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A combinatorial optimization problem is trying to find out the value (combination) of variables that optimizes an index (value) from among many options under various constraints.

The optimization process using this annealing machine involves several instances where mathematics is utilized.

I will explain the first step of the mathematics necessary for optimization, along with Python programs that illustrate algebraic notation.

Most of the information devices we use today, such as PCs and smartphones, web servers that send out information on websites, IoT devices, and mission-critical systems that control power supply, are processed by computers called Neumann-type computers.

The Ising model is the simplest model in a field of physics 'statistical mechanics'.

With the outbreak of COVID-19, we used an annealing machine to create shifts for our researchers under constraints that took into account the newly created risks of infection.

Reinsurance is critical against natural disaster risks that have increased in recent years. We have used an annealing machine to formulate a reinsurance portfolio utilizing the vast amount of data collected by insurance companies.

Those who have followed the path of science may not need an explanation as to why an annealing machine derives the optimal solution from the cost function, but for those who have not, it may not be quite so clear.

Not every optimization problem can be dramatically improved with an annealing machine.

A linear programming problem is one that can be represented by a linear function.

The aforementioned first-order equations can be easily solved by other methods, whereas the second-order optimization problem is considered to be efficiently solved by an annealing machine.

In the second part, we will discuss the structural specifications and technical challenges of the annealing machine that actually derives the ground state of the Ising model.

In this section, we will look back at the roles that hardware and software have played in the shift from the dawn of annealing machines to their widespread use, and also consider the roles they will play in the future.

In general, computers often employ procedures and algorithms that lead to the only correct solution (exact solution), but let's learn about the different heuristic features and the significance of annealing machines in this perspective.

In order to encourage more people to use an annealing machine, we have published an article explaining the process of solving optimization problems with annealing machines for beginners.

With the Fitness diagnostic tool, you can confirm whether the optimization examples or problems you are familiar with are actually compatible with an annealing machine.