This proposal suggests research and development of optimization methods that combine machine learning with mathematical optimization techniques to obtain practically useful approximate solutions for problems where obtaining exact solutions is difficult. By doing so, it aims to extend the applicability of optimization methods to a broader range of real-world problems and to expand the support provided during decision-making to derive optimal solutions.

Optimization is the process of finding the most desirable solution under various constraints in order to achieve a certain objective. Mathematical optimization methods are techniques that perform optimization based on mathematical models. The solutions obtained by mathematical optimization methods are called exact solutions, and it is possible to mathematically prove that they are the most desirable solutions.

In decision-making by individuals or organizations, whether a decision is optimal may sometimes be judged based on the individual's subjective value criteria; however, in this proposal, it is assumed that the optimal solution will be presented when attempting to make judgments based on objective evaluation criteria. In solving social issues, numerous important decisions are required, such as policy planning, resource allocation, and risk management. Optimization methods are useful as systematic and quantitative means to support these decisions. Similarly, optimization methods are useful for quantitative support of the various decisions required in the management of organizations and businesses such as companies.

Mathematical optimization methods, which began with linear programming announced in 1947 and have progressed alongside the development of computers, have the following problems.

• - When the problem is large-scale and high-dimensional (involving a vast number of variables), the computational complexity increases explosively, making the calculations infeasible.
• - Data may be missing or contain errors and/or biases, making accurate calculations difficult.
• - It can be difficult to construct the model for optimization, or the target may change dynamically.
• - The fundamental objective of optimization may be unclear, making it impossible to define an objective function.
• - The obtained results may be impractical, or there may be no consensus among stakeholders on implementation.

For these reasons, the application of mathematical optimization methods to real-world problems has been progressing slowly.

Considering this situation, this proposal suggests the promotion of research and development on hybrid optimization methods that combine mathematical optimization techniques and machine learning, focusing on the following three tasks.

• 1. Research and development of optimization methods to handle large-scale, high-dimensional optimization problems
  Research and development of optimization methods that find appropriate optimal solutions even when the data includes uncertainties such as errors, missing values, and biases.
• 2. Research and development of optimization methods for cases involving uncertain data
  Research and development of optimization methods that find appropriate optimal solutions even when the data includes uncertainties such as errors, missing values, and biases.
• 3. Research and development of optimization methods that reduce computation time and repeatedly find optimal solutions
  Research and development of optimization methods that respond by repeatedly finding optimal solutions in a short time according to rapidly changing conditions.

With the remarkable progress in artificial intelligence technology, it is expected that research and development will advance by integrating machine learning and mathematical optimization methods.

To expand the social application scope of optimization methods, research and development alone are insufficient; it is important to promote strategies that link these achievements to the realization of social value. This proposal suggests the following three promotion strategies.

Strategy 1: Collaboration between machine learning and mathematical optimization methods
Research and development of hybrid optimization will be advanced through collaboration between the fields of machine learning and mathematical optimization methods.

Strategy 2: Problem-solving process using hybrid optimization methods
Create opportunities for research and development by backcasting from the application of hybrid optimization methods to real-world problems, promoting the integration of machine learning and mathematical optimization. Make the knowledge gained there widely available as software tools (solvers).

Strategy 3: Promotion of hybrid optimization methods
To widely apply hybrid optimization methods to real-world problems and support decision-making, efforts will be made to clearly communicate the meaning and value of hybrid optimization methods in practice.

Through these research and development efforts and promotion strategies, many decisions that were previously based on experience and intuition can be replaced with decisions supported by the proposed hybrid optimization methods, and appropriate decision support will become possible for problems that were too complex to handle adequately. As a result, it leads to the reduction or elimination of inefficiencies, waste, and disparities present in various aspects of society, economy, public policy, and industry, thereby contributing to society through increased efficiency. Furthermore, improvements in resource utilization efficiency are expected to enhance the sustainability of society. Moreover, it becomes possible to take into account more diverse and highly uncertain situations, which is also expected to contribute to the construction of a more equitable society.

• (in Japanese) Innovations in Optimization Technology to Support Decision-Making - Contributing to the Creation of Social Value -