A combinatorial optimization system includes an input unit to which a multivalued optimization problem is input, a halving unit configured to perform halving to select half of candidate solutions of the multivalued optimization problem, and an optimization control unit configured to obtain an optimal solution of the multivalued optimization problem by causing the halving unit to repeat the halving.

A system comprises a memory, a plurality of memory banks, and an organizer. The memory is configured to store elements of a matrix, wherein the elements are distributed into overlapping subgroups and each shares at least one element of the matrix with another overlapping subgroup. The plurality of memory banks is configured to store the overlapping subgroups, wherein the subgroups are distributed among the memory banks using a circular shifted pattern. The organizer is configured to read specific ones of the overlapping subgroups in the plurality of memory banks in a specified pattern associated with transposing the matrix.

A method is provided for solving a given combinatorial problem includes providing a function that has been established for a family of combinatorial problems including the given combinatorial problem. For each problem in the family, the function relates a secondary measure of the problem to a quality metric of a characteristic solution to the problem. The function may be applied to a value of the secondary measure for the given problem to obtain a value of the quality metric of the characteristic solution to the given problem. The given problem may be solved to obtain a solution to the given problem; and the solution evaluated based on comparison of a value of the quality metric of the solution, and the value of the quality metric of the characteristic solution. And in at least one instance based on the evaluation, the solution may be communicated to guide performance of a task.

A combinatorial optimization system includes an input unit to which a multivalued optimization problem is input, a halving unit configured to perform halving to select half of candidate solutions of the multivalued optimization problem, and an optimization control unit configured to obtain an optimal solution of the multivalued optimization problem by causing the halving unit to repeat the halving.