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: 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: 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.