Patent Document ID: 8046316
Application ID: 11878139
Patent Flag: 1

Claim One:
1. A cyclic combinatorial integer linear programming optimization method for optimizing constraint models in scheduling problems, comprising the steps of: identifying a linear objective function and its linear constraints for optimization; codifying the objective function and the linear constraints as a plurality of matrices and storing the plurality of matrices in computer readable memory; enumerating cyclically distinct combinations of basic dual variables related to any of the matrices having cyclic 0-1 properties so as to identify cyclically distinct solutions, wherein said enumerating includes using a procedure that generates monotonic partitions, said procedure comprising the steps of: expressing a partition of a positive integer n into m parts (m≦n) as n=V 1 +V 2 +. .. +V m , where Vi>0, i=1,. .. , m; denoting a number of unordered partitions of n into m parts by P m (n), such that P 1 (n)=P n (n)=1, P 2 (n)=└n/2┘; and determining remaining values of P m (n) by means of the relationship P m (n)=P 1 (n−m)+P 2 (n−m)+. .. +P m (n−m) such that if n≦3, n−m≦1, or v m , the current combination is stored in the computer readable memory and the next partition is processed; applying a set of rules to the cyclically distinct solutions in order to provide a set of dominant solutions to thereby solve the problem; and displaying the set of dominant solutions to a user.