Cyclic Scheduling Method for Integer Linear Programming
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Solution Overview
Problem
Existing methods for solving integer linear programming (ILP) problems with cyclic 0-1 matrices are inefficient due to the high computational complexity of identifying cyclically distinct solutions, particularly in applications like cyclic scheduling, transportation timetabling, and data packet transmission.
Innovation Solution
A cyclic combinatorial integer linear programming method that replaces the partition and cyclic permutation steps with a procedure to identify dominant cyclically distinct dual solutions, reducing the number of iterations and improving computational efficiency by eliminating the most intensive step.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If partition and cyclic permutation steps are used to identify cyclically distinct solutions, then comprehensive solution coverage is achieved, but computational complexity increases significantly
Solution Approach 1:
The patent extracts and eliminates the most computationally intensive step (cyclic permutation) from the solution process. By recognizing that cyclic symmetry already provides sufficient solution coverage, the method removes the need for exhaustive cyclic permutation operations while maintaining solution completeness through the reduced procedure of identifying only dominant cyclically distinct dual solutions.
Solution Approach 2:
The patent segments the solution process into identifying only the essential components (dominant cyclically distinct dual solutions) rather than processing all possible cyclic permutations. This segmentation allows the method to focus computational resources on the critical subset of solutions that determine the optimal objective function value.
2Measurement precision
If exhaustive cyclic permutation is performed to ensure all cyclically distinct solutions are found, then solution accuracy is improved, but computational time increases
Solution Approach 1:
The patent replaces the expensive exhaustive cyclic permutation process with a cheaper, simplified procedure for identifying dominant cyclically distinct dual solutions. This substitution maintains solution accuracy by focusing on the essential solutions that determine optimality, while dramatically reducing computational time and resources required.
3Adaptability or versatility
If the complete cyclic permutation procedure is used, then all possible solutions are enumerated, but the number of iterations becomes excessively large
Solution Approach 1:
The patent applies partial action by enumerating only the necessary subset of cyclically distinct solutions (dominant dual solutions) rather than all possible solutions. This partial enumeration is sufficient to determine the optimal objective function value, achieving the required solution coverage without the excessive iterations of complete cyclic permutation.
Data Source
AI summary
A method, computer software product and system for solving cyclic scheduling problems. Specifically, the present disclosure significantly improves the method in a previous patent (H. K. Alfares, 2011, “Cyclic Combinatorial Method and System”, U.S. Pat. No. 8,046,316), by eliminating a time-consuming combinatorial procedure. A procedure is described which significantly decreases the number of iterations, and hence computational time and cost. The processes of the present disclosure have many applications in cyclic workforce scheduling, cyclic transportation system scheduling, cyclic scheduling of data packet transmitting as applied to networks having a plurality of nodes and cyclic production scheduling.