaluation time and user cognitive characteristics, which effectively improves the convergence of the algorithm. Other methods can still be utilized to improve the algorithm performance, such as artificial immune algorithms [36], candidate elimination algorithms [10], and convolutional neural networks [37]. In this study, fuzzy fitness was adopted because of its effectiveness in accurately obtaining user preferences. Therefore, the AR-IGA is ideal for the integration of two-category research.

Research Framework

The research framework proposed in this study is divided into four stages (Fig. 1): The first includes the background to customization and a review of the existing literature. By analyzing the background to product customization, the user evaluation is presented as a crucial factor in applying the IGA to customization. Based on a review of the existing methods of individual evaluation, this studysuggests that the IGA needs to be improved to simultaneously meet three conditions, namely, simplification of evaluation operations, reduction of psychological loads, and efficient convergence of algorithms. In the second stage, an alternation ranking method was adopted to simplify the user operation and relieve the psychological load. To ensure effective convergence, the ranking results were processed by combining human cognitive characteristics and evaluation time, and then transformed into fuzzy fitness values, which help to accurately reflect user preferences. Then, an existing method of comparison was used to recognize superior individuals. The third stage is the case application. The shortcomings of the existing sneaker customization system were analyzed. Then, the rules of chromosome coding were built, and the initial parameters were set. The convergence and termination conditions were depicted. The system interface was designed, and two customization systems for sneakers were constructed based on the AR-IGA and the TIGA. Finally, the two methods were comparedusing the following four indicators: (1) the number of generations, (2) the number of individuals evaluated, (3) the total evaluation time, and (4) the average time taken to evaluate an individual. With the above four indicators, the proposed method was comprehensively evaluated.

Fig. 1. Research frame.

Interactive Genetic Algorithm with the Alternation Ranking Method

The proposed method has three primary aspects (Fig. 2). First, the alternation ranking method is utilized for individual evaluation. The specific mechanism and application method are represented in detail in Section 4.1. Second, the individual rankings were transformed into fuzzy fitness to accurately reflect user preferences. Section 4.2 describes the method of calculating the individual fuzzy fitness, which includes the calculation of the center and the width. Then, comparisons and tournament selections among individuals were conducted based on fuzzy fitness, which is described in Section 4.3. Crossover and mutation operations were performed to generate the next-generation population, and are similar to those in the TIGA. The evolution process continues until the terminal condition is reached.

Fig. 2. Methodology flow chart of the AR-IGA.

Evaluation based on the Alternation Ranking Method
Without loss of generality, let $x_i$($t$) denote an individual in the population of the t-th generation, i-1,2,...,N, where N is the size of the population. Generally, the size of the population in the IGA should not be very large [38, 39]. Thus, to make the result of the alternation ranking more accurate, let users select one best individual and one worst individual each time. Sorting the individuals that have been evaluated from bad to good, we can obtain a sorted list R. Let r($x_i$($t$)) denote the index of $x_i$($t$) in the list R. The minimum value of r($x_i$($t$)) is 1, and the maximum value of r($x_i$($t$)) is N. The specific evaluation steps are as follows:
(1) In the t-th generation, users first select one best individual from among the population, which is denoted as $x_g1$($t$). Users select one worst individual, which is denoted as $x$$b1(t). In list R, their indices r(x$$g1$($t$)) and r($x$$b1(t)) are equal to N and 1, respectively. (2) In the selection of the second iteration, users select one best individual x$$g2$($t$) and one worst individual $x$$b2(t) from the remaining individuals. Their indices r(x$$g2$($t$)) and r($x$$b2(t)) are equal to N-1 and 2. (3) In the selection in the l-th iteration, users select one best individual x$$g1$($t$) and one worst individual $x$$b1(t), and their indices are r(x$$g1$($t$)) = $N + 1 - I$ and r($x$$b1(t)) = I, respectively. Then, I = I + 1 (4) Repeat the step (3) until: If N is an odd number, there is one remaining individual in the population, and the index of this individual is \frac{N+1}{2} ; if 𝑁 is an even number, all individuals are selected. Finally, we can obtain the rankings and evaluation time of all individuals in the population of the 𝑡-th generation. Calculation of Individual Fuzzy Fitness In the sorted list R, the distance between any two adjacent indices is always equal to 1. In other words, one can only know which individual is better and which is worse in the sorted list, but one cannot accurately determine the difference between them. This is also a major disadvantage of the alternation ranking method [34]. Therefore, this study proposes a method of transforming individuals’ indices in a sorted list to individuals’ fitness values in order toreflect user preferencesmore accurately. As previously mentioned, there are various methods of expressing an individual’s fitness, such as discrete fitness, interval fitness, and fuzzy fitness. Compared with other methods, fuzzy fitness can effectively reflect ambiguity and gradual changes in users’ perceptions [15]. Therefore, fuzzy numbers are adopted to express an individual’s fitness. The proposed method adopts the Gaussian membership function to express an individual’s fuzzy fitness. Let f(x_i(t)) denote the fuzzy fitness of x_i(t). The function is defined in the range [f$$min$,$f$$max] belonging to f(x_i(t)), where f$$min$ and $f$$max are the smallest and the largest fitness values of individuals, respectively. The membership function of f(x_i) is defined as follows: (1) where c(x_i(t)) is the center of f(x_i(t)) and \sigma(x_i(t)) is the width of f(x_i(t)). In the previous research [29, 40], c$$x_i$($t$) is equal to the evaluation result assigned by users, and $\sigma$($x_i$($t$)) is related to the degree of user ambiguity during the evaluation process. In general, when user ambiguity is large in the evaluation, the result is inaccurate, and $\sigma$($x_i$($t$)) should be large, and vice versa. Therefore, how to comprehensively consider the characteristics of user cognition and information related to user evaluation so as to reasonably calculate $c$$x_i(t) and \sigma(x_i(t)) is the key to ensuring the effectiveness of the proposed method. Next, the method of calculating c$$x_i$($t$) and $\sigma$($x_i$($t$)) will be depicted in AR-IGA.
The method of calculating $c$$x_i(t) is mainly based on the characteristics of user cognition in the evaluation process. In general, users have less uncertainty about the best or worst individual, while they have greater uncertainty about individuals with intermediate fitness [41]. Thus, in the AR-IGA, the closer an individual’s index r(x_i(t)) is to 1 or N, the greater the difference between the center of this individual and the center of an adjacent individual. In contrast, the closer an individual’s index r(x_i(t)) is to the middle, namely, \frac{N+1}{2}, the smaller the difference between this individual’s center and the center of its adjacent individual. Therefore, c(x_i(t)) can be expressed as follows: (2) where w(t) is used to control the degree of the differences among the centers of individuals. Fig. 3. Relationship between c(x_i(t)) and r(x_i(t)) :assume that the distance between the indices r(x_n(t)) and r(x_h(t)) is fixed. It is obvious that the farther the two indices are from the middle value, the greater the difference between their corresponding c(x_n(t)) and c(x_h(t)), as shown in panel (a); the closer the two indices are to the middle, the smaller the difference between their centers, as shown in panel (b). When the value of w is fixed, the relationship between c(x_i(t)) and r(x_i(t)) can be observed in Fig. 3. The function c(x_i(t)) has the following characteristics: first, it is an increasing function, so the larger the index r(x_i(t)) is, the larger the value of c(x_i(t)); second, the closer r(x_i(t)) is to the middle, the smaller the slope of the function is, and the slower the value of c(x_i(t)) changes. The farther r(x_i(t)) is from the middle, the greater the slope of the function. These characteristics can make good individuals and bad individuals more prominent, which makes good individuals easier to inherit in the next generation. In addition, these characteristics can also retain the diversity of the middle individuals by weakening the differences in their center values. In addition, as shown in Fig. 4, the larger w is, the greater the difference between the centers of two indices; conversely, the smaller w is, the smaller the difference between the centers. In general, in the initial stage of the evolution, users’ cognition is relatively uncertain, which leads to greater randomness in the evaluation results [15]. As the evolution proceeds, users gradually become more familiar with their preferences, and their evaluation results become more accurate. Therefore, in the initial stage of evolution, a smaller w should be set to reduce the impact of the randomness of the user evaluations. A smaller w can also ensure diversity in the population. As the number of generations increases, a larger w should be set to accelerate the convergence of the algorithm. Based on the above, w can be expressed as follows: (3) (4) where T is the maximum number of generations. w$$min$ is set manually before using the algorithm. Equation (4) can be obtained according to the following: when $r$($x_i$($t$)) = $N$, , the value of $c$($x_i$($t$)) is at its maximum, and the maximum value should be less than or equal to $f$$min . Thus, the following can be obtained: (5) Fig. 4. Relationship between the functionc(x_i(t)) and the value of (w_1 < w_2) The method of calculating \sigma(x_i(t)) is based on the index r(x_i(t)) and the time taken to evaluate the individual x_i(t) . Specifically, the following two aspects are considered: (1) the best or worst individual can be explicitly determined by users, while an intermediate individual does not elicit an explicit feeling in users. Thus, in the AR-IGA, the farther the index r(x_i(t)) of x_i(t) is from the middle, the smaller the width \sigma(x_i(t)) is; (2) the width \sigma(x_i(t)) is also related to the time taken to evaluate the individual x_i(t). There are two views on the relationship between the width and the time: some researchers [29, 30] consider them to be inversely related. If the time taken for a user to evaluate an individual is longer, they consider the user to be more confident in the evaluation result. Therefore, the width \sigma(x_i(t)) is smaller. However, some researchers [7, 26, 27] have advanced a different opinion. They think that the longer the evaluation time is, the more hesitant the user is in making the evaluation, and thus the more likely it is that the evaluation result will be inaccurate. Therefore, \sigma(x_i(t)) is larger. These two views were combined to propose the following conjecture: the specific optimization problem determines the relationship between the width \sigma(x_i(t)) and the evaluation time. If the optimization problem relies mainly on users’ intuition, such as fashion design and pattern design, then the shorter the individual’s evaluation time, the more accurate the user’s intuition is and the smaller \sigma(x_i(t)) is. If the optimization problem requires more rational analysis, such as in interior design, construction machinery design, etc.,the longer the time taken to evaluate an individual, the more thoughtful the user is, the more confident the user is in the evaluation result, and the smaller \sigma(x_i(t)) is. Based on the above, \sigma(x_i(t)) can be expressed as follows: (6) where D(x_i(t)) denotes the impact of the distance between the index r(x_i(t)) and the middle \frac{N+1}{2}, and H(x_i(t)) denotes the impact of the individual’s evaluation time. As mentioned above, the farther the index r(x_i(t)) is from the middle, the smaller the width \sigma(x_i) is. Therefore, D(x_i(t)) can be expressed as follows: (7) Based on the above conjecture, when the optimization problem is related to user intuition, the shorter the evaluation time h(x_i(t)) of x_i(t) is, and the smaller \sigma(x_i(t)) is. Let H$$ui$($x_i$($t$)) denote $H$($x_i$($t$)) in this condition; $H$$ui(x_i(t)) can be expressed as follows: (8) When the optimization problem is related to the rational analysis of users, the longer the evaluation time h(x_i(t)) is, the smaller \sigma(x_i(t)) is. Let H$$ur$($x_i$) denote $H$($x_i$($t$)) in this condition; $H$$ur(x_i) can be expressed as follows [29]: (9) can be expressed as follows [29]: Since fuzzy numbers are adopted to express an individual’s fitness, comparisons among individuals are difficult. The method proposed by Gong et al. [28] was adopted to compare individuals’ fuzzy fitness and identifysuperior individuals; this process includes the following three main steps: First, the method consists in choosingthe fuzzy level α, and obtains two α-cut sets of individuals’ fuzzy fitness values. Assume that there are two individuals x_i(t), x_j(t), and that their fuzzy fitness values are f(x_i(t)) and f(x_j(t)). The a - cut sets of f(x_i(t)) and f(x_j(t)) can be expressed as follows: (10) (11) Second, f_a(x_i) and f_a(x_j) are compared. It is obvious that the centers of different individuals in the same population are different in the AR-IGA. Namely, c(x_i(t)) ≠ c(x_j(t) . The method first considers the case that c(x_i(t)) < c(x_j(t). Let a_0 = maxf∈[f$$min$,$f$$max]\mu$$f$$a(x_i(t))∩f$$a$($x$j($t$))($f$).
I$fa$ > $a$0, as shown in Fig. 5, it is obvious that $f_a(x_j(t))$>$f_a(x_i(t))$, which means that the lower limit of $f_a(x_j(t))$ is larger than the upper limit of $f_a(x_i(t))$. Thus $x_j(t)$ dominates $x_i(t)$ with a probability of 1.
If $a$ ≤ $a_0$, as shown in Fig. 6, then $f_a(x_j(t))$$f_a(x_i(t)), which means that their fitness intervals are superposed. In the interval [f_a(x_i(t)),f_a(x_j(t))], x_j(t) dominates x_i(t) with a probability of 1, and the fitness of x_j(t) falls into this interval with a probability of \frac{f_a(x_j(t))-f_a(x_i(t))}{f_a(x_j(t))-f_a(x_j(t))}. In the interval [f_a(x_j(t)),f_a(x_i(t))],x_j(t) dominates x_i(t) with a probability of 1 - 0.5 \frac{f_a(x_i(t))-f_a(x_j(t))}{f_a(x_i(t))-f_a(x_i(t))} , and the fitness of x_j(t) falls into this interval with a probability of \frac{f_a(x_i(t))-f_a(x_j(t))}{f_a(x_j(t))-f_a(x_j(t))}. Therefore, x_j(t) dominates x_i(t) with a probability of (12) Fig. 5. Two individuals’ fitness in the condition that c(x_i(t)) < c(x_i(t)) and a > a_n [28]. Similarly. x_i(t) dominates x_j(t) with a probability of (13) In addition, it is obvious that p(x_j(t),x_i(t)) + p(x_i(t),x_j(t)) = 1. Fig. 6. Two individuals' fitness in the condition that c(x_1(t)) < c(x_i(t)) anc a ≤ a_n [28]. Finally, the method adopts tournament selection with size two. For two individuals x_i(t) and x_j(t) that are selected randomly, because p(x_j(t),x_i(t)) + p(x_i(t),x_j(t)) = 1, a roulette method of selection can be used to select the superior individual between them based on p(x_i(t),x_j(t)) and p(x_j(t),x_i(t)). In addition, as previously mentioned, in the initial stage of evolution, users’ cognition is relatively inexplicit. Thus, at this stage, a smaller 𝛼 should be set to ensure the diversity of the population. As evolution proceeds, users gradually become more familiar with their preferences, and the results of evaluation gradually become more accurate. At this stage, a larger 𝛼 should be set to accelerate the convergence of the algorithm. Therefore, 𝛼 can be expressed as follows: (14) where a$$min$ is set manually before using the algorithm.
To further illustrate the main idea of the AR-IGA, the pseudocode is provided as shown in Fig. 7.

Fig. 7. Pseudo-code of the AR-IGA.

Case Application

Currently, many young people are interested in beautiful personalized clothing. Their enthusiasm for sneakers in particularhas reached a very high level. Due to the complicated structures and colors of sneakers, their overall appearance is generally conceived by professional designers. For customers without any design training, however, it is difficult to participate in the process of designing sneakers. However, since design is closely related to customers’ preferences, it is vital to involve customers in the process. Hence, some companies have begun to provide online customization services, such as “Nike By You”, whose method of implementation is as follows: based on a specific sneaker, the system provides several material and color options for each part of the sneaker. Potential customers select and combine these options based on their preferences. However, the system has a negative impact on the overall style of the sneaker. In each operation, users pay more attention to one part of the sneaker than to the whole. It is difficult to predict the overall appearance of the sneaker after the combination of all parts. Users need to repeatedly try to change the combinations of the parts. Therefore, compared with the existing system, if a sneaker design system can adopt the IGA, it will deliver the following advantages: users can evaluate the overall sneaker design from beginning to end, which is similar to the process of selecting products in a mall, rather than focusing on the characteristics of each part; and more diverse schemes can be generated.

Individual Coding
The sneaker selected for evolutionary design is the Air Jordan 1. The Air Jordan 1 was released by Nike in 1985. Each update of the sneaker hasusually concerned the color of each part, while the shape has barely changed. The Air Jordan 1 is different from sneakers with a single color, and its colors are more diverse. Therefore, this paper selected the Air Jordan 1 for application of the sneakers’color design based on the AR-IGA.
Comprehensiveexamination of the color characteristics of the Air Jordan 1 shows the sole is mostly white, while the color of the body varies infive main areas, as shown in Fig. 8. The color of each area is coded as a binary string of 4 bits. The relationships between colors and codes are listed in Fig. 9. The genotype of an evolutionary individual is a binary string of 20 bits, as shown in Fig. 10, where the first 4 bits express the color of area A, the 5th to 8th bits express the color of area B, the 9th to 12th bits express the color of area C, the 13th to 16th bits express the color of area D, and the 17th to 20th bits express the color of area E. It is easy to determine the search space of the candidate solutions as 2^20=1,048,576.

Fig. 8. Areas of the sneaker.
Fig. 9. Relationship between colors and codes.
Fig. 10. Relationship between the genotype and phenotype of an individual.

Parameter Setting
To effectively compare the performance of the AR-IGA with that of the TIGA, the same evolutionary parameters are set in both algorithms. The population size N is set to 6. The minimum fitness $f$$min is 1, and the maximum fitness f$$max$ is 10. One-point crossover and one-point mutation mechanisms are adopted, and their probabilities $p_m$ are 0.6 and 0.01. Generally, the maximum number of generations should be less than 20. Thus, the maximum number of generations Twas set as 20. Based on the above conditions, $w$$max can be calculated as \frac{1}{2} × (f_max - f$$min$) × ($\frac{1}{N-1}$)3 = 0.228. To reasonably control the convergence rate of the population, we set the population convergence to be fastest when the number of generations is equal to half of $T$, namely, 10. At this time, $w(t)$ and $a(t)$ are maximized. Therefore, $w$$min is set so that \frac{1}{2}$$w$$max = 0.144, and a$$min$ is set to 0.5.

Convergence and Terminal Condition
In the related research, there are two explanations for the convergence of the IGA: on the whole, algorithm convergence refers to the finding of satisfactory individuals [9, 15],while from the perspective of the population, convergence refers to the moment when thenumber of individuals with similar phenotypes reaches the preset threshold in the population [28]. The above explanations are combined as follows: When users find satisfactory individuals or individuals with similar phenotypes who reach the threshold, the algorithm converges. The convergence speed of the algorithm is reflected by the number of generations.
The termination conditions of the algorithm are as follows: (1) If the algorithm cannot coverage after 20 generations, the system stops automatically; (2) in any one generation, if two-thirds of the phenotypes of all individuals are the same, the system stops automatically; (3) if users find a satisfactory individual, they can manually stop the evolution. Among them, the first condition is set in consideration of evaluation fatigue. Under this condition, the algorithm is regarded as not having reached the state of convergence, whereas the two remaining conditions are considered to have achieved convergence.

Evolutionary Interface
The human-computer interface in the AR-IGA comprises four parts, as shown in Fig. 11. The first part is the information related to the evolution, including the number of the current generation and the evaluation time. The second part is the settings of the genetic parameters, including the probabilities of crossover and mutation; these are equal to the number entered in the initial interface by default. The third part is the individuals’ phenotypes. When users want to select a given individual, they simply click on that individual. The fourth part is the components of the evaluating individuals, including the prompt message, OK button, and Return button.

Fig. 11. Interface of the AR-IGA.
The operation process of the AR-IGA is as follows: first, users observe the prompt information (Fig. 11). There are two kinds of prompt information: (1) the red sneaker and the words “Best One”, which mean that users need to select the best individual among the individuals presented, and(2) the blue sneaker and the words “Worst One,” which mean that users need to select the worst individual. Next, users combine their preferences to find the individual that matches the prompt information and click on this individual to select it. As shown in Fig. 12, the selected individual is moved to the location where the prompt information is placed. Then, users click the OK button to complete the individual’s evaluation. If they click on an individual by mistake, they can click the Back button. Then, the individual automatically returns to its original location, and the prompt information reappears. When an individual’s evaluation is completed, the fourth step moves right as a whole, and new prompt information is presented (the blue sneaker and the words “Worst One”), as shown in Fig. 13. Users then need to select the worst individual from the remaining individuals. The selection process continues until one individual remains in the population, as shown in Fig. 14. At this point, a Next button appears. When the selection of the last individual is complete, users can click the Next button to start the next generation.

Fig. 12. The operation of the AR-IGA (1).
Fig. 13. The operation of the AR-IGA (2).
Fig. 14. The operation of the AR-IGA (3).
Fig. 15. Interface of the TIGA.
The human-computer interface in the TIGA, as shown in Fig. 15, isbroadly similar to that in the AR-IGA. The interface in the TIGA includes three main parts: the first and second parts are the same as those in the AR-IGA, i.e., the evolution-related information and the genetic parameters, while the third part comprises the phenotypes and evaluations of individuals. Users drag the slider to evaluate an individual, with the slider value ranging from 1 to 10. The default value of the slider is 1. This means that if the users do not move the slider, the fitness of the individual above the slider is automatically assigned a value of 1. After all individuals have been evaluated, the users can click the Next button to start the next generation.

Analysisof Results

In previous related studies,the IGA evaluation criteria mainly include the number of evolution generations [42], the total evaluation time [4], the number of individuals evaluated [10], and the value of individual fitness [27]. In the AR-IGA, users only select individuals and do not assign fitness values. Thus, when evaluating the proposed method, it is difficult to evaluate the change in individual fitness. This study uses the number of generations, the mean number of individuals being evaluated, the total time taken to complete the evaluation process, and the average time taken toevaluate an individualin order tovalidate the performance of the AR-IGA. Among them, the number of generations, i.e., the number of iterations, is used to verify the convergence speed of the algorithm; the mean number of individuals evaluated and the total time are related to the user’s psychological load; the time taken to evaluate an individual is used to reflect the easiness of evaluation. Ten masters of industrial design were asked to carry out the process of designing the sneaker colors individually using the AR-IGA and TIGA. Each subject was asked to learn how to operate the system before conducting the formal experiment. In cases in which it was difficult to find relatively good individuals in the first generation, the subject could reinitialize the population. The number of generations, the mean number of individuals being evaluated, and the total time of the evaluation for each experiment are recorded and presentedin Figs. 16, 17, and 18, respectively. The average and standard deviation of the number of generations and the total time of evaluation are calculated and listed in Table 2.
Fig. 16 shows that each experiment was completed in fewer than 20 generations. This indicates that the two systems can facilitate the customization of sneaker color. Users can find a satisfactory sneaker design within the maximum number of generations. In most experiments, the number of generations of the AR-IGA is clearly less than that of the TIGA, except for subjects 2 and 8. Furthermore, as is shown in Table 2, the average number of generations of the AR-IGA is 2.1 less than that of the TIGA. These results indicate that the AR-IGA has an advantage in terms of accelerating the convergence of the algorithm. In addition, the standard deviation of the number of generations of the AR-IGA is also less than that of the TIGA, which means that the AR-IGA is more consistent in this regard than the TIGA.

Fig. 16. Number of generations in the AR-IGA compared to that in the TIGA.
Fig. 17. Mean number of individuals evaluated in the AR-IGA compared of that in the TIGA.
Fig. 18. Total time in the AR-IGA compared to that in the TIGA.

Table 2. Results of the number of generations and the evaluation time of the two algorithms
Number of generations Evaluation time (s)
Average SD Average SD
AR-IGA 8.4 1.7 138.9 31.6
TIGA 10.5 2.4 207.3 44.9
Fig. 17 shows a 15% decrease in the mean number of individuals being evaluated. This indicates that users can evaluate fewer individuals with the AR-IGA. Fig. 18 shows that the total time taken to evaluate the AR-IGA was lower than that of the TIGA in all experiments. It is obvious from Table 2 that the average evaluation time of the AR-IGA is 138.9 seconds, which is 68.4 seconds less than that of the TIGA (207.3 seconds), and the standard deviation of the evaluation time of the AR-IGA is less than that of the TIGA. This means that it takes the subjects less time to design a satisfactory sneaker by using the AR-IGA. These results verify that the proposed method is effective in alleviating the psychological load.
To further compare the performance of the two algorithms in simplifying the operation process, the average time for evaluating an individual is calculated and listed in Table 3. The average time taken to evaluate an individual with the AR-IGA was 0.9 seconds less than that taken with the TIGA, i.e.,there was a decrease of 22.5% in the average time taken to evaluate an individual.

Table 3. Average time taken to evaluate an individual by the two algorithms
 Mean number of individuals being evaluated Total time of evaluation (s) Average time taken to evaluate an individual (s) AR-IGA 44.4 138.9 3.1 TIGA 52.3 207.3 4
The results indicate that the AR-IGA has several advantages in that it simplifies the evaluation operation, mitigates the psychological load, and ensures the convergence of the algorithm. From the perspective of human-computer interaction, users only need to select and click in the AR-IGA, which is more natural and easier than moving the slider in the TIGA. From the perspective of user cognition, users only need to choose the best and worst individuals each time in the AR-IGA, without considering other individuals each time, and they do not need to quantify their preferences. In addition, in the TIGA, when users evaluate individuals with roughly similar phenotypes, they tend to assign the same scores to those individuals without making a careful distinction between them. In the AR-IGA, for individuals with roughly similar phenotypes, users need to think carefully. When combined with fuzzy fitness, the AR-IGA can more accurately reflect the user’s preferences for individuals. Correspondingly, in the AR-IGA, the convergence speed is faster, and the convergence direction is more closely matched with users’ preferences. Thus, the number of generations in the AR-IGA is less than that of the TIGA. In summary, the AR-IGA performs well.

Conclusion

This paper proposes an interactive genetic algorithm with an alternation ranking method. It describes three aspects of the proposed algorithm: the steps used in the alternation ranking evaluation, the calculation of individuals’ fuzzy fitness values, and the comparison between and selection of individuals. Based on the results of experiments with the customization of sneakers, this study demonstrates that the proposed method is advantageous and effective for both user evaluation and sneaker customization.
During the experiments, some subjects suggested that there were still some problems with the proposed algorithm. For example, as the algorithm converges, the number of similar individuals in the population increases, making it difficult for users to select a single best or worst individual. Therefore, future research will aim to dynamically set the number of individuals selected each time according to the convergence of the algorithm. In addition, it will be necessary to apply the proposed algorithm to a wider range of customization fields to test its performance.

Acknowledgements

Not applicable.

Author’s contributions

Conceptualization, DZ, MH. Investigation and methodology, DZ, MH. Writing of the original draft, DZ, MH. Writing of the review and editing, ZZ, CT.

Funding

This research was supported by the Fundamental Research Funds for the Central Universities (No. 2019XKQYMS46), and the Graduate Education and Reform Project of China University of Mining and Technology (No. 2019Y08).

Competing Interests

The authors declare that they have no competing interests.

Author Biography

Name : Dong Zeng
Affiliation : School of Architecture and Design, China University of Mining and Technology, Xuzhou, China;School of Information and Control Engineering, China University of Mining and Technology, Xuzhou, China
Biography : Dong Zeng received his B.S. degree inindustrial designfrom Central South University,Changsha, China, in 2002, and M.S. degree in artdesignfrom Hunan University, Changsha, China, in 2005.He is currently pursuing Ph.D. degree in control theory and control engineering from China University of Mining and Technology, Xuzhou, China. He is currently an Associate Professor with the China University of Mining and Technology.
He has over 30 publications. His current research interests include intelligent design, human-computer interaction, and user-centered design.

Name : Mao-en He
Affiliation : School of Architecture and Design, China University of Mining and Technology, Xuzhou, China
Biography : Mao-en He received hisB.S. degree in network engineering from China University of Mining and Technology, Xuzhou, China, in 2018. He is currently pursuing M.S. degree inindustrial design engineeringfrom China University of Mining and Technology, Xuzhou, China.
His current research interests include computer-aided design, human-computer interaction and user-centered design.

Name : Zhuan Zhou
Affiliation : Hexiangning College of Art and Design, Zhongkai University of Agriculture and Engineering, Guangzhou, China
Biography : Zhuan Zhou received hisM.S. degree in industrial design engineering from China University of Mining and Technology, Xuzhou, China, in 2019.
He is currently an assistant teacher with the Zhongkai University of Agriculture and Engineering. His current research interests include computer-aided design and design thinking.

Name : Chaogang Tang
Affiliation : School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, China
Biography : Chaogang Tang received his B.S. degree from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2007, and Ph.D. degree from the School of Information Science and Technology, University of Science and Technology of China, Hefei, China, and the Department of Computer Science, City University of Hong Kong, under a joint Ph.D. Program, in 2012.
He is currently an assistant professor with the China University of Mining and Technology. His research interests include mobile cloud computing, fog computing, Internet of Things, big data, and WSN.

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Dong Zeng1,2, Mao-en He1,*, Zhuan Zhou3, and Chaogang Tang4, An Interactive Genetic Algorithm with an Alternation Ranking Method and Its Application to Product Customization, Article number: 11:15 (2021) Cite this article 3 Accesses

• Recived5 September 2020
• Accepted22 February 2021
• Published31 March 2021

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