MILP Decomposition with Graph-Based Subproblems
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Solution Overview
Problem
Current methods for solving mixed-integer linear programming (MILP) problems require complex input and increased processing resources, making them inefficient and difficult to manage, especially when dealing with large or complex problems.
Innovation Solution
The approach involves decomposing MILP problems into a master problem and graph-based subproblems, using minimal syntax query instructions to apply graph-based algorithms, allowing for parallel solution derivation and reducing the complexity of input and processing requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If traditional MILP solving methods are used, then the problem can be solved using standard mathematical programming algorithms, but the input complexity and processing resource requirements increase significantly
Solution Approach 1:
The patent segments the MILP problem into a master problem and multiple graph-based subproblems. The master problem handles the overall optimization framework while subproblems handle specific graph-related computations. This segmentation reduces input complexity by allowing users to specify problems in terms of graphs and constraints rather than full MILP formulations, while enabling parallel processing of subproblems to reduce overall processing resource requirements.
Solution Approach 2:
The patent introduces graph-based algorithms as intermediaries between the user's high-level problem specification and the underlying MILP solver. The graph-based subproblems act as mediators that translate complex MILP constraints into graph theory problems, which are then solved using specialized algorithms. This intermediary layer simplifies the input interface while managing computational complexity through efficient graph algorithms.
2Productivity
If traditional MILP solving methods are used, then the problem can be solved using mathematical programming algorithms, but the processing time increases for large or complex problems
Solution Approach 1:
By dividing the MILP problem into master and subproblems, the patent enables parallel processing of independent subproblems. This segmentation allows multiple computations to occur simultaneously, significantly reducing total processing time for large-scale problems while maintaining solution accuracy through the iterative coordination between master and subproblems.
Solution Approach 2:
The patent performs preliminary decomposition of the MILP problem into graph-based subproblems before executing the main optimization algorithm. This preliminary action prepares the problem structure in advance, allowing the solver to work with simpler, more manageable subproblems rather than the full complex MILP formulation, thereby reducing overall computation time.
3Ease of operation
If traditional MILP solving methods are used, then the problem can be solved using standard algorithms, but the difficulty of managing and implementing increases
Solution Approach 1:
The patent introduces graph-based algorithms as intermediaries that bridge user-friendly problem specifications and complex MILP solving. Users can specify problems in terms of graphs, nodes, and constraints rather than requiring detailed MILP formulations. The graph-based subproblems automatically handle the translation and computation, simplifying both problem specification and implementation while maintaining rigorous mathematical programming capabilities.
Solution Approach 2:
The patent implements self-service through automated decomposition, where the system automatically divides the MILP problem into master and subproblems without requiring manual intervention. The graph-based algorithms automatically handle the complexity of problem breakdown and coordination, freeing users from manual implementation details while maintaining full control over the solving process.
Data Source
AI summary
Embodiments include techniques to receive computer-executable query instructions to solve a MILP problem, the query instructions including a first expression conveying an objective function and side constraint that define a master problem of the MILP problem, a second expression conveying a mapping of graph data to a graph, and a third expression conveying a selection of a graph-based algorithm to solve a subproblem of the MILP problem; a subproblem component to replace the third expression with a fourth expression during decomposition of the MILP problem, the fourth expression including instructions to implement the graph-based algorithm to solve the subproblem; and an execution control component to perform iterations of solving the MILP problem that include executing the first expression to derive a solution to the master problem; and executing the fourth expression to derive a solution to the subproblem based on the mapping and the master problem solution.