Abstract: According to an aspect of an embodiment, operations may include obtaining a first matrix associated with an optimization problem associated with a system and obtaining a second matrix associated with the optimization problem. The operations may include obtaining a local field matrix that indicates interactions between the variables of the system as influenced by their respective weights. The operations may include updating the local field matrix. Updating the local field matrix may include performing arithmetic operations with respect to a first portion of the first matrix and a second portion of the second matrix that correspond to a third portion of the local field matrix that corresponds to the one or more variables. The operations may include updating an energy value of the system based on the updated local field matrix and determining a solution to the optimization problem based on the energy value.

Abstract: A storage unit stores a flow matrix representing the flows between a plurality of entities to be assigned to a plurality of destinations, and a distance matrix representing the distances between the plurality of destinations. A processing unit calculates a first change in an evaluation function, which is to be caused by a first assignment change of exchanging the destinations of first and second entities among the plurality of entities, with vector arithmetic operations based on the flow and distance matrices, determines based on the first change whether to accept the first assignment change, and when determining to accept the first assignment change, updates an assignment state and updates the distance matrix by swapping the two columns or two rows (two columns in the example of FIG. 2) of the distance matrix corresponding to the first and second entities.

Abstract: According to an aspect of an embodiment, operations may include performing, based on weights and local field values associated with an optimization problem, a stochastic process with respect to changing a respective state of one or more variables that each represent a characteristic related to the optimization problem. The stochastic process may include performing trials with respect to one or more of the variables, in which a respective trial determines whether to change a respective state of a respective variable. The operations additionally may include determining an acceptance rate of state changes of the variables during the stochastic process and adjusting a degree of parallelism with respect to performing the trials based on the determined acceptance rate.

Abstract: According to an aspect of an embodiment, operations may include obtaining a first matrix associated with an optimization problem associated with a system and obtaining a second matrix associated with the optimization problem. The operations may include obtaining a local field matrix that indicates interactions between the variables of the system as influenced by their respective weights. The operations may include updating the local field matrix. Updating the local field matrix may include performing arithmetic operations with respect to a first portion of the first matrix and a second portion of the second matrix that correspond to a third portion of the local field matrix that corresponds to the one or more variables. The operations may include updating an energy value of the system based on the updated local field matrix and determining a solution to the optimization problem based on the energy value.