SIMULATION APPARATUS AND SIMULATION METHOD
A simulation apparatus is an apparatus that obtains a solution of a combinatorial optimization problem by SA, in which a local optimal solution of an objective function is acquired by using a local search method of changing a temperature parameter, a statistic is calculated based on the local optimal solution and a probability distribution function of a variable included in the objective function, a maximum value (temperature parameter when a standard deviation related to a state of the local optimal solution is large) and a minimum value (temperature parameter when the standard deviation is small) as a search range for the temperature parameter are obtained based on the calculated statistic (standard deviation), and a good solution is obtained by executing the simulated annealing a plurality of times in the search range having the maximum value and the minimum value for the temperature parameter.
1 . A simulation apparatus that obtains a solution of a certain combinatorial optimization problem by simulated annealing, wherein
a local optimal solution of an objective function of the problem is acquired by using a local search method of changing a temperature parameter,
a statistic is calculated based on the local optimal solution and a probability distribution function of a variable included in the objective function,
a maximum value and a minimum value as a search range for the temperature parameter are obtained based on the calculated statistic, and
the solution is obtained by executing the simulated annealing a plurality of times in the search range having the maximum value and the minimum value for the temperature parameter.
2 . The simulation apparatus according to claim 1 , wherein
the statistic is a standard deviation of the variable when a state update is performed with respect to a state of the local optimal solution and an expected value of a moving distance when the state update is performed a predetermined number of times.
3 . The simulation apparatus according to claim 1 , wherein
the statistic is a standard deviation of the variable when a state update is performed with respect to a state of the local optimal solution, a temperature when the standard deviation is larger than a predetermined threshold is set as the maximum value of the search range for the temperature parameter, and a temperature when the standard deviation is smaller than the predetermined threshold is set as the minimum value of the search range for the temperature parameter.
4 . The simulation apparatus according to claim 1 , wherein
the objective function is a function describing a state of an interaction model including a plurality of nodes.
5 . The simulation apparatus according to claim 1 , wherein
the objective function is an energy function, and
the local optimal solution is obtained as a state where energy of the energy function is minimized.
6 . The simulation apparatus according to claim 1 , wherein
a ground state search using the simulated annealing is performed by transitioning a state using a probability distribution function including the temperature parameter as a variable.
7 . The simulation apparatus according to claim 6 , wherein
the probability distribution function is a function based on a Boltzmann distribution.
8 . The simulation apparatus according to claim 6 , wherein
the state is transitioned by using a Markov Chain Monte Carlo method.
9 . The simulation apparatus according to claim 1 , wherein
the variable is a binary variable or a continuous variable.
10 . A simulation method performed by using a simulation apparatus that obtains a solution of a certain combinatorial optimization problem by simulated annealing, the simulation method comprising:
a step of the simulation apparatus acquiring a local optimal solution of an objective function by using a local search method of changing a temperature parameter;
a step of the simulation apparatus calculating a statistic based on the local optimal solution and a probability distribution function of a variable included in the objective function;
a step of the simulation apparatus obtaining a maximum value and a minimum value as a search range for the temperature parameter based on the calculated statistic; and
a step of the simulation apparatus obtaining the solution by executing the simulated annealing a plurality of times in the search range having the maximum value and the minimum value for the temperature parameter, wherein
in the simulation apparatus, the statistic is a standard deviation related to a state of the local optimal solution, and a temperature when the standard deviation related to the state of the local optimal solution is larger than a predetermined threshold is set as the maximum value of the search range for the temperature parameter, and a temperature when the standard deviation related to the state of the local optimal solution is smaller than the predetermined threshold is set as the minimum value of the search range for the temperature parameter.