Optimization apparatus and control method thereof

1 . An information processing apparatus comprising:

a computing circuit configured to search for a ground state of energy value of an Ising model with simulated annealing or a replica exchange method, based on Ising model information and a temperature parameter, the Ising model information representing the Ising model; and

a control circuit configured to

receive, from a control apparatus, a resolution in value of the Ising model information and a first reference value which indicates an acceptance probability of state transition in the Ising model at a minimum value of the temperature parameter, wherein the resolution is a constant value which indicates a limit of representation capacity of the computing circuit and is determined by a characteristic of hardware of the computing circuit,

determine the minimum value by dividing the resolution by a natural logarithm of the first reference value,

determine a maximum amount of change in the value of the Ising model information, based on the Ising model information,

determine a maximum value of the temperature parameter, based on the maximum amount of change in the value of the Ising model information and a second reference value, the second reference value being greater than the first reference value and indicating the acceptance probability at the maximum value of the temperature parameter, and

cause the computing circuit to search for the ground state of the energy value of the Ising model based on change in energy by the simulated annealing or the replica exchange method using the temperature parameter having a range defined by the minimum value and the maximum value.

2 . The information processing apparatus according to claim 1 , wherein the control circuit determines the maximum value of the temperature parameter by dividing the maximum amount of change by a natural logarithm of the second reference value.

3 . The information processing apparatus according to claim 1 , wherein the control circuit determines the maximum amount of change by dividing a sum of absolute values of weight coefficients included in the Ising model information by a total bit count of the Ising model.

4 . The information processing apparatus according to claim 1 , wherein the control circuit determines the maximum amount of change by dividing a sum of absolute values of weight coefficients included in the Ising model information by a total bit count of the Ising model and adding, to a result of the dividing, a maximum value among absolute values of bias coefficients of all bits included in the Ising model information.

5 . The information processing apparatus according to claim 1 , wherein the control circuit calculates first maximum amounts of change that are respectively caused by changing all bits included in the Ising model, and determines, as the maximum amount of change, a maximum of the first maximum amounts respectively calculated for all the bits.

6 . The information processing apparatus according to claim 1 , wherein the computing circuit searches for the ground state with simulated annealing by receiving temperature drop control information indicating how to decrease a value of the temperature parameter and decreases the value of the temperature parameter from the maximum value to the minimum value in accordance with the temperature drop control information.

7 . The information processing apparatus according to claim 1 , wherein:

the computing circuit includes replicas each of which performs update process with respect to same bits of the Ising model and the computing circuit searches for the ground state with a replica exchange method by using the replicas; and

the control circuit determines temperature schedule information including, for each of the replicas, a value of the temperature parameter in a range from the maximum value to the minimum value, and sends the temperature schedule information to the computing circuit.

8 . A control method of an information processing apparatus, the control method comprising:

receiving, by a control circuit of the information processing apparatus, a resolution in value of Ising model information and a first reference value which indicates an acceptance probability of state transition in an Ising model at a minimum value of the temperature parameter from a control apparatus, wherein the resolution is a constant value which indicates a limit of representation capacity of a computing circuit and is determined by a characteristic of hardware of the computing circuit which is configured to search for a ground state of energy value of the Ising model with simulated annealing or a replica exchange method, based on the Ising model information representing the Ising model and the temperature parameter,

determining, by the control circuit, the minimum value by dividing the resolution by a natural logarithm of the first reference value;

determining, by the control circuit, a maximum amount of change, based on the Ising model information;

determining, by the control circuit, a maximum value of the temperature parameter based on the maximum amount of change and a second reference value, the second reference value being greater than the first reference value and indicating the acceptance probability at the maximum value of the temperature parameter; and

causing, by the control circuit, the computing circuit to search for the ground state of the energy value of the Ising model based on change in energy by the simulated annealing or the replica exchange method using the temperature parameter having a range defined by the minimum value and the maximum value.

9 . A non-transitory computer-readable recording medium storing a control program of an information processing apparatus that causes a computer to execute a process comprising:

receiving, from a control apparatus, a resolution in value of Ising model information and a first reference value which indicates an acceptance probability of state transition in an Ising model at a minimum value of the temperature parameter, wherein the resolution is a constant value which indicates a limit of representation capacity of a computing circuit and is determined by a characteristic of hardware of a computing circuit which is configured to search for a ground state of energy value of the Ising model with simulated annealing or a replica exchange method, based on the Ising model information representing the Ising model and the temperature parameter,

determining the minimum value by dividing the resolution by a natural logarithm of the first reference value;

determining a maximum amount of change, based on the Ising model information;

determining a maximum value of the temperature parameter based on the maximum amount of change and a second reference value, the second reference value being greater than the first reference value and indicating the acceptance probability at the maximum value of the temperature parameter; and

causing the computing circuit to search for the ground state of the energy value of the Ising model based on change in energy by the simulated annealing or the replica exchange method using the temperature parameter having a range defined by the minimum value and the maximum value.