研究最前線 No.69

寺本 央 准教授


Formulation of Social Problems in terms of Multi-objective Optimization



Elucidation of Structures of Pareto Set in terms of Singularity Theory

Development of Optimization Algorithm by Holding Programing Contests in Collaboration with Hitachi Ltd. and Hokkaido University


寺本 央 准教授

Faculty of Engineering Science

Associate Professor Hiroshi Teramoto


Hiroshi Teramoto, an associate professor in the Faculty of Engineering Science, has been working on the development of theoretical frameworks and algorithms through a mathematical approach and applying them to various scientific fields.








Dynamical system theory and singularity, which have many applications to various scientific fields

What is your area of expertise?

The area I study is dynamical systems theory and applied singularity theory. Dynamical systems theory is to elucidate dynamics of various things ranging from small molecules to celestial bodies through a mathematical approach using differential equations. Applied singularity theory aims to apply singularity theory to various scientific fields. Singularity can mean different things to different fields of science. In the current context, the simplest example of singularity is a stationary point of a function, which can be generalized to that of a mapping. Recently, I have been working on mathematical structures of Pareto sets and fronts in multi-objective optimization problems by using singularity theory.
 Multi-objective optimization is a field that attempts to optimize multiple objective functions simultaneously under certain constraints. However, in general, trying to optimize the value of one objective function results in a deterioration of the values of the other objective functions, and it is impossible to literally optimize multiple objective functions simultaneously. In multi-objective optimization, we therefore consider what is called the Pareto solution, which is the solution where the value of at least one other objective function must deteriorate in order to improve the value of a certain objective function. In general, there can be several Pareto solutions, and we need to select the appropriate solution from among the Pareto solutions depending on the situation. To do that appropriately, we need to know the overall structure of Pareto solutions. Our recent study elucidates the mathematical aspect of the overall structure of Pareto solutions for a certain class of multi-objective optimization problems.

What made you choose this field of research?

One of the usual practices in singularity theory is to reduce problems in geometry to those in algebra. I am interested in the fact that a problem on a seemingly elusive geometric object can be reduced to a solid algebraic problem by using singularity theory.
 Once a problem is reduced to an algebraic problem, it may be solved on a computer using methods such as computational algebra. I also find it fascinating to be able to use the power of computers to solve problems that could never be solved by human hands.
 The Pareto set in a multi-objective optimization problem is also a subset of the singularity set on the map defined by the objective function, and it is possible to investigate the properties of the Pareto set by examining the singularity set of the map. Another reason I have continued this research is that there are various applications. I am also conducting joint research with companies on this theme.

How has the research theme changed so far?

"Nature does not know the boundary of science." are the words of Professor Kenichi Fukui, who was the first Asian recipient of the Nobel Prize in Chemistry in 1981 and the founder of theoretical chemistry in Japan. This is one of my favorite words.
 Fields of specializations are boundaries created by people, We may miss big picture of natural or mathematical phenomena if we get caught in a specific field. For this reason, I have studied what I consider to be important from time to time, rather than focusing too much on a specific field.
 However, research themes also come in and out of fashion, and these changes are especially intense these days. I wish to seek something invariant because we are in an age of rapid change, and I have chosen research themes that do not follow trends and that can solidify the foundation.

  • システム理工学部  寺本 央 准教授
  • 特異点の定義とそのパレート集合との関係

    Definition of singularity and its relation to the Pareto Set





「Hitachi Hokudai Lab. & Hokkaido University Contest」は、日立製作所と北海道大学共催のプログラミングコンテストで、関西大学も問題作成等で協力しています。2020年度は国内外から1,700人の参加がありました。複雑化する社会課題解決に向けて、明確な評価基準とアルゴリズムの考案を目的としたコンテストで、これまで、アニーリングマシンの前処理技術に関する問題、買物支援サービスや地域エネルギーシステムの時空間最適化技術に関する問題等を出題しました。最適解を求めるアルゴリズムの問題ですが、その背景にあるのが、前述の多目的最適化です。

Application of the multi-objective optimization method to solve social problems

What exactly is the methodology called multi-objective optimization?

A multi-objective optimization problem is, for example, a problem to find the mode of transportation to get to a city as quickly and cheaply as possible. In general, there is a trade-off relationship between speed and cheapness, and it is common to find that we arrive faster by plane but more cheaply if we take the train. In this case, the two objective functions are time and cost. For example, besides going by train or plane it is possible to go by bicycle, but if you go by bicycle, it is more expensive than going by train if you include the accommodation fee, etc. along the way. It also takes more time than going by plane, so going by bicycle cannot be a Pareto solution. A Pareto solution is in a sense a trade-off, a curve that expresses gaining something and losing something.
 Although which mode of transportation should actually be used depends on the situation at the time, we need to know the overall structure of the Pareto solutions, which are a set of all possible choices, in order to select the appropriate solution for the situation.

What kind of joint research are you conducting with corporations?

"Hitachi Hokudai Lab. & Hokkaido University Contest" is a programming contest co-sponsored by Hitachi, Ltd. and Hokkaido University. Kansai University also cooperates in creating the problems. In FY 2020, there were 1,700 participants from Japan and overseas. It is a contest that aims to devise clear evaluation criteria and algorithms for solving social issues that are becoming increasingly more complex, and so far we have set questions concerning pre-processing technologies for annealing machines, shopping support services, and spatio-temporal optimization technologies for regional energy systems, etc. They are problems of algorithms to derive the optimal solution, and what lies in the background is the multi-objective optimization described previously.
 The algorithms developed through the contest are examined for practical application, and research results are presented at international conferences. In FY 2020, we published a paper "Multi-objective Spatio-temporal Optimization of Transportation and Power Management by Using Multiple Electric Vehicles in Nanogrid Networks," which summarized the top performers and the outcomes.









Topology optimization to construct the optimal structural design

What are your aspirations for the future?

I am currently engaged in joint research on topology optimization. Topology optimization is to optimize material distributions under certain constraints to maximize or minimize a certain objective function. For example, maximizing body stiffness of a car under a weight constraint is a typical problem in topology optimization. In the previous studies, manufacturability of optimum material distributions has not been taken into account and thus their application to the actual manufacture was limited. We proposed a method in topological optimization taking manufacturability of optimum material distributions into account in the paper "Topology optimization with geometrical feature constraints based on the partial differential equation system for geometrical features (Overhang constraints considering geometrical singularities in additive manufacturing)", which was awarded the Japan Society of Mechanical Engineers Medal for Outstanding Paper in April 2021. In the example of car design, by taking its manufacturability into account on top of body stiffness, its optimization problem becomes a multi-objective optimization problem.

It has been a year since you started working at Kansai University. Please tell us your impression of Kansai University.

The university is unique and different from others in that the Department of Mathematics is independent under the Faculty of Science and Engineering, and that specialized education is being developed. I think this is one of the characteristics of the university. Also, the professors at the mathematics department are wonderful, and I am hoping to do joint research with many of them.

Finally, can you give a message to the students?

In recent years, research fields come in and out of fashion rapidly. For example, technologies such as deep learning, which were unheard of a few decades ago, have suddenly gained attention as the performance of computers and other devices has improved, and new technology such as quantum computers is expected to emerge in the future. However, the foundation of mathematics underlying these technologies has not changed significantly even in this time of rapid changes. I hope you will not only acquire skills that are immediately useful, but also the knowledge to survive through this time of rapid changes at the university.

システム理工学部  寺本 央 准教授