Calculation Device Solving Combinatorial Optimization via Variable Segmentation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Combinatorial optimization problems are challenging due to the 'combinatorial explosion' issue, where the number of combinations increases exponentially with problem size, making it difficult to find optimal or approximate solutions within a practical time frame.
Innovation Solution
A calculation device and method that updates variables alternately and sequentially for each unit time, using real-number representations, and applies specific threshold-based changes to variables to efficiently solve combinatorial optimization problems through parallel processing and distributed algorithms, such as the simulated bifurcation algorithm.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional sequential algorithms are used to solve combinatorial optimization problems, then solution accuracy can be maintained, but calculation time increases exponentially with problem size due to combinatorial explosion
Solution Approach 1:
The patent segments the combinatorial optimization problem into multiple independent sub-problems by dividing the set of discrete variables into groups. Each sub-problem is solved independently using parallel processing, avoiding the exponential time complexity of solving the entire problem sequentially. This segmentation allows the system to maintain solution accuracy while dramatically reducing calculation time for large-scale problems.
Solution Approach 2:
The patent implements a dynamic parallel processing approach where multiple processors simultaneously update different sets of variables based on real-time feedback from the objective function evaluation. The system dynamically adjusts the search direction and step size for each variable group, enabling faster convergence to optimal solutions without sacrificing accuracy even as problem size increases.
2Adaptability or versatility
If the problem size increases to handle real-world applications, then the applicability and value of the solution increases, but the number of combinations increases exponentially making optimal solutions unattainable
Solution Approach 1:
The patent divides large-scale combinatorial optimization problems into smaller manageable sub-problems that can be processed in parallel. By segmenting the variable space and using distributed computing resources, the system can handle real-world problem sizes (hundreds to thousands of variables) without the computational complexity exploding, thereby improving adaptability to practical applications.
Solution Approach 2:
The patent develops a universal parallel processing framework that can handle various types of combinatorial optimization problems (maximization, minimization, constrained, unconstrained) using the same fundamental approach. This multi-functional algorithm structure allows the system to adapt to different problem scales and types without requiring fundamentally different computational approaches, reducing the effective complexity for diverse real-world applications.
3Measurement precision
If more computational resources are allocated to solve larger problems, then solution quality can be maintained, but the cost and time consumption increase significantly
Solution Approach 1:
The patent implements dynamic resource allocation across parallel processors based on the convergence status and complexity of different variable sub-groups. The system continuously monitors solution quality metrics and dynamically adjusts the computational effort distributed to each processor, maintaining high solution quality while optimizing calculation efficiency. This dynamic approach prevents wasteful allocation of resources to already-converged sub-problems.
Solution Approach 2:
The patent ensures continuous productive computation across all parallel processors by implementing an iterative update scheme where each processor continuously refines its portion of the solution based on feedback from the objective function. This continuous useful action eliminates idle computational periods and maintains high productivity throughout the optimization process, achieving both high solution quality and computational efficiency.
Data Source
AI summary
According to an embodiment, a calculation device includes a memory and one or more processors configured to update, for elements each associated with first and second variables, the first and second variables for each unit time, sequentially for the unit times and alternately between the first and second variables. In a calculation process for each unit time, the one or more processors are configured to: for each of the elements, update the first variable based on the second variable; update the second variable based on the first variables of the elements; when the first variable is smaller than a first value, change the first variable to a value of the first value or more and a threshold value or less; and when the first variable is greater than a second value, change the first variable to a value of the threshold value or more and the second value or less.