Optimization function generation apparatus, optimization function generation method, and program

1. An optimization function creation apparatus comprising:

an input setting circuitry configured to set a set Path of paths, a set Edge of edges, a maximum bandwidth Max, a bandwidth p.bandwidth required by a path p(∈Path), and a set e.paths(⊆Path) of paths that include an edge e(∈Edge), as input to a bandwidth allocation plan problem for creating a bandwidth allocation plan for paths so as to satisfy a condition (hereinafter referred to as an “optimization condition”) of minimizing a bandwidth allocated for the paths of the set Path as a whole under a predetermined constraint condition;

an optimization function creation circuitry configured to create an optimization function for solving the bandwidth allocation plan problem using the input, the optimization function relating to a variable that represents a quantum state; and

another circuitry configured to allocate, based on the created optimization function, a minimized bandwidth allocated for the path of the set Path and transmit data through the path of the set Path.

2. The optimization function creation apparatus according to claim 1 , wherein

the constraint condition is a condition (hereinafter referred to as a “first constraint condition”) that |{p∈e.paths|bottom(p)≤b<bottom(p)+p.bandwidth}|≤1 (where bottom(p) represents the lower limit of a bandwidth allocated for the path p) is satisfied with respect to each band b up to the maximum bandwidth Max and each edge e∈Edge, and

the optimization function is a function designed so as to take the minimum value when the first constraint condition is satisfied.

3. The optimization function creation apparatus according to claim 2 , wherein

the variable that represents a quantum state is a quantum bit that represents a particular state by taking the value 1 and represents a state other than the particular state by taking the value 0,

the optimization function is an objective function of Quadratic Unconstrained Binary Optimization (QUBO) defined based on a function that expresses the first constraint condition and a function that expresses the optimization condition,

the function expressing the first constraint condition is a function that takes the value 0 when the first constraint condition is satisfied, and otherwise takes a value greater than 0, and

the function expressing the optimization condition is a function defined such that the value of the function decreases as the total value of bands each allocated for at least one path decreases.

4. The optimization function creation apparatus according to claim 3 , wherein

the variable that represents a quantum state is a variable that is defined so as to represent, with the value 1, a state where a band b is higher than or equal to the lower limit of a bandwidth allocated for a path p.

5. The optimization function creation apparatus according to claim 2 , wherein

the variable that represents a quantum state is a spin that represents a particular state by taking the value 1 and represents a state other than the particular state by taking the value −1,

the optimization function is an Ising Hamiltonian defined based on a function that expresses the first constraint condition and a function that expresses the optimization condition,

the function expressing the first constraint condition is a function that takes the value 0 when the first constraint condition is satisfied, and otherwise takes a value greater than 0, and

the function expressing the optimization condition is a function defined such that the value of the function decreases as a total value of bands each allocated for at least one path decreases.

6. The optimization function creation apparatus according to claim 5 , wherein

the variable that represents a quantum state is a variable that is defined so as to represent, with the value 1, a state where a band b is higher than or equal to the lower limit of a bandwidth allocated for a path p.

7. A non-transitory computer-readable recording medium storing a program for causing a computer to function as the optimization function creation apparatus according to claim 1 .

8. A method for creating an optimization function, comprising:

an input setting step of setting, by an optimization function creation apparatus, a set Path of paths, a set Edge of edges, a maximum bandwidth Max, a bandwidth p.bandwidth required by a path p(∈Path), and a set e.paths(⊆Path) of paths that include an edge e(∈Edge), as input to a bandwidth allocation plan problem for creating a bandwidth allocation plan for paths so as to satisfy a condition (hereinafter referred to as an “optimization condition”) of minimizing a bandwidth allocated for the paths of the set Path as a whole under a predetermined constraint condition;

an optimization function creating step of creating, by the optimization function creation apparatus, an optimization function for solving the bandwidth allocation plan problem using the input, the optimization function relating to a variable that represents a quantum state; and

an allocating and transmit step of allocating, based on the created optimization function, a minimized bandwidth allocated for the path of the set Path and transmit data through the path of the set Path.