Abstract: An apparatus of acquiring a solution to a permutation optimization problem represented by an energy function of an Ising model, the apparatus being configured to perform processing including: obtaining problem information which indicates M2 state variables (M is an integer equal to or more than 3) in the permutation optimization problem; generating information on a first energy function which includes N2 state variables obtained by adding (N2?M2) state variables (N is an integer more than M) to the M2 state variables, based on the problem information; inputting the information on the first energy function to a search unit; obtaining, from the search unit based on the first energy function, a first solution represented by values of the N2 state variables; and generating a second solution to the permutation optimization problem by removing values of the (N2?M2) state variables from the first solution.

Abstract: An information processing apparatus configured to: store N2 state variables included in an energy function of an Ising model, values of the N2 state variables being determined based on a constraint that the N2 state variables are arranged in N rows and N columns, and search for a solution to a permutation optimization problem by switching fixing and non-fixing a value of a state variable of a K-th row and an L-th column in N rows and N columns to 1; and repeating changing values of four state variables of the N2 state variables in accordance with a change amount of a value of the energy function when the values of the four state variables are changed to satisfy the constraint.

Abstract: An information processing apparatus configured to: store N2 state variables included in an energy function of an Ising model, and execute a traveling transition process of returning from a first state to the first state through a plurality of states by repeating a state transition of changing values of four state variables so as to satisfy a constraint in which a sum of values of state variables included in each row is 1 and a sum of values of state variables included in each column is 1 when the N2 state variables are arranged in N rows and N columns, specify a second state in which an accumulation of a change amount of a value of the energy function for each state transition satisfies a certain determination criterion, and search for a solution to a permutation optimization problem represented by the energy function by starting from the second state.

Abstract: An information processing apparatus including: a search unit of searching for a solution of a problem to which a constraint condition including two-way one-hot constraint is given, by using a first matrix based on an objective function as a weight matrix; and a processor configured to perform transition processing that includes: changing, when the search reaches a specific state, a part of values in the solution; and perform weight matrix switch processing including, when the part of values of a plurality of variables in the solution is changed by the transition processing, causing the search unit to perform the search by setting, as the weight matrix, a return matrix generated by using a penalty coefficient in the weight matrix, and when the search result reaches a state satisfying the two-way one-hot constraint, causing the search unit to perform the search by returning the weight matrix to the first matrix.

Abstract: An information processing apparatus of obtaining a solution to a problem in which constraint that includes two-way one-hot constraint is given, by using an objective function that has a predetermined number of variables, the information processing apparatus including: a processor configured to exclude, when determining sets of candidates that have values which are to be changed based on the constraint from expanded variables obtained by adding a plurality of redundant variables to the predetermined number of variables, one of the sets of the candidates in which values of the redundant variables are exchanged with each other; and a search unit that changes, according to the constraint, the values of the sets of the candidates, and performs a search based on the objective function, wherein the processor is further configured to determine the solution on the basis of a result of the search by the search unit.

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 computer of searching for a combination of state variables with which an evaluation function including the state variables becomes a local minimum or maximum, the computer including: a memory storing a first coefficient indicating a magnitude of interaction between k state variables in a kth order term of the evaluation function; and a processor that performs: calculating a first local field indicating a change amount of the kth order term when a first state variable among the k state variables changes by the first coefficient and a first variable obtained by the k state variables and second coefficients; and determining whether to allow a change in the first state variable based on a result of comparison between a predetermined value and a product of a sum of the first local field and a second local field indicating a change amount of quadratic and lower-order terms of the evaluation function.

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: An optimization device includes: k first calculation circuits, N?k second calculation circuits, a selection circuit, an identification information calculation circuit and an update circuit. The first calculation circuit calculates a first energy change of an Ising model due to a change of a value of one of k first bits having values of 1 and a change of a value of a second bit having a value of 0 selected based on a generated first random number. The second calculation circuit calculates a second energy change of the Ising model due to a change of a value of one of (N?k) third bits having the values of 0 and a change of a value of a fourth bit having a value of 1 selected based on a generated second random number.

Abstract: An information processing device includes: a memory; and a processor coupled to the memory and configured to calculate, for a plurality of bits corresponding to a plurality of spins included in an Ising model obtained by converting a problem to be calculated, in a case where the plurality of bits is divided into a plurality of groups, on the basis of a first local field value for a first bit having a value of 1 and a second local field value for a second bit having a value of 0 among a plurality of bits included in each of the plurality of groups, a first energy change of the Ising model due to a change of the value of the first bit from 1 to 0 and a change of the value of the second bit from 0 to 1.

Abstract: An optimization apparatus includes one or more processors configured to search for an optimum solution that minimizes energy based on a change amount of the energy when a value of state variables included in an evaluation function which represent the energy of an Ising model changes, determine an upper limit or a lower limit of a second identification number of a second state variable for which a change from the second value is permitted in a second state variable group out of the plurality of state variable groups, based on a first identification number of a first state variable that has a first value in a first state variable group out of a plurality of state variable groups included in the plurality of state variables and in each of which one of the state variables has the first value and other state variables have a second value.

Abstract: An optimization device includes a plurality of calculation circuits; a selection circuit; an identification information calculation circuit, and an updating circuit. Each of the plurality of calculation circuits calculates, for a plurality of bits corresponding to a plurality of spins included in an Ising model obtained by converting a problem to be calculated, a first energy change of the Ising model due to a value of a first bit having the value of 1 being changed from 1 to 0 and a value of a second bit having the value of 0 being changed from 0 to 1. The selection circuit outputs first bit identification information identifying one second bit having a value permitted to be updated from 0 to 1, based on a magnitude relationship between thermal excitation energy and the first energy change output by each of the plurality of calculation circuits.

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 method includes: accessing first storage configured to store a first weight coefficient group which is at least some of a plurality of weight coefficients indicating a magnitude of interaction between a plurality of state variables in an evaluation function representing energy of an Ising model; accessing a plurality of second storages each of the plurality of second storage being configured to store a second weight coefficient group related to a state variable having a value of 1 in any of a plurality of state variable groups respectively including the plurality of state variables among the plurality of weight coefficients; outputting, for each of the plurality of state variable groups, a search result obtained by performing searching processing configured to perform processing of searching for an optimum solution by repeatedly performing a first update process with a first constraint or a second update process with a second constraint.

Abstract: A method includes: calculating a change amount of energy of an Ising model, the change amount being caused when values of four states are changed, for each of a plurality of first states having a value of 0 before change, so as to satisfy a constraint that a sum of values of states included in each row is 1, and a sum of values of states included in each column is 1, when N (an integer of 2 or larger) squared state variables included in an evaluation function representing the energy of the Ising model are arrayed in N rows and N columns; selecting the four states allowed to change by using the change amount calculated for each of the plurality of first states, and outputting identification information for identifying the four states; and updating values of the four states allowed to change by using the identification information.

Abstract: A position detection system includes a GNSS sensor terminal that receives a satellite signal from a GNSS satellite as a snapshot, at least one relay device that receives the snapshot GNSS signal transmitted by the GNSS sensor terminal, and a calculation device that measures a position of the GNSS sensor terminal by using a code phase and a Doppler frequency of the GNSS satellite obtained from the snapshot GNSS signal, wherein the calculation device estimates an initial position of the GNSS sensor terminal by using position information of the relay device that has received the snapshot GNSS signal transmitted by the GNSS sensor terminal.

Abstract: An information processing device includes: a memory; and a processor coupled to the memory and configured to calculate, for a plurality of bits corresponding to a plurality of spins included in an Ising model obtained by converting a problem to be calculated, in a case where the plurality of bits is divided into a plurality of groups, on the basis of a first local field value for a first bit having a value of 1 and a second local field value for a second bit having a value of 0 among a plurality of bits included in each of the plurality of groups, a first energy change of the Ising model due to a change of the value of the first bit from 1 to 0 and a change of the value of the second bit from 0 to 1

Abstract: A position detection system includes a GNSS sensor terminal that receives a satellite signal from a GNSS satellite as a snapshot, at least one relay device that receives the snapshot GNSS signal transmitted by the GNSS sensor terminal, and a calculation device that measures a position of the GNSS sensor terminal by using a code phase and a Doppler frequency of the GNSS satellite obtained from the snapshot GNSS signal, wherein the calculation device estimates an initial position of the GNSS sensor terminal by using position information of the relay device that has received the snapshot GNSS signal transmitted by the GNSS sensor terminal.

Abstract: An optimization device includes a plurality of calculation circuits; a selection circuit; an identification information calculation circuit, and an updating circuit. Each of the plurality of calculation circuits calculates, for a plurality of bits corresponding to a plurality of spins included in an Ising model obtained by converting a problem to be calculated, a first energy change of the Ising model due to a value of a first bit having the value of 1 being changed from 1 to 0 and a value of a second bit having the value of 0 being changed from 0 to 1. The selection circuit outputs first bit identification information identifying one second bit having a value permitted to be updated from 0 to 1, based on a magnitude relationship between thermal excitation energy and the first energy change output by each of the plurality of calculation circuits.

Abstract: An optimization device includes: k first calculation circuits, N?k second calculation circuits, a selection circuit, an identification information calculation circuit and an update circuit. The first calculation circuit calculates a first energy change of an Ising model due to a change of a value of one of k first bits having values of 1 and a change of a value of a second bit having a value of 0 selected based on a generated first random number. The second calculation circuit calculates a second energy change of the Ising model due to a change of a value of one of (N?k) third bits having the values of 0 and a change of a value of a fourth bit having a value of 1 selected based on a generated second random number.