Quadratic Assignment Matrix Memory Reduction
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Solution Overview
Problem
Existing methods for solving large-scale quadratic assignment problems face challenges in reducing memory footprint, particularly as the scale of the assignment problem increases, leading to insufficient reduction in memory usage due to the large amount of information required for storing flow and distance matrices.
Innovation Solution
A data processing apparatus and method that selectively stores either a flow matrix or a distance matrix, generating patterned matrix elements on demand to calculate changes in the evaluation function, allowing for reduced memory usage by avoiding the need to store both matrices simultaneously.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If both flow matrix and distance matrix are stored in memory, then complete information is available for calculation, but memory footprint increases significantly
Solution Approach 1:
The patent extracts only one matrix (either flow matrix or distance matrix) from the pair and stores it in memory, while generating the other matrix on-demand through computation. This extraction principle reduces memory storage requirements while maintaining the ability to obtain complete information when needed.
Solution Approach 2:
The patent implements a dynamic approach where the second matrix is generated on-demand based on computational needs rather than being statically stored. The system dynamically computes matrix elements using stored data and generation rules, allowing memory usage to adapt to actual calculation requirements rather than pre-allocating for both matrices.
2Measurement precision
If conventional techniques store and compute with both flow and distance matrices, then accurate evaluation function calculation is achieved, but memory capacity is insufficient for large-scale problems
Solution Approach 1:
The patent introduces an intermediary computation process that generates the second matrix element from stored data and generation rules. This intermediary step allows the system to obtain complete matrix information for accurate evaluation function calculation without physically storing both complete matrices in memory, thus bridging the gap between memory constraints and calculation accuracy requirements.
Data Source
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AI summary
A storage unit stores one of flow and distance matrices for an assignment problem having an evaluation function represented by a matrix operation of the flow and distance matrices, and a processing unit selects first and second entities from entities to be assigned to destinations, reads at least one first matrix element corresponding to the first and second entities from the stored flow or distance matrix, generates at least one second matrix element for the other of the flow and distance matrices, which is a patterned matrix, based on the first and second entities, calculates a change in the value of the evaluation function resulting from an assignment change of changing the destination of the first or second entity, using the first and second matrix elements, determines based on the change whether to allow the assignment change, and updates an assignment state when determining to allow the assignment change.