Mathematics of Evolutionary Computation
| Reference No. | 20200017 |
|---|---|
| Type/Category | Grant for General Research-Workshop（Ⅰ） |
| Title of Research Project | Mathematics of Evolutionary Computation |
| Principal Investigator | Naoki Hamada（Artificial Intelligence Laboratory, Fujitsu Laboratories Ltd.・Researcher） |
| Research Period |
September 7,2020. ～
September 8,2020. |
| Keyword(s) of Research Fields | singularity theory, evolutionary computation, optimization |
| Abstract for Research Report |
Many industrial problems, such as product design and system operation planning, are formulated as optimization problems to find the minimum point of a given function. Evolutionary computation has been used in a variety of real-world problems as a general-purpose solver that can be applied even when functions are non-convex or derivatives are unavailable. In many cases, evolutionary computations can find satisfactory approximate solutions in practice, but their mathematical mechanisms are not fully understood. It is known that under some very restricted class of functions, theoretical behaviors such as convergence to the minimum point can be guaranteed. However, since the advantage of evolutionary computation lies in its versatility, a theory that holds for as wide a class of functions as possible is desired. The purpose of this workshop is to create future exchanges between researchers in evolutionary computation and mathematics with a view to establishing a mathematical theory that supports the versatility of evolutionary computation. Through introductory talks and research presentations by researchers in each field, we will mutually understand the current situation in both fields and explore the direction of future research. From the side of evolutionary computation, we mainly introduce the current research on the theory of evolutionary computation. From the mathematical side, we will mainly introduce the work on a singularity theory approach to multi-objective optimization initiated by Smale in his series of papers entitled "Global Analysis and Economics I-VI". Smale founded in the 1970s a wide-ranging theory for dealing with generic optimization problems in a mapping space, but it has not been applied to evolutionary computation until today due to the lack of exchange between the fields. This workshop is expected to deepen the exchange between evolutionary computation and mathematics and to advance the study of fundamental theory of evolutionary computation. In the future, such a theory will make it possible to appropriately judge which solver to use when faced with various real-world problems, and to guarantee the convergence of the solutions. |
| Organizing Committee Members (Workshop) Participants (Short-term Joint Usage) |
Naoki Hamada（Fujitsu Laboratories Ltd. / RIKEN AIP・Researcher / Visiting Researcher） Hirokazu Anai（Fujitsu Laboratories Ltd.・Project Director） Yuhei Umeda（Fujitsu Laboratories Ltd.・Senior Researcher） Kazuhisa Chiba（University of Electro-Communications・Professor） Hiroyuki Sato（University of Electro-Communications・Associate Professor） Yusuke Nojima（Osaka Prefecture University・Associate Professor） Yutaro Kabata（Kyushu University・Assistant Professor） Shunsuke Ichiki（Kyushu University・JSPS SPD） Kenta Hayano（Keio University / RIKEN AIP・Lecturer / Visiting Researcher） Osamu Saeki（Kyushu University・Professor） |