Sum-Product Objective Function for Assignment Problem Decomposition
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Solution Overview
Problem
Assignment problems often involve large solution spaces, making it impractical to exhaustively search for optimal solutions, and existing methods struggle to efficiently find near-optimal solutions within a reasonable time frame.
Innovation Solution
The use of a sum-product objective function decomposes the assignment problem into smaller optimization subproblems, allowing for a 'divide-and-conquer' approach that leverages quantum computers or other specialized processors to iteratively explore the solution space and find near-optimal solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If exhaustive search is used to find optimal solution, then solution optimality is improved, but time consumption increases exponentially
Solution Approach 1:
The patent applies segmentation by decomposing the assignment problem into multiple smaller subproblems based on a partition of assignment options. Each subproblem involves a subset of assignees and a specific assignment option set, making them computationally tractable. The overall optimal solution is then constructed by combining solutions to these subproblems, thus achieving global optimality without exhaustive search of the entire solution space.
Solution Approach 2:
The patent introduces an intermediary structure - a partition of assignment options into multiple sets - that mediates between the original complex assignment problem and its solvable subproblems. This partition acts as a bridge, allowing the problem to be broken down systematically while preserving the ability to find the global optimum through coordinated solution of subproblems.
2Reliability
If solution space is explored exhaustively, then absolute optimum is guaranteed, but computational complexity increases
Solution Approach 1:
The patent segments the large solution space into smaller, manageable sub-solution spaces corresponding to different assignment option sets in the partition. Each subproblem searches only its localized solution space rather than the entire space, dramatically reducing computational complexity while maintaining reliability through systematic combination of subproblem solutions.
Solution Approach 2:
The patent performs partial action by solving subproblems for specific assignment option sets rather than attempting to solve the complete problem in one exhaustive search. This partial approach to each subproblem, when coordinated across all partitions, achieves the complete solution with reduced computational burden.
3Productivity
If near-optimal solutions are found quickly, then time efficiency is improved, but solution optimality may be compromised
Solution Approach 1:
The patent segments the optimization task into subproblems that can be solved efficiently and quickly. Each subproblem focuses on a specific assignment option set, allowing rapid solution finding. The combination of these quick subproblem solutions yields the global optimal solution, thus achieving both time efficiency and solution optimality simultaneously.
Data Source
AI summary
Various embodiments include systems, methods, and non-transitory computer-readable media for processing a computational problem that embodies, describes, or defines an assignment problem (or any other problem) with an objective function in sum-product form.