Theme
The development of catalysts, materials that accelerate chemical reactions, is one of the crucial research
themes for achieving carbon neutrality. In recent years, there has been active research on catalysts composed
of multiple elements. However, due to the vast number of possible combinations of these elements, it is
extremely difficult to determine each element’s arrangement. In this project, we focused on alloys, materials
made up of multiple metal elements, and developed a program to determine the arrangement of metals using an
annealing machine. Furthermore, we also developed a program to visualize the alloy structures and their
structural information.
Details of the combinatorial optimization problems
This is an optimization problem of the arrangement of metals within a crystal structure. Metals are allocated
within the crystal structure to achieve the ratios specified by the user. At the same time, the arrangement is
determined to minimize the energy to make the alloy as stable as possible.
Decision variables
Two-dimensional decision variables of metal species × metal position in the alloy (1 if that metal species is
present, 0 if not)
Image of decision variable
|
Metal Species |
| Metal A |
Metal B |
・・・ |
| Metal Position |
0 |
q (0 or 1) |
q (0 or 1) |
|
| 1 |
q (0 or 1) |
q (0 or 1) |
|
| 2 |
q (0 or 1) |
q (0 or 1) |
|
| ・ |
|
|
|
| ・ |
|
|
|
| ・ |
|
|
|
Objective function
Minimize energy in metal arrangement (search for the most stable arrangement of metals)
Constraints
- The metal species match the ratios specified by the user
- 1 metal species is assigned to each metal position
Challenges
When creating the objective function, we quantified the impact of the arrangement of metals and metal pairs
within the crystal structure to be used for the coefficients of QUBO and HUBO. By considering the symmetry of
the alloy's crystal structure, we could significantly reduce the computational load, but it was necessary to
assign the coefficients to all corresponding positions of metal pairs with the same symmetry. It was
particularly challenging in the coding to make the lists of metal pairs with the same symmetry and the
conversion to QUBO or HUBO.
Future Outlook
We have developed a program to search for the most stable metal arrangements in alloy catalysts using an
annealing machine and to visualize the stability and physicochemical information of optimized arrangements.
Moving forward, we plan to further improve this program, and we are considering releasing it as open-source
software to make it more accessible to researchers in catalytic chemistry. We aim to contribute to the
development of high-performance catalysts for achieving carbon neutrality by 2050 by providing tools that
assist researchers in understanding catalyst structures in catalyst development.
Achievements / Gratification
Before starting the project, it was unclear how we should formulate the objective function, but we were very
delighted when we were able to do it based on the advice from the project manager and other teams as well as
referring to the prior paper. Additionally, we were able to gain insights into the problem sizes that the
current annealing machine can handle, which should be beneficial for our future projects.
To Viewers
Through the MITOU Target Program, by looking at the themes tackled by the other teams, it was very
interesting to realize that a variety of social challenges can be treated as combinatorial optimization
problems. We look forward to seeing how problems in fields and areas we hadn't even imagined will be defined
and solved as combinatorial optimization problems in the future.
* All information in this article is based on information available at the time of the interview.
