Multi-Valued Spin Optimization for Range-Constrained Energy Search
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Solution Overview
Problem
Existing Ising calculation devices face inefficiencies in solving combinatorial optimization problems with range constraints due to the use of numerous auxiliary spins, leading to biased spin state selection and prolonged search times.
Innovation Solution
An optimization apparatus and method that utilizes a reduced number of auxiliary spins, allowing them to take multiple values and calculates energy changes efficiently, combined with a temperature control mechanism and stochastic state transition determination to improve processing performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If numerous auxiliary spins are used to handle range constraints, then the constraint satisfaction is improved, but the time to reach minimum energy increases and search efficiency deteriorates
Solution Approach 1:
The patent combines multiple auxiliary spins into a single auxiliary spin that can take multiple values (0, 1, 2, ...) to represent the number of selected normal spins. This merging reduces the number of auxiliary elements from multiple binary spins to one multi-valued spin, thereby satisfying the range constraint with fewer elements and reducing the time to reach minimum energy.
Solution Approach 2:
The auxiliary spin is designed to serve multiple functions: it simultaneously represents the count of selected normal spins and enforces the range constraint through its interaction term. By making the auxiliary spin multi-functional, the patent eliminates the need for multiple separate auxiliary spins, improving search efficiency while maintaining constraint satisfaction.
2Reliability
If multiple auxiliary spins are used for range constraints, then the constraint coverage is improved, but the device complexity increases
Solution Approach 1:
The patent merges multiple auxiliary spins into a single auxiliary spin with multi-valued states. Instead of using several binary auxiliary spins to cover the range constraint, one auxiliary spin with states representing different count values is used, thereby reducing device complexity while maintaining comprehensive constraint coverage.
Solution Approach 2:
The patent transitions from multiple one-dimensional binary auxiliary spins to a single auxiliary spin with extended state dimensionality (multiple values). This dimensional change allows the system to represent the same constraint information with fewer elements, reducing overall device complexity.
3Reliability
If traditional auxiliary spins are used, then the constraint enforcement is maintained, but the search efficiency decreases
Solution Approach 1:
The patent combines the constraint enforcement function into a single auxiliary spin with reduced interaction terms. By merging multiple auxiliary spins into one, the number of interaction calculations during search is reduced, thereby improving search efficiency while maintaining effective constraint enforcement through the optimized interaction formula.
Solution Approach 2:
The patent changes the parameter representation from multiple binary auxiliary spins to a single auxiliary spin with multi-valued states. This parameter change reduces the computational burden during search operations while maintaining the same constraint enforcement capability, thereby improving search efficiency.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enhances the efficiency of solving combinatorial optimization problems by reducing the reliance on auxiliary spins and optimizing state transitions, thereby shortening the time to reach minimum energy solutions.
Implementation Method 1
a minimum energy search method using the simulated annealing method will be simply described. The Ising calculation device starts a search from an initial state in which zero or one is assigned to each variable of the evaluation function expressing a problem to be solved.
Data Source
AI summary
An optimization apparatus includes a processor. The processor configured to calculate a change amount of energy represented by an evaluation function of a case of changing a state of any one of a plurality of state variables so as to increase or decrease a value by 1 in a case of a state variable taking multiple values, the evaluation function representing the energy including the plurality of state variables, determine whether to set a state change in the state variable as a candidate according to a correlation between a threshold and a total change amount, stochastically determine whether to adopt the state change set as the candidate, calculate post-transition energy after executing a state transition of the state variable according to the state change, and obtain minimum energy by setting the post-transition energy as the minimum energy when the post-transition energy is less than the minimum energy.