Ising Model Constraint Coefficient Determination via Expected Cost Change
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Solution Overview
Problem
Existing methods for determining the constraint coefficient in combinatorial optimization problems using Ising machines require numerous adjustments and significant time, making it inefficient for obtaining high-quality solutions.
Innovation Solution
The proposed system calculates the expected value of the change in the cost term when transitioning from a constraint satisfaction solution to a constraint violation solution, using this value to determine the constraint coefficient, thereby reducing the need for multiple adjustments and shortening the time required to find an appropriate coefficient.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the constraint coefficient is set too small, then the solution space search is improved, but constraint violation solutions are generated frequently
Solution Approach 1:
The patent calculates the expected change amount of the cost term before actually performing the optimization search. This preliminary calculation of E[ΔC(x)] allows the system to determine an appropriate constraint coefficient in advance, preventing constraint violations before they occur during the search process.
Solution Approach 2:
The patent establishes a feedback mechanism where the expected cost change is calculated based on the constraint coefficient, and this information is used to adjust and determine the optimal constraint coefficient. The processing circuit uses the calculated expected value to feedback and set the constraint coefficient that balances search efficiency and constraint satisfaction.
2Reliability
If the constraint coefficient is set too large, then constraint satisfaction is improved, but the energy barrier between constraint satisfaction solutions increases hindering solution space search
Solution Approach 1:
The patent dynamically determines the constraint coefficient by calculating the expected cost change E[ΔC(x)] rather than using a fixed or manually set value. This parameter adjustment based on calculated expectations allows the system to find the optimal balance point where constraints are satisfied without creating excessive energy barriers.
3Measurement precision
If repeated adjustment of the constraint coefficient is performed, then the accuracy of the solution is improved, but the time required to determine the coefficient increases significantly
Solution Approach 1:
The patent performs preliminary calculation of the expected cost change E[ΔC(x)] to determine the constraint coefficient before the optimization search. This upfront calculation eliminates the need for repeated adjustments during the search process, significantly reducing the time required while maintaining solution accuracy.
Solution Approach 2:
The system determines the constraint coefficient autonomously by calculating E[ΔC(x)] itself, without requiring external manual adjustment or iterative trial-and-error processes. The processing circuit self-determines the optimal coefficient based on the calculated expected value, eliminating time-consuming repeated adjustments.
Data Source
AI summary
An information processing system configured to calculate a combinatorial optimization problem that includes a constraint condition based on an energy function of an Ising model represented by a sum of a cost term and a constraint term that corresponds to the constraint condition, the information processing system including: a processing circuit configured to obtain problem information of the combinatorial optimization problem, calculate, based on the problem information, an expected value of a change amount of the cost term when transition from a solution that satisfies the constraint condition to a solution that does not satisfy the constraint condition occurs, determine a coefficient of the constraint term based on the expected value, and output information of the energy function using the determined coefficient; and a search circuit that searches for a ground state of the Ising model based on the output information.