Linear Programming Division Granularity for Time-Constrained Solutions
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Solution Overview
Problem
Large-scale linear programming problems often exceed user-defined allowable time for solution, as the time needed to solve them increases exponentially with problem size, making it impossible to obtain a solution within the allotted time.
Innovation Solution
The problem is divided into smaller partial problems based on determined division granularity, with objective functions and constraint expressions created for each partial problem using the original problem's data and past allocation results, allowing for sequential solving to obtain a solution within the allowable time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a large-scale linear programming problem is solved directly, then the solution accuracy is maintained, but the solution time exceeds the allowable time
Solution Approach 1:
The patent divides the large-scale linear programming problem into multiple partial problems based on determined division granularity. Each partial problem is solved sequentially to obtain intermediate results, which are then integrated to form the final solution. This segmentation approach reduces the computational burden of each individual problem while maintaining the accuracy of the overall solution.
2Loss of time
If the problem size is reduced by division, then the solution time is shortened, but the problem complexity increases
Solution Approach 1:
The patent systematically segments the original problem into partial problems with clearly defined boundaries and relationships. By establishing a structured division methodology where each partial problem can be solved independently and then integrated, the patent manages complexity through organization rather than elimination.
Solution Approach 2:
The patent employs feedback mechanisms where intermediate results from solving partial problems are used to inform and adjust subsequent solving steps. This feedback loop ensures that the segmentation process remains controlled and that the integration of partial solutions maintains consistency with the original problem constraints.
3Productivity
If the division granularity is increased, then the number of partial problems decreases, but the solution time for each partial problem increases
Solution Approach 1:
The patent dynamically adjusts the division granularity parameter based on the characteristics of the specific linear programming problem and computational resources available. By optimizing this parameter, the patent finds the optimal balance between the number of partial problems and the computational effort required for each, maximizing overall processing efficiency.
Data Source
AI summary
An information processing device configured to perform processing, the processing including: determining a division granularity when a linear programming problem is divided into a plurality of partial problems on the basis of an allowable time needed to solve the linear programming problem to be solved; creating an objective function of each of partial problems divided from the linear programming problem on the basis of the determined division granularity from an objective function of the linear programming problem; creating a constraint expression of each of the partial problems on the basis of a constraint expression group of the linear programming problem and past allocation result data regarding a variable included in the linear programming problem; and obtaining a solution for the linear programming problem by sequentially solving each of the partial problems on the basis of the objective function and the constraint expression created for each of the partial problems.