K-spin Parameter Setting for Discrete Optimization Solvers
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Solution Overview
Problem
Existing discrete optimization solvers, such as the D-Wave device and Hamze-de Freitas-Selby algorithm, face limitations in connectivity, requiring complex mapping and parameter setting processes that are computationally costly and restricted to 2-spin problems, making it challenging to solve discrete optimization problems with different connectivity than the solver graph.
Innovation Solution
A method that converts a discrete optimization problem into a K-spin problem, allowing for parameter setting and solving using a K-spin optimization solver, by computing a parameter Cj for each variable, evaluating a variable selection criterion, and distributing parameters J and h to reduce the problem, enabling solution with a quantum annealer or other optimization solvers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Minor Embedding techniques are used to map discrete optimization problem to solver graph, then the problem can be solved on solvers with limited connectivity, but the parameter setting process becomes computationally costly and complex
Solution Approach 1:
The patent transforms the parameter setting problem by changing the approach from empirical parameter finding to a systematic method based on computing Cj parameters from the embedded graph structure. This parameter transformation resolves the contradiction by making the parameter setting process deterministic and computationally efficient while maintaining compatibility with solvers having different connectivity patterns.
Solution Approach 2:
The patent segments the parameter setting process into distinct steps: computing Cj for each variable, evaluating selection criteria, fixing variables that meet criteria, and distributing parameters J and h to remaining variables. This segmentation makes the complex parameter setting process manageable and efficient, resolving the contradiction between adaptability and complexity.
2Reliability
If empirical parameter finding is used for 2-spin problems, then the parameter setting can be completed, but the process requires significant computational resources and time
Solution Approach 1:
The patent performs preliminary actions by computing the Cj parameter for each variable before the actual solving process. This pre-computation of critical parameters eliminates the need for time-consuming empirical parameter finding during execution, thereby resolving the contradiction between solution reliability and time efficiency.
Solution Approach 2:
The method enables the system to self-determine optimal parameters through the Cj computation and selection criterion evaluation, eliminating the need for external empirical parameter tuning. This self-service approach ensures solution correctness while dramatically reducing the time required for parameter setting.
3Ease of manufacture
If the optimization solver uses a fixed graph structure, then the solver implementation is simplified, but it cannot solve discrete optimization problems with different connectivity patterns
Solution Approach 1:
The patent introduces the embedded graph Gemb as an intermediary structure that bridges the discrete optimization problem with the solver's fixed graph structure. This intermediary allows the solver to maintain its simple fixed structure while the embedding layer handles the connectivity transformation, resolving the contradiction between implementation simplicity and connectivity flexibility.
Data Source
AI summary
A method and system are disclosed for setting parameters of a discrete optimization problem embedded to an optimization solver and solving it. The method comprises converting the discrete optimization problem to a K-spin problem, wherein the K-spin problem is defined asminHK-spin=∑j=1Nhjsj+∑k=2K∑j1j2…jkJj1j2…jksj1sj2…sjkwherein parameter K is the order of the discrete optimization problem, wherein parameter J is a coupling value between two vertices and parameter h is a local field value; generating a reduced K-spin problem and a corresponding reduced embedded graph; setting the parameter J of each edge of the reduced embedded graph; setting the parameter h of each given vertex of the reduced embedded graph; setting the parameter J of each edge of the reduced embedded graph connecting two vertices representing the same corresponding variable in the reduced K-spin problem; solving the reduced K-spin problem and combining at least one solution obtained from the optimization solver with a partial solution list.