1 Current State of Mobility Society

Due to the rapid information processing by computers and the evolution of communication equipment, we have become a society in which a large amount of information is constantly generated, stored, and transmitted. Information is becoming more and more important, and society has come to rely heavily on it in our daily lives. The 5th Science and Technology Basic Plan in Japan, which has been implemented since 2016, aims to realize a future society so-called a super smart society (Society 5.0) [1] that creates social prosperity through the evolution of Information and Communication Technology (ICT) and the creation of new values and services. In 2018, the Ministry of Economy, Trade and Industry in Japan compiled the Guidelines for Promoting Digital Transformation (DX) [2]. In this guideline, DX means that companies (1) respond to drastic changes in the business environment, utilize data and digital technology, and create new products, services, and business models based on the needs of customers and society, and (2) establish competitive advantages by transforming not only their business processes but also their organizations and corporate cultures.

On the other hand, in the automotive industry, the concept of the car itself is about to change due to technological innovations called CASE and MaaS. CASE is a coined word that takes the initials of Connected, Autonomous/Automated, Shared, and Electric, and represents the axis of future new vehicle development, while MaaS stands for Mobility as a Service, and indicates the future that transportation including cars, trains, and airplanes aims for. Automobiles that automatically run on electric power while exchanging large amounts of data over the Internet are nothing more than information terminals, and automobiles that are not owned but shared are already part of the social infrastructure.

In CASE, “Connected” means connection with the internet, and by connecting the car to the network in real time, it is possible to send and receive all kinds of data obtained while driving, such as map, accident, and weather information. “Autonomous/Automated” means self-driving without human intervention, and “Shared” means sharing the cars. It was common to purchase and use a car individually. Currently, it is popular to share a car so that it can be used whenever you want. Finally, “Electric” means environmentally friendly electric vehicles.

MaaS makes cloud-based and seamless transportation even if it consists of multiple operating units such as bus, train, and airplane. Even now, when traveling using multiple modes of transportation, you can use the route search to find out how to get to your destination and how long it will take, without having to follow the timetables one by one to derive the itinerary. Even so, it is still inefficient, since reserving and purchasing tickets must be made by each operator. In the world of MaaS, it is possible to search for the most suitable means of transportation, make reservations, and make payments all at once using smartphone apps.

By accelerating these technological innovations related to mobility, it is expected that significant contribution will be made to environmental issues that have become a challenge in recent years, particularly in reducing carbon emissions.

2 Project Titled Advanced Mathematical Science for Mobility Society

While the automotive industry has made steady progress in technological innovations under the names of CASE and MaaS, Toyota Frontier Research Center, one of Toyota Motor Corporation’s research bases, considers that mathematical science is the most important tool for conceiving future mobility services, in light of Toyota’s vision of turning mobility into social potential.

Mathematical technologies are, of course, adopted in many situations throughout the automotive industry. For example, mathematical optimization technique is widely used and contributes in some way, from design, manufacturing, to service design. In the future mobility society, however, it is not always possible to satisfy all requirements with today’s mathematical technologies. For example, design space for the mobility service will become complex and large scale. Therefore, further progress will be required in optimization technology to find the optimal conditions in such complex spaces. It is also necessary to search for better solution and control the systems while responding to changing environments every moment, dynamically. Furthermore, as individual values diversify in the future, we believe that it is necessary to design a mechanism that is fair to match each individual’s value, not just the overall optimum, in order to provide a service in close contact with each customer.

Based on the above motivation, we started the joint project of Kyoto University and Toyota Motor Corporation, titled “Advanced Mathematical Science for Mobility Society” in 2020. The project is a collaboration between Toyota Frontier Research Center, Toyota Motor Corporation and Graduate School of Informatics and Research Institute for Mathematical Sciences (RIMS), Kyoto University. However, it involves not only researchers at Kyoto University and Toyota Motor Corporation, but also prominent domestic researchers in the fields of mathematical science and informatics. The project takes a broader view of the concepts of mobility and movement which includes the flow of people through public transportation, the distribution of information, and the energy flow to capture the essence of the future mobility society, and deals with the following three topics

  1. 1.

    Mathematical models of flow,

  2. 2.

    Mathematical methods for huge data and network analysis, and

  3. 3.

    Algorithms for mobility society.

The first topic is a mathematical model on flow. Here, we consider to handle the flow of objects (e.g., goods), people, and information. As for flow of objects and people, traffic flow is typical, but it also includes delivery of parts and products in the manufacturing process. The flow of “information” is also important for mobility society. For example, Toyota Motor Corporation uses a well-known “Toyota Production System” [3] technique for the production processes. Here, a flow diagram of objects and information, called “Value Stream Map”, is created and the flow of information is visualized. This is because the stagnation of the information flow affects the stagnation of the production process. Thus, we have studied mathematical techniques to model the flow and to construct a smooth mobility society without stagnation.

The second topic then describes mathematical techniques dealing with enormous data on mobility from the viewpoints of machine learning, numerical analysis, statistical physics, etc. Needless to say, handling of big data is an important issue in the future. Especially with the progress of the connected technology, the type and size of the data to be handled become enormous. Even if the computational power advances, it will be difficult to effectively handle these enormous data without ingenuity. In order to compress necessary information effectively, or to extract useful information, the progress of basic mathematical technology is necessary. We will also consider techniques for handling sensitive data, such as personal privacy and company secret information, as well as mathematical techniques for secure distributed systems such as block-chains.

The last topic discusses algorithmic problems on mobile society. An example of a mobility system is a car-sharing service. Such a service requires, for example, both convenience for individuals and robustness and efficiency as a system. Mechanisms that are always optimal in response to changing situations every moment and the needs of people are also required. Furthermore, in the future society where the sense of value is diversifying, a mechanism that is fair to all customers will also be important. From these viewpoints, this topic examines a method for constructing and analyzing algorithms for controlling and optimizing systems and services.

In this monograph, we discuss some of the results obtained by nine groups of the project on the three research topics above, as well as the related research areas.

The rest of the monograph is organized as follows. Part 2 discusses mathematical models of flow, which consists of two chapters.  

Chapter 2::

Analysis of Autonomous Many-Body Particle Models from Geometric Perspective and its Applications

Chapter 3::

Integrable Systems Related to Matrix LR Transformations

  and Part 3 discusses mathematical methods for huge data and network analysis:

 

Chapter 4::

Numerical Analysis for Data Relationship

Chapter 5::

Application of Tensor Network Formalism for Processing Tensor Data

Chapter 6::

Machine Learning Approach to Mobility Analyses

Chapter 7::

Graph Optimization Problems and Algorithms for DAG-type Blockchains

 

Finally, Part 4 treats algorithm issues for mobility society, consisting of the following three chapters.

 

Chapter 8: :

System-Control-Based Approach to Car-Sharing Systems

Chapter 9: :

Algorithms for Future Mobility Society

Chapter 10::

Mechanism Design for Mobility.