Study of the convergence of Interactive Genetic Algorithm in iterative user s tests: application to car dashboard design

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1 Original Article Proceedings of IDMME - Virtual Concept 2010 Bordeaux, France, October 20 22, 2010 HOME Study of the convergence of Interactive Genetic Algorithm in iterative user s tests: application to car dashboard design Emilie Poirson 1, Jean-François Petiot 1, Emmanuel Aliouat 2, Ludivine Boivin 2 and David Blumenthal 2 (1) : IRCCyN (UMR CNRS 6597) Ecole Centrale de Nantes {emilie.poirson, jeanfrancois.petiot}@irccyn.ec-nantes.fr (2) : Renault, Direction de la Recherche, Groupe Perception et Analyse sensorielle DREAM/DTAA, Technocentre Renault, France Abstract: The development of new products that satisfy consumers needs and preferences is a very important issue. In particular, the shape of a product is an important factor in the success or the failure of a product. Since several years, in various research fields, many works are dedicated to the design of shapes by the analysis of user s perception. The work proposed in this paper is based on the use of interactive users assessment tests to enhance creativity, by the way of interactive genetic algorithms (IGA) for capturing users responses. This paper presents a study of the convergence of the IGAs, where the fitness function of a classical GA is replaced by a selection by the userof the well suited products. The paper presents the methodology used to tune the input parameters of the IGAs for a convergence of the results. The proposed application concerns the design of innovative car dashboards and is briefly described. Key words: IGA (Interactive Genetic Algorithm), convergence, shape design, car dashboard 1- Introduction In automotive design, fitting with the expectations of the users is a crucial issue. These expectations can be functional or can concern subjective aspects (sensory or semantics). In particular, the external form of a product is an important factor in the success or the failure [B1], as it conditions the ergonomics, the aesthetics but also the product semantics [KB1]. When industrials address a new specific semantic dimension, such as a need of "innovative dashboard", the challenge for the company is to clearly understand what does the verbatim "innovative" mean for the users, and to translate it in design attributes. On the one hand, consumers know what they want (and what they don t) but they generally are not able to formulate precisely their need in technical terms or to justify their choices according to design attributes [HC1]. On the other hand, companies develop competences in product design but they encounter difficulties to anticipate precisely the consumer's acceptance. Therefore, a key challenge in product design is to analyze consumer's evaluation to extract useful information for product innovation [H1]. Many research works in form design are dedicated to the integration of users response in the design process. In Japan, Kansei engineering is a powerful approach to product design involving user s perceptions [N1] [YA1]. In engineering, the multiattribute utility theory (MAUT) has become the basic theory to express an objective function including consumers perceptions and preferences [LC1]. For example, Interactive genetic algorithms (IGA) are proposed for capturing aesthetics intention of users [GT1]. IGAs are based upon the idea of involving a human as an evaluator in an evolutionary process. The concept is that human interaction with potential designs can be useful when the traditional fitness evaluation used in normal Genetic Algorithms is difficult or impossible to describe with an explicit expression.. Our work is in this context. We propose to use Interactive user assessments in order to extract design attributes corresponding to a specific semantic dimension of a particular product, an innovative car dashboard. The method is based on an iterative selection process by the user of representative models of the dashboard, defined by their CAD model. The choices of the user are interpreted by an Interactive Genetic Algorithm (IGA), and constitute a dynamic way to explore the design space, and possibly converge toward particular products (the product space changes iteratively in regard to the responses of the consumer). In previous papers [PP1, PP2], we presented the general methodology for the study of innovative dashboard by IGA, and the definition of the CAD models. In this paper, we particularly focus on the tuning of the input parameters of the IGA and on the study of the convergence ability of the IGA, according to the size of the design space. This paper is structured as follows: Section 2 gives backgrounds on Interactive Genetic Algorithm and describes its position in the complete study of the car dashboard [PP1] [PP2]. Section 3 presents the methodology used to prove the convergence of the algorithm and to tune the different input parameters. The results are presented in this Section 3, before giving some concluding remarks in section 4. Paper Number -1- Copyright of IDMME - Virtual Concept

2 2- Backgrounds on IGAs 2.1 Interactive Genetic Algorithm Genetic algorithms (GA) are evolutionary optimization methods [G1]. The principle of GA is based on iterative generations of populations of individuals, converging step by step toward solutions which are adapted to the problem. Individuals are described by a set of factors which are coded (their genes). Based on the principle of Darwin s natural evolution theory, the algorithm proceeds to a selection of parents, which will spread in the next generation their genetic dominant heritage, suitable for a desired objective. Classically, the fitness evaluation of the individuals is numerically calculated, ignoring the user. A particular category of GA, called Interactive Genetic Algorithms (IGA) introduces the user in the optimization loop to assess the fitness. At each iteration, the user selects individuals (products) that he/she considers as the most interesting for the desired objective. After a number of iterations (convergence loop), the method may converge toward solutions that satisfy the objective desired by the user. These algorithms are used for example to explore design spaces and to encourage creativity [KP1] [KC1] [YD1] [KP2]. They have the advantage to not require an explicit formulation of the fitness function, given that the user plays this role. For some applications, this advantage is crucial [T1]. 2.2 IGAs in context The key point of the methodology is that the user s assessments are iterative (the user navigate in the design space) and that the IGA may lead to the convergence of the navigation toward representative designs. A computational framework is proposed for the capture of the user s response to a set of virtual designs (Figure 1). It is based on the following stages: 1. Definition of the design factors: design attributes of the dashboard (for example the type of vents) 2. Definition of the design variables: entities that drive the CAD model (for example the depth of the control panel) 3. CAD modelling. Each dashboard is contextualized in the interior of a car. 4. Interactive user s tests. An interactive and iterative assessment test is proposed to a set of users. From a population of dashboards, the user has to select the ones which are the most representative of the considered semantic dimension. The IGA generates new population of dashboards which are iteratively proposed to the user for evaluation. 5. Analysis of the results. The final choices of each user are analyzed in order to uncover common properties and representative attributes. This paper will not describe all the stages of the methodology (made in previous papers [PP1, PP2]). The aim of the paper is to focus on the IGA stage and to describe it in detail. Figure 1: Synoptic of the methodology and definition of the different stages. 2.3 Specification of our IGAs This subsection presents the mechanism of the IGAs used and describes the input parameters of the IGA Encoding of the designs factors Each design factor of the dashboard can take different values defined in advance (called levels ). A particular design is represented by a chromosome containing one level for each factor. The interactive user test is in fact an optimization problem represented by: - variables: the design factors - an objective function: the distance between what a user has in mind as innovative and the representation that are showed. This function has to be minimized. A design is a chromosome of x variables, each variable having a particular number of levels. A variable is represented by a binary string where the length of the string depends on the number of allowed values for the variables IGA process Figure 2 presents the mechanism of the IGAs used. The IGA creates an initial population of designs (by their chromosomes) and presents them to a user, who then selects a subset of these individuals based on preference. Thanks to a roulette method, the selected individuals are favoured to be parents of the following population. A new population is thus created and the hand is given to the user to select again their favourite. This cyclic method runs till the maximum of generation is reached. As in the MOGA-II algorithm (see [PR1]), each chromosome of the population is a parent of the following Paper Number -2- Copyright IDMME - Virtual Concept

3 generation, that gives robustness to the algorithm. Furthermore, the use of directional crossover helps the fastness of the convergence. Chromosome Factor 1 Factor n Final user selection Carlo process, several runs of the tests will be computed so as to study the probability of convergence of the IGA and to propose optimal values for the input parameters of the IGA. Population User Selection Parent 1 Roulette wheel Selection of parent 2 Parent 2 Child Mutation Selection Crossover Figure 2: IGA process to acquire user perception At each iteration, the user selection will be done thanks to a Matlab Interface, as illustrated in figure 3. Figure 4: Example of interface for user selection, applied to 2D geometrical forms. The user has to select maximum 2 individuals, considered as the nearest to the target The efficiency of the IGA is ruled by its operators and by the values of input parameters: - crossover and crossover rate Rc - mutation and mutation rate Rm - selection and selection rate Rc - Roulette wheel rate Rw Let s focus on the reproduction strategy, in the grey square in dotted line on Figure 2. Each parent of the population is chosen one after one. An indicator (i) is randomly chosen between 0 and 1. The crossover rate (Rc), mutation (Rm) or selection (Rs) are real values chosen between 0 and 1 as following: Rc + Rm + Rs = 1 Figure 3: Interface for user selection of innovative dashboard The task of the user is to select 0, 1 or 2 dashboards which are representative (according to his/her point of view) of the semantic term innovative. Several choices are asked to the user, and this process may converge toward particular design attributes of the dashboard. In this paper, in order to study the convergence of the IGA, we used a simpler design problem, defined by 2D symmetrical geometrical forms defined by control points (polylines). The number of points and their coordinates, which constitute the levels, can be variable. Figure 4 presents the case of a form defined by 3 control points (y = 0, y = 1, y = 2) and represents a population of 8 individuals of the design space. In order to study the convergence of the IGA, we also defined explicitly a target in the design space, i.e. a form which is the objective to reach (form in red in figure 4). So, it will be possible to study the ability of the IGA to converge towards predefined forms, and more interesting, to simulate the choices of a user by computing a fitting distance. In this way, like in a Monte The random indicator (rand (i)) is thus compared to Rc, Rm and Rs (Figure 5) and the result gives the operation to make. rand (i) Crossover Mut Selection 0 Rc Rc+Rm 1 Figure 5: Choice of the operation of reproduction. In this case, the chosen operation is crossover. If (rand (i)) < Rc, the operation is a crossover. If Rc<(rand (i)) < Rc+Rm, the operation is a mutation. If (rand (i))> Rc+Rm, the operation is a simple selection. Crossover The crossover is a classical operator of reproduction. It is a one point crossover. This operation needs a second parent, selected randomly in the other individuals. The point of crossing is also randomly chosen between the variables and the binary strings are cut at that point. The two head pieces are swapped that allows the creation of two new Paper Number -3- Copyright IDMME - Virtual Concept

4 individuals (figure 6). Crossover - n strings of x variables are randomly generated, each coded on y bits, n being the number of individuals in the population. Var.n-1 Figure 6: Representation of the crossover Mutation The mutation is an operator that ensures diversity from one generation to the next, which means robustness of the algorithm because the mutation is a tool to explore a bigger part of the design space. Selection The parent selected is directly introduced in the new population, without change. The reproduction is done till reaching the maximum number of generations The input parameters of the IGA The set of input parameters is composed of: - Number of variables : in our case, the variables are the control points of the geometrical form (or the design factors of the dashboard) - Interval in which the variables can take their values - Number of levels of each variables (how many values can take each variable) - Number of individuals in a population - Maximum number of possible selections by the user - Maximum number of generation - Wheel rate : weight given to a selected individual - Crossrate (0<Rc<1) - Mutrate (0<Rm<1-Rc) A given problem is defined by a number of variables, their corresponding levels, a number of individuals and a max. number of generations, and how many selection the user can make. The wheelrate, crossrate and mutrate are difficult to define, they are often defined empirically. This study aims to prove that there are some ideal values of these parameters, depending on the number of variables. The next section presents the protocol used to test the ideal values of these parameters. 3- Study of the convergence of the IGA In order to do study the convergence of the IGA and the tuning process of the Wheelrate, Rc, Rm and Rs, we simulated the selection process by computing a distance between each individual and a given target Var. The first step is to verify that the IGA converges in an acceptable number of generations for a perceptive test: - a target on x variables is defined The evaluation of the fitness is made by the Euclidian distance between each individual and the target. The simulated selected individuals are the 2 closest to the target. Each simulation, with a given combination of input variables is performed 1000 times and the mean is presented (Figure 7). 3 targets, representing problems of different size, have been considered: - a diamond shape: 3 variables on 25 levels - a square : 4 variables on 11 levels - a circle : 21 variables on 10 levels Figure 7 shows the evolution of the distance to the target according to the number of generations considered, for the 3 different cases. The first results is that bigger the problem, slower the convergence. Figure 7: Mean distance (left) and minimum distance (right) between the population and the target (diamond in blue, square in red and circle in green) with Rc = 0.5, Rm = 0.1, Wheelrate = 6. In the application on the dashboard, we envisage to consider 15 variables (factors) with 3 or 4 levels each. So, we can expect a faster convergence than the circle case (green line). 3.1 Roulette-Wheel strategy The interactive genetic algorithm is based on a roulette wheel selection: Higher the wheelrate coefficient, more important the chance to be chosen as a parent for the selected individuals. To determine the best value to attribute to wheelrate, a simulated test was carried out. Most common values were taken for Rm and Rc (respectively 0.1 and 0.5). The wheelrate varied from 1 to 10 (a selected individual can have 1 to 10 times more chance to be parents 2 in the crossover). Each evaluation was done 100 times and averaged.. Paper Number -4- Copyright IDMME - Virtual Concept

5 Figure 8: Simulation results of the mean and the mini Euclidean distance to target for varying wheelrate values Figure 8 shows the influence of wheelrate value on the convergence of the algorithm. With wheelrate (Rw) equal to 1, all the individuals have the same chance to be parent 2. If Rw = 10, the selected individual have 10 times more chance to be the parent 2 of a crossover, that implies a faster convergence: More important the roulette-wheel, faster the convergence. But the Rw has a so big influence that to converge so fast, the exploration of the design space is more local. In order not to be trapped in a local minimum which is not the global minimum, the exploration of the design space must be complete. A compromise must be found between fastness of convergence and exploration of the design space. In our algorithm, every individual is selected as parent 1 and in the case of crossover, a parent 2 is chosen. The influence of Rw is not of the primary (choice of parent 1) but secondary level (case of the crossover). As every individual is parent, the exploration of design space is conserved. The Rw is thus chosen between 5 and 7: it allows a fast convergence without a too reduced exploration of the design space. 3.2 Mutation strategy In our case, the mutation is a modification of one factor in the design space. The value of one factor chosen randomly is also chosen randomly among the other levels. More important the mutation rate, more mutation will occur. The default of the mutation is that, in too large proportions, it can slow down the convergence of the algorithm, jumping at another area of the design space. A compromise must be found on the mutation rate Rm to keep a good convergence when exploring a large design space. Our test was carried out with the value found previously for the roulette-wheel (7) and Crossover was 0.5. Rm evolves from 0 to 0.5 (1 Rc), by step of Figure 9 presents the results. Figure 9: Simulation results of the mean and the mini Euclidean distance to target for varying mutation rate On figure 9, the yellow line is the convergence of the IGA without mutation (Rm = 0). We are looking to values of Rm which improve the convergence of IGA. The four values found are 0.05, 0.1, 0.15, 0.2. A second test, with a Rc of 0.6 confirms these results. For the following of the study, we will thus keep the value of 0.1 or 0.2 for Mutation Rate (Rm). 3.3 Crossover strategy As explained in a previous section, the population is subjected to a mutation, or a selection or a crossover (requiring a second individual as parent). The rate of crossover is between 0 and 1 - (Rm + Rs). The compromise to find is between a large exploration of the design space and the fact to keep selection in the IGA. In the case of finding the ideal model in the first population, if the Rc is very high, the user won t have any luck to find his ideal back in the next populations. We have tested, with Rw= 7 and Rm = 0.1 the evolution of the convergence for variables values of Rc (step of 0.1). Figure 10 presents the results. Figure 10: Simulation results of the mean and the mini Euclidean distance to target for varying crossover rate Paper Number -5- Copyright IDMME - Virtual Concept

6 Figure 10 shows that Crossover is a fundamental operation in IGA (there is no convergence with Rc = 0). Then, there is a sort of threshold around 0.4: from 0.1 to 0.4, evolution is clearly visible for the mean or the mini. From 0.5 to 0.9, the differences are less important and, what s more, the order is different between the mean (entire population) and the mini (one element of the population). The best values seem here to be 0.5, 0.6 or 0.7. It depends also on the type of problem. 4- Conclusion In this paper, we studied the convergence of IGAs, integrated in iterative user s tests. These tests are used to enhance innovation and to understand a given semantic dimension. It will be applied to the particular case of a car dashboard and its innovative character. We described first the mechanism of the IGA implemented. Second, to study the convergence of IGA, we defined problems of different size, according to the number of design factors and their corresponding levels. A simple representation of the product using 2D geometrical shapes, defined by polylines, has been proposed to study the convergence of IGA. Furthermore, in order to obtain robust results according to the convergence, the fitness evaluation of the IGA has been simulated using computed distances to a given predefined target. We showed that for a fairly large number of factors, and for a large number of levels, the IGA converge in a relatively low number of generations. Given that the IGAs must be used in a perceptual test, a relatively small number of generations (<20) must be proposed, so as to not fatigue the user. A compromise must be found between a fast convergence and a large exploration of the design space. To determine the best compromise, this paper showed the process of simulated evaluation and the results of the most suitable values of the input parameters of the IGAs for a simple model (3 variables of 11 levels). The perspectives of this work are to test different settings of the algorithm. For example, the way to select the parents is typical from MOGA. The NSGA (Nondominated Sorting Genetic Algorithm), which do not require each individual to be parent, could be tested. Is the same way, different changes in the definition of mutation could be tested (restrict the mutation to the neighbouring elements). Finally, we will implement our framework to tackle a real design problem, i.e. a problem with 15 variables of 3 or 4 levels (like our real example) and make a link toa CAD model of the dashboard. These perceptual test will be usefull to define the attributes making an "innovative" dashboard for a set of users. 5- Acknowledgments Acknowledgments to Julien Benabes for his substantive hand in programming interface with Matlab. 6- References [B1] Bloch P. Seeking the ideal form: Product Design and Consumer Response. 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