Experience the CMOS Annealing Machine

# Chapter 3: Annealing Machines, Quadratic Expressions, and Discrete Values

## Section 5: Continuous or discrete is up to user's choice

Solving an optimization problem with an annealing machine means representing elements as an Ising model. The system leads to an answer where each element is either $+1$ or $-1$. This is very different from the method for continuous values, where any point on the curve of the energy function can be a solution. "Intermediate solutions" between a solution and another solution do not exist.

For example, in our shift optimization example, we formulate the problem in the form of whether or not Mr. A will work on a certain day (say, February 10th). This is a discrete problem since it can be represented by two values, $1$ or $0$. A bit more complicated, if we choose among three options, whether Mr. A will be in charge of the hall on February 10th, in charge of cooking, or on vacation, this is also a discrete value. Such a task assigning something will be a discrete value, so this is the type of problem where the annealing machine can be very effective.

In some cases, however, there are problems you can choose to define as discrete or continuous for the convenience of the calculation. For example, cutting pizza is a continuous problem if you consider it as dividing the area of a pizza. However, in reality, we would like each person to divide the pizza at an angle of about 30 degrees, so if we include such considerations in the problem, we can say that it is a discrete problem.

### SNS Sharing

If you want to know specific examples of solving combinatorial optimization problems with an annealing machine

#### What is the combinatorial optimization problem?

Combinatorial optimization will be explained by using two easy-to-understand examples of familiar combinatorial optimization problems. The importance of finding and using fast solution methods for combinatorial optimization processes in an IoT society will also be discussed.

#### Optimization of researcher shifts with consideration for COVID-19 infection control

In the wake of the COVID-19 epidemic, we present a use case in which an annealing machine is used to create shifts for researchers under constraints that take into account the risk of infection.

#### Optimizing reinsurance portfolio

This article presents a use case in which an annealing machine is used to formulate a reinsurance portfolio that leverages the vast amount of data held by an insurance company to address natural catastrophe risks.

If you want to know how to use an annealing machine

#### Easy-to-learn optimization flow

For beginners, this article explains the procedures and key points of the process of solving optimization problems with an annealing machine. The process involves dividing the problem into four stages: "organizing problem and defining problem," "formulation," "input data preparation," and "executing CMOS annealing machine".