# Development of a school lunch recommendation system using an annealing machine

###### Member

Ochanomizu University, Department of Computer Science
Yuka INOUE
Haruka AKISHIMA

##### Theme

In the 2022 IPA MITOU Target Program, we worked on developing a web application for meal recommendations targeted at general households. In this project, it became clear that for meal suggestions in households, recommending recipes based on the combination of ingredients available in the refrigerator is more important than focusing on calorie and nutrient values. Based on those results, in the 2023 IPA MITOU Target Program, we shifted our focus to the domain of school lunches where calorie and nutrient values are more emphasized and continued the development of the web application.

##### Details of the combinatorial optimization problems

This is a combinatorial optimization problem that selects the best combination from numerous menus while satisfying requirements. We created a month's school lunch menus that meet specific requirements such as target nutritional values and calorie counts tailored to the ages of students, as well as budget constraints.

###### Decision variables

Two-dimensional decision variables, Menu (i) x Day (r) (1 when menu i is selected for day r, otherwise 0)

Image of decision variables

Day (r)
4/1 4/2 4/3 4/4 4/5 ・・・
Menu (i) Rice q (0 or 1) q (0 or 1) q (0 or 1) q (0 or 1) q (0 or 1)
Bread q (0 or 1) q (0 or 1) q (0 or 1) q (0 or 1) q (0 or 1)
Tomato Pasta q (0 or 1) q (0 or 1) q (0 or 1) q (0 or 1) q (0 or 1)
Pork cutlet q (0 or 1) q (0 or 1) q (0 or 1) q (0 or 1) q (0 or 1)

###### Objective function
• Bring nutrient content closer to ideal values
• Bring costs closer to ideal values
• Align the genres of menus within a single day
• Avoid serving similar menus consecutively
• Taking user feedback into consideration
###### Constraints
• 1 staple food and 1 main dish, while side dishes, soup, and dessert may be 0 or 1.
• Max 1 time per menu per month.
##### Challenges

We conducted interviews with dietitians from multiple elementary schools to better understand the school lunch menu planning process, Based on the information obtained, we carefully set the problem and constraints to closely mimic the actual process of creating school lunch menus. Despite the many constraints and the difficulty in adjusting weights, we diligently tackled the problem using grid search. During the evaluation of the mockup, dietitians provided feedback such as "This menu takes a long time to cook" and "This menu takes students a long time to eat." While it was challenging to incorporate all these aspects into the model, this led to the idea of collecting feedback from dietitians via the web app to improve future menu planning.

##### Future Outlook

We hope to eventually turn this into a service, but at the moment, we want to continue refining the app with feedback from many users, including dietitians. Additionally, if possible, we would like to expand its use to hospitals as well.

##### Achievements / Gratification

When dietitians first viewed the web app, their initial reactions to the proposed menus were not very positive. However, after multiple rounds of interviews and improvements, it was gratifying to hear comments about a better balance between meat and fish dishes and that several days' menus could be directly adopted as is into the actual plan.

##### To Viewers

Using tools like Fixstars Amplify can lower the barrier to formulation. If you have any combinatorial optimization problems you'd like to solve, please try using an Ising machine. Additionally, you can try the web application we developed at the following link (in Japanese). Please give it a try!