# Combining a Genetic Algorithm and a Fuzzy System to Optimize User Centricity in Autonomous Vehicle Concept Development

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Contextual Issue

#### 2.1. Conventional Vehicle Concept Development

#### 2.2. Mobility Solutions

#### 2.3. Development of Autonomous Vehicle Concepts

## 3. Methods

#### 3.1. Analysis of the Contextual Issue

- The number of required vehicle concepts for satisfying user needs must be minimized in order not to design a vehicle concept for every single need;
- The users’ mobility needs must be converted into vehicle properties in order to design vehicle concepts for heterogeneous user groups and their mobility needs instead of a customer-oriented persona.

#### 3.2. Method Selection

#### 3.2.1. Optimization

_{i}(x) <= 0 for i = 1, …, m and h

_{j}(x) = 0 for j = 1, …, p must be satisfied. The global optimum x

_{k}minimizes or maximizes the scalar f(x

_{k}), where x

_{k}is the n-dimensional decision vector of the solution space. The functions g

_{i}(x) and h

_{j}(x) represent constraints. The solution x

_{k}must satisfy these constraints. For example, the constraints can restrict the solution space and guarantee the physical feasibility of a solution. Coelle et al. [30] distinguish three solution strategies for global optimization problems. Enumerative methods are the simplest option. Within a defined search space, each possible solution to the problem is considered, and the best one is determined by comparison. However, these types of methods are unsuitable for large multidimensional search space [30]. Deterministic methods use problem-specific knowledge to control the search in the solution space.

#### 3.2.2. Genetic Algorithm

_{j}of the decision vector x. The optimization problem is defined by an objective function F(x) whose equivalent is the fitness function $\mathsf{\varphi}\left(\mathrm{a}\right)$ of genetic optimization. The fitness function measures how well an individual solves the optimization problem. The mapping function $\mathsf{\Gamma}$ connects the fitness function with the objective function.

_{i}. The second element evaluates these individuals based on the fitness value $\mathsf{\varphi}\left({\mathrm{a}}_{\mathrm{i}}\right)$. A selection of individuals for offspring using the fitness value represents the third element. From the population, $\mathsf{\mu}$ individuals are selected but with laying them back. The probability with which an individual is selected measures the selection probability ${\mathrm{p}}_{\mathrm{s}}\left({\mathrm{a}}_{\mathrm{i}}\right)$ as follows:

#### 3.2.3. Multicriteria Decision Methods

#### 3.2.4. Fuzzy Logic

_{s}).

## 4. Integration of User-Centered Mobility Needs in Autonomous Vehicle Concept Development

_{p}(p = 1, ..., 5) for user description. In the case of the first four secondary activities, we call them the key activities. Due to the possibility of ridesharing, the field of privacy and security needs comes to the fore. Therefore, in the user description, with how many users AMN

_{p}(p = 1, ..., 4), we include a secondary activity that may be performed during the ride. The index p relates to the secondary activities N

_{p}. For the fifth activity load, this consideration is not necessary.

_{1}, the willingness to invest C

_{2}, and the need for security and safety C

_{3}.

_{1}), rural (DP

_{2}), and highway (DP

_{3}) parts and the general daily demand (DP

_{4}) driving scenarios for this purpose.

_{p}activity is linked to a VT. We know which user chooses which VT (private, taxi, or shuttle) for a mobility need to perform the desired secondary activity N

_{p}.

#### 4.1. From User-Centered Mobility Needs to Vehicle-Bound Mobility Provision

_{p}and the number of people AMN

_{p}in this secondary activity. As described, the five secondary activities considered by us are driving, relaxing, working, sleeping, and load N

_{p}(p = 1, ..., 5), and the three additional personal characteristics are willingness to use MaaS C

_{1}, willingness to invest C

_{2}, and need for security C

_{3}. These three characteristics impact the choice of vehicle design and address the hurdles of sharing from the customer’s perspective. Moreover, regarding the customer-valued characteristics, the driving profile DP of a user is decisive.

_{k,j}and the global driving profile GD

_{p,j}of the users of this proposal, in addition to the characteristic of the vehicle interior D

_{p,j}and the number of passenger seats D

_{6,j}. We use the uniform scale from 0 to 10 for the characteristics, only limiting the number of passenger seats D

_{6,j}and the corresponding desire for passengers AMN

_{p,i}to nine people. In summary, the presented input and output variables subsequently result in the first step (Figure 6).

#### 4.1.1. Methodology

_{1}–N

_{4}with the expected vehicle type VT. As input parameters, this system uses the importance of the secondary activity N

_{p}, the number of passengers AMN

_{p}, the willingness to MaaS C

_{1}, the willingness to invest C

_{2}, and the need for safety C

_{3}. Qualitative rules are used to determine the choice of vehicle type. The fuzzy system uses 21 rules and represents a necessary preliminary work for genetic optimization. Therefore, we do not show this system in more detail.

_{p,i}of a user i should be satisfied with which vehicle type VT. Therefore, the genetic optimization runs separately for each vehicle expression VT. It is considered that a user uses a private AV and a taxi or shuttle for different trips.

_{x}= 8 m). Six of the eight variables are associated with the vehicle derivative and describe, on the one hand, the quality of the secondary activities D

_{p,j}and, on the other hand, the number of passenger seats D

_{6,j}of the proposal j = 1, ..., m. The remaining variables of the optimization represent the global investment willingness GC

_{2,j}and the global safety need GC

_{3,j}of the users of proposal j. The willingness to MaaS of a user is only used for the preliminary element of determining the vehicle type and is therefore not necessary in the optimization. The global driving profile GDP

_{j}of a proposal j based on the driving profiles DP of the users is not part of the optimization due to the strongly increasing dimensionality (+4) but is determined via minimum squared distances according to the users, which are assigned to the considered vehicle.

_{i}of each user i by the optimized vehicle-bound mobility provision with m vehicles, the number m is iteratively increased until the following condition is satisfied:

_{wish}. If this condition is not met, the number m is increased by one, and the optimization is restarted. We show the calculation of user fulfillment in detail below.

#### Calculation of the User Fulfillment

_{i}of a user by the vehicle-bound mobility provision is composed of three quantities (Figure 7). The fulfillment of the secondary activities N

_{p,i}by the quality of the secondary activities D

_{p,j}of the flock of derivatives m is measured by FF

_{i,N}. The match of the number of passenger seats D

_{6,j}with the desired number AMN

_{p,i}is denoted by FF

_{i,AMN}. In addition, user fulfillment includes the match of the global characteristics GC

_{2,j}and GC

_{3,j}with those of the associated users C

_{2,i}and C

_{3,i}. This match is denoted by FF

_{i,C2}and FF

_{i,C3}. In general, it is important to consider whether a derivative j satisfies user i in a secondary activity N

_{p,i}in the calculation. Therefore, an assignment of the users to the derivatives proposed by the optimization forms the basis.

_{i}of user i, we first show the computation of some auxiliary quantities in matrix notation. The quantity ff

_{i,jp}measures how well the wish of secondary activity N

_{p,i}of the user i is satisfied through the derivative j with the expression of the interior D

_{p,j}.

_{w}is a weighting function. The quantities ff

_{gc,jk}for k = 2,3 is required to calculate the proportions FF

_{i,Ck}from the character features. If derivative j best satisfies user i in one of the secondary activities N

_{p,i}among all m derivatives, the character features C

_{k,i}are compared with the global features GC

_{k,j}of the derivative.

_{i}of user i by the vehicle-bound mobility provision, consisting out of m derivatives, can be easily calculated.

_{i,N}from the secondary activities is calculated as the average over all of the five secondary activities p of the maximum values over the derivatives j since only one derivative has to fulfill the wish N

_{p,i}.

_{i,AMN}, first, the derivative j is determined that best satisfies user i in the secondary activity N

_{i,p}. Its characteristic D

_{6,jpmax}is used for the comparison. The fulfillment results as an average value over the four central secondary activities.

_{i,Ck}is calculated using the quantity ff

_{gc,jk}. Therefore, all derivatives j that have an entry in ff

_{gc,jk}greater than zero are used.

#### Calculation of the Fitness Function

_{ip}and ID

_{j,ip}contain the information which derivative j best satisfies the user i in the secondary activity N

_{p,i}.

_{ip,j}stores the wish for additional seat places AMN

_{p,i}of user i at the secondary activity N

_{p,i}if derivative j best supports secondary activity N

_{p,i}among all derivatives m.

_{k,ji}(k = 2,3), the expression of the character feature C

_{k,i}of user i is stored if derivative j best supports user i in one of the secondary activities N

_{p,i}.

_{N}(x) addresses the users’ wish for secondary activities and, correspondingly, the offer to exercise them in the derivatives. Therefore, we calculate the deviation devND

_{ip,j}between the wish and associated expression of the interior of the derivative. We weigh this by the user’s willingness to invest, giving more weight to users with a higher willingness to invest.

_{ip}over the derivatives j. If one derivative satisfies the user perfectly, this product disappears, and this part of the fitness function becomes minimal.

_{ip}are summed over all secondary activities p and users i.

_{6,j}of a derivative j based on the customer’s desired AMN

_{p,i}depending on the secondary activity. This is carried out by relying on the auxiliary variable AMN

_{ip,j}, which contains the desired number of passengers AMN

_{p,i}of user i if derivative j best supports secondary activity N

_{p,i}. The maximum number of desired passenger seats placed over all users of derivative j enters the fitness function.

_{k,i}and the global characteristics of the vehicle-bound mobility provision GC

_{k,j}.

_{ff}(x) is then calculated by summing over all users i.

_{ff}, the proportion that leads to a weighted equal fulfillment of the users can be weighted strongly. To ensure the feasibility of the vehicle concepts resulting from the vehicle-bound mobility provision, the solution space must be constrained. For this, we use several constraints.

#### Introduction of the Constraints

_{eq}(x) and unbalanced constraints C

_{ueq}(x). As a balanced constraint, we specify that human driving is not possible in an autonomous shuttle, which is assumed due to the expected low price and higher number of passenger seats.

_{5,j}of a derivative, we propose a distinction. If the derivative is primarily optimized for load (logistics), the characteristic is included in the calculation of the sum. If, however, load matters subordinately, the characteristic is excluded from the condition in order to be able to provide a specific amount of luggage space in each vehicle concept if the assigned users express this as a wish.

_{ueq,2}also concerns the feasibility of a solution. This constraint ensures that a maximum vehicle interior size R

_{max}(VT) is not exceeded due to an excessive number of passenger seats. The maximum available interior size depends on the vehicle type VT and is defined in the three spatial directions,

_{pp,j}via the characteristic D

_{p,j}and the global willingness to invest of the users GC

_{2,j}of the derivative j.

_{p,j}. The required space R

_{req,j}can be determined via the number of passenger seats and the seat topology. The second unbalanced constraint C

_{ueq,2}is then obtained by subtracting the maximum available vehicle interior space.

_{ueq,3}to reduce the search space and increase the convergence speed. The minimum values, excluding zero, of the vehicle-bound mobility provision are not to be less than the minimum values of the characteristic expressions of the user group. Similarly, the maximum values of the vehicle-bound mobility provision features are bounded by the maximum values of the user features.

_{p,j}, number of passenger seats D

_{6,j}, and global character features GC

_{k,j}), we describe a vehicle-bound mobility provision by the global driving profile. This is obtained as the minimum squared distance to all users assigned to the considered vehicle. We describe the driving profile by the city, rural, and highway fractions, and the level of overall mobility demand. This is also scaled up from 0 to 10.

#### 4.1.2. Vehicle-Bound Mobility Provision of the Use Case

#### 4.2. From Vehicle-Bound Mobility Provision to Customer-Relevant Properties

#### 4.2.1. Methodology

#### 4.2.2. Customer-Relevant Properties of the Use Case

## 5. Discussion

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Conventional vehicle concept development process, based on [24].

**Figure 3.**Development process of autonomous vehicle concepts, based on [17].

**Figure 4.**Analysis of the contextual issue, based on [17].

**Figure 5.**Operation of fuzzy systems according to Traeger [37].

**Figure 6.**First step “user needs to vehicle-bound mobility provision” and its input and output parameters.

**Figure 10.**Vehicle-bound mobility provision, with the point of view of the Derivative 3 on the left and the father on the right side.

**Figure 11.**The second step of “Vehicle-Bound Mobility Provision to Customer-Relevant Properties” and its input and output parameters.

Characteristics | Variable | Father | Mother | Son | Daughter |
---|---|---|---|---|---|

Importance of Self-Driving | N1 | 0 | 8 | 7 | 0 |

Importance of Relaxing | N2 | 6 | 5 | 4 | 7 |

Importance of Working | N3 | 7 | 0 | 0 | 0 |

Importance of Sleeping | N4 | 2 | 4 | 3 | 6 |

Importance of Load | N5 | 4 | 5 | 5 | 3 |

Preferred number of passengers while self-driving | AMN1 | 0 | 2 | 4 | 0 |

Preferred number of passengers while relaxing | AMN2 | 2 | 4 | 4 | 4 |

Preferred number of passengers while working | AMN3 | 4 | 0 | 0 | 0 |

Preferred number of passengers while sleeping | AMN4 | 2 | 2 | 2 | 4 |

Willingness for MaaS | C1 | 7 | 5 | 6 | 8 |

Willingness to Invest | C2 | 8 | 7 | 6 | 3 |

Need of Security and Safety | C3 | 4 | 6 | 3 | 7 |

DP Urban Proportion | DP1 | 6 | 5 | 3 | 5 |

DP Rural Proportion | DP2 | 2 | 3 | 7 | 3 |

DP Highway Proportion | DP3 | 5 | 3 | 3 | 0 |

DP General Need | DP4 | 7 | 5 | 6 | 4 |

Input Parameter | Numerous Range | Linguistic Range |
---|---|---|

expression of driving | [0, 10] | [no expression, high expression] |

expression of relaxing | [0, 10] | [no expression, high expression] |

expression of working | [0, 10] | [no expression, high expression] |

expression of sleeping | [0, 10] | [no expression, high expression] |

load capacity | [0, 10] | [very low, high] |

number of passengers | [2, 9] | [low, high] |

axial space requirement | [0, 10] | [low, high] |

lateral space requirement | [0, 10] | [low, high] |

vehicle type | [1, 2, 3] | [Private, Taxi, Shuttle] |

global invest readiness | [0, 10] | [low, high] |

global safety readiness | [0, 10] | [low, high] |

DP city share | [0, 10] | [low, high] |

DP rural share | [0, 10] | [low, high] |

DP highway share | [0, 10] | [low, high] |

DP daily need | [0, 10] | [low, high] |

Output Parameter | Numerous Range | Linguistic Range |
---|---|---|

Quality of Axial Dynamics | [0, 10] | [low, high] |

Quality of Lateral Dynamics | [0, 10] | [low, high] |

Quality of Vertical Dynamics | [0, 10] | [low, high] |

Maneuverability | [0, 10] | [low, high] |

Bad Road Capability | [0, 10] | [low, high] |

Passive Safety | [0, 10] | [low, high] |

Luggage Space | [0, 10] | [low, high] |

Boarding Comfort | [0, 10] | [low, high] |

Boarding Time | [0, 10] | [low, high] |

Leg Room | [0, 10] | [low, high] |

Shoulder Room | [0, 10] | [low, high] |

Head Room | [0, 10] | [low, high] |

External Communication | [0, 10] | [standardized, high] |

Built-in Infotainment | [0, 10] | [purposeful, user individual] |

Infotainment Individualization | [0, 10] | [low, high] |

Interior Recognition | [0, 10] | [conforming to approval, high expression] |

Driving Style: Comfort | [0, 10] | [low, high] |

Driving Style: Safety | [0, 10] | [low, high] |

Driving Style: Time Potential | [0, 10] | [low, high] |

Driving Style: Consumption | [0, 10] | [low, high] |

Driving Style: Degree of Freedom | [0, 10] | [low, high] |

Quality Exterior Design | [0, 10] | [low, high] |

Range | [0, 10] | [low, high] |

Acoustic Interior | [0, 10] | [tolerable, very silent] |

Environmental Monitoring | [0, 10] | [drivable, high] |

Active Safety | [0, 10] | [drivable, high] |

Costs | [0, 10] | [low, high] |

Ecology | [0, 10] | [low, high] |

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**MDPI and ACS Style**

Schockenhoff, F.; Zähringer, M.; Brönner, M.; Lienkamp, M.
Combining a Genetic Algorithm and a Fuzzy System to Optimize User Centricity in Autonomous Vehicle Concept Development. *Systems* **2021**, *9*, 25.
https://doi.org/10.3390/systems9020025

**AMA Style**

Schockenhoff F, Zähringer M, Brönner M, Lienkamp M.
Combining a Genetic Algorithm and a Fuzzy System to Optimize User Centricity in Autonomous Vehicle Concept Development. *Systems*. 2021; 9(2):25.
https://doi.org/10.3390/systems9020025

**Chicago/Turabian Style**

Schockenhoff, Ferdinand, Maximilian Zähringer, Matthias Brönner, and Markus Lienkamp.
2021. "Combining a Genetic Algorithm and a Fuzzy System to Optimize User Centricity in Autonomous Vehicle Concept Development" *Systems* 9, no. 2: 25.
https://doi.org/10.3390/systems9020025