Abstract: A storing unit stores, amongst coefficients, values of a coefficient group associated with one selected from multiple variable groups, which are obtained by dividing state variables of an evaluation function. A searching unit searches for a solution to an optimization problem by repeating update processing, which includes calculating, using the values of the coefficient group, a value change of the evaluation function responsive to changing the value of each state variable of the variable group and changing the value of one state variable thereof based on the value change and temperature. A processing unit calculates multiplicity indicating the iteration count in which the values of the variable group are maintained in a search using Markov chain Monte Carlo (MCMC), and causes, responsive to cumulated multiplicity exceeding a threshold, the searching unit to perform the update processing using the values of the coefficient group associated with a different variable group.

Abstract: A method may include obtaining variables that represent characteristics related to an optimization problem and weights that correspond to the variables. The variables may be divided into groups that each include a sub-set of the variables. The method may include obtaining a group local field matrix for each group of variables. Each local field matrix may include local field values that indicate interactions between a respective variable and the other variables as influenced by their respective weights. The method may include performing a semi-sequential trial process, which may be a stochastic process that includes performing trials with respect to the variables in which each trial determines whether to change a state of a variable. The semi-sequential trial process may include updating all of the group local field matrices based on the stochastic process results, and a solution to the optimization problem may be determined based on the results.

Abstract: According to an aspect of an embodiment, operations may include obtaining a first fixed temperature and a second fixed temperature of a replica exchange Markov Chain Monte Carlo (MCMC) process used to solve an optimization problem associated with a system, and obtaining a plurality of replicas of the system. The operations may also include obtaining a target swap acceptance probability with respect to swapping, during the replica exchange MCMC process, between replicas that correspond to adjacently ordered temperatures of a set of temperatures between the first fixed temperature and the second fixed temperature. The operations may include determining a respective average swap acceptance probability with respect to one or more respective adjacent pairs of temperatures. Further, the operations may include adjusting one or more of the variable temperatures based on a relationship between the target swap acceptance probability and each of one or more of the respective swap acceptance probabilities.

Abstract: A storage unit stores some of a plurality of coupling coefficients stored in a storage device. A processing unit takes a plurality of first state variables among a plurality of state variables as a trial target set. The processing unit performs a process of reading a plurality of first coupling coefficients corresponding to a plurality of first pairs of the first state variables belonging to the trial target set from the storage device, storing the plurality of first coupling coefficients in the storage unit, and conducting, a plurality of times, a trial on whether to update the value of any first state variable belonging to the trial target set using the plurality of first coupling coefficients. The processing unit repeats change of the trial target set and the process, so as to target all the plurality of state variables in the trials.

Abstract: A data processing apparatus configured to: search for a combination of values of a plurality of state variables that minimizes or maximizes a value of an Ising-type evaluation function that includes the plurality of state variables, repeat determining whether to permit a change in a value of a first state variable among the plurality of state variables based on the first local field, and when the change in the value of the first state variable is permitted, updating the first local field based on the first weight value, updating the second local field that corresponds to a constraint condition in which the second weight value with the first state variable is non-zero based on the second weight value, and updating the first local field based on the second local field before the updating and the second local field after the updating.

Abstract: A data processing apparatus configured to search for a combination of values of a plurality of state variables that minimizes or maximizes a value of an Ising-type evaluation function, when a change in a value of a first state variable is permitted, updating the value of the first state variable, updating a first local field based on a first weight value related to the first state variable, and updating a second local field based on a second weight value related to the first state variable, when the change in a value of the first auxiliary variable is permitted, updating the value of the first auxiliary variable, and updating the first local field based on a second weight value related to the first auxiliary variable.

Abstract: A computer-readable recording medium storing a program for causing a computer of searching for a solution for a combinatorial optimization problem represented by an energy function including state variables, to execute processing including: executing search processing of searching for the solution by performing determination whether or not to accept a change of each value of a plurality of first state variables, for the plurality of first state variables selected from among the state variables in parallel and executing processing of changing the value of one state variable of which the change of the value is determined to be accepted while changing the plurality of selected first state variables; and specifying the number of the plurality of selected first state variables, based on a search status of the search processing or search information that indicates a search record of another combinatorial optimization problem and repeating the search processing.

Abstract: An optimization apparatus calculates a first portion, among energy change caused by change in value of a neuron of a neuron group, caused by influence of another neuron of the neuron group, determines whether to allow updating the value, based on a sum of the first and second portions of the energy change, and repeats a process of updating or maintaining the value according to the determination. An arithmetic processing apparatus calculates the second portion caused by influence of a neuron not belonging to the neuron group and an initial value of the sum. A control apparatus transmits data for calculating the second portion and the initial value to the arithmetic processing apparatus, and the initial value and data for calculating the first portion to the optimization apparatus, and receives the initial value from the arithmetic processing apparatus, and a value of the neuron group from the optimization apparatus.

Abstract: An optimization method executed by a computer upon attempting to solve a ground state of an Ising model by simulating a state change of the Ising model when a magnetic field applied to the Ising model is reduced, the Ising model representing a problem to be solved, the method including: executing a first process, the first process being a real time propagation in which an intensity of the magnetic field is reduced with progress of time in simulation; and in response to the progress of time in the real time propagation of the first process, executing a second process, the second process including reducing energy of the Ising model based on an imaginary time propagation method.

Abstract: Operations may include identifying variables corresponding to an optimization problem, each variable having an initial value. The operations may include calculating an objective function value based on the initial value of each variable and a plurality of function value changes. Each function value change may be calculated based on a different variable value change, each variable value change corresponding to a respective change made to a different one of the variables. The operations may include selecting a subset of the variables based on the respective function value changes and corresponding variable value changes made to the respective initial values of the variables of the subset and generating a surrogate quadratic unconstrained binary optimization (QUBO) model using the subset. The operations may include determining a solution to the optimization problem including a set of solution values using the surrogate QUBO model, each of the solution values corresponding to a different variable.

Abstract: A calculation circuit calculates, among a plurality of neurons whose states are represented by variables each having m values (m is a positive integer of 3 or greater), two energy changes caused by a state change of a second neuron by 2n (n is an integer of 0 or greater) in positive and negative directions, based on a state change direction of a first neuron whose state has been updated and a weighting coefficient indicating magnitude of an interaction between the first and second neurons. A state transition determination circuit determines, based on magnitude relationships among a thermal excitation energy and the two energy changes, whether to allow updates of the state of the second neuron that cause the two energy change, outputs the determination results, and limits updates by which the state of the second neuron exceeds an upper limit value or falls below a lower limit value.

Abstract: A program for causing a computer to execute processing that searches for a combination of a plurality of state variable values with which a value of an evaluation function is minimized or maximized by a Markov chain Monte Carlo (MCMC) method, the processing including: reading time-series data from a storage device storing the time-series data indicating a time change of the value of the evaluation function at a time of a search by the MCMC method that uses a first temperature; generating a plurality of time-series data sets that includes the value of the evaluation function for each period on a basis of the time-series data; calculating an index value based on magnitude of correlation between each of the plurality of time-series data sets; and determining a second temperature to be used for the search based on the index value.

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 transition control unit detects, when stochastically determining based on a temperature, energy changes, and a random number whether to accept any of a plurality of state transitions according to a relative relationship between the energy changes and thermal excitation energy, a minimum value among the energy changes. The transition control unit then subtracts, when the minimum value is positive, an offset obtained by multiplying the minimum value by a value M that is greater than 0 and less than or equal to 1 from each of the energy changes corresponding to the plurality of state transitions.

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 apparatus of searching for a combination of values of state variables with which a value of an evaluation function of an Ising-type becomes a local minimum or maximum, the data processing apparatus including: a memory configured to store first local fields representative of first change amounts of the value of the evaluation function in a case where a value of each of the state variables changes, first coefficients indicative of strength of influence of each of the state variables on each of constraint terms representative of a constraint condition, and second local fields represented by a sum of a total sum of products of each of the first coefficients and each of the state variables and a second coefficient related to the constraint condition; and a processor configured to perform: reading any of the first coefficients related to a first state variable being any of the state variables.

Abstract: An optimization method includes holding combining destination information indicating a combining destination neuron to be combined with a target neuron which is one of a plurality of neurons corresponding to a plurality of spins of an Ising model obtained by converting an optimization problem, the target neuron being different in a plurality of neuron circuits; holding a weighting coefficient indicating a strength of combining between the target neuron and the combining destination neuron, and outputting the weighting coefficient corresponding to the combining destination information; permitting an update of a value of the target neuron by using the weighting coefficient output and the value of the update target neuron, and outputting a determination result indicating whether or not the value of the target neuron is permitted to be updated; and determining the update target neuron based on the plurality of determination results respectively output and outputting the update target information.

Abstract: In an optimization apparatus, calculation circuits individually calculate a change in energy based on first local field values each associated with one of n bits (n is an integer greater than or equal to 2) amongst a plurality of bits corresponding to spins in an Ising model, values of the n bits, and one or more weight values representing strength of interaction among the n bits. The change in energy is caused by flips of the n bits. An update bit selection circuit selects the n bits for which value update is accepted, based on the magnitude relationship between thermal excitation energy and each of the calculated changes in energy. An update circuit flips the n bits, and also updates, based on the flips of the n bits, second local field values including the first local field values and each associated with the plurality of individual bits.

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.