Arithmetic Program with Genetic-Seeded One-Hot Ising Sampling
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Solution Overview
Problem
Existing binary variable sampling techniques, particularly those using the Ising model in a QUBO format, suffer from inefficient sampling and increased sampling times to achieve high accuracy solutions due to limited sampling regions and difficulty in expressing complex problems, leading to potential local solutions.
Innovation Solution
An arithmetic program and method that incorporates a genetic algorithm with a one-way one-hot constraint to generate initial points and convert them into bit arrays, combined with a factorization machine using digital annealing, to optimize the sampling process and reduce sampling times while ensuring compliance with constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a sampling technique using an Ising model in QUBO format is used to sequentially sample recommended points, then the sampling process can be performed, but the sampling region becomes limited and the number of sampling times increases
Solution Approach 1:
The patent applies preliminary action by generating multiple initial points using a genetic algorithm before the main sampling process. These pre-generated initial points expand the sampling region and provide better starting positions, reducing the number of iterations needed to achieve high-accuracy solutions.
Solution Approach 2:
The patent changes parameters by introducing a one-way one-hot constraint mechanism that modifies how binary variables are sampled. This constraint structure transforms the sampling approach, allowing the system to explore a broader solution space while maintaining the ability to achieve high-accuracy results with fewer sampling iterations.
2Productivity
If the Ising model is used for optimization, then recommended points can be retrieved, but the sampling region is limited leading to increased sampling times
Solution Approach 1:
The genetic algorithm is used in advance to generate diverse initial points that cover a broader region of the solution space. This preliminary exploration allows the subsequent Ising model sampling to start from multiple advantageous positions, improving both the coverage of the sampling region and the overall optimization speed.
Solution Approach 2:
The patent segments the optimization process into two distinct phases: a first sampling process using the Ising model and a second sampling process using genetic algorithm with one-way one-hot constraints. This segmentation allows each phase to contribute different strengths, with the first phase providing rapid sampling and the second phase expanding the exploration region.
3Measurement precision
If binary variable sampling is performed to achieve high accuracy solutions, then the optimization quality improves, but the number of sampling times increases
Solution Approach 1:
The one-way one-hot constraint mechanism is applied preliminarily to structure the binary variables in a way that facilitates more efficient sampling. By pre-organizing the variable structure, the system achieves high-accuracy solutions with fewer sampling iterations, improving sampling efficiency without sacrificing solution quality.
Solution Approach 2:
The patent introduces the one-way one-hot constraint as an intermediary mechanism between the binary variables and the sampling process. This intermediary structure enables more effective exploration of the solution space, allowing the system to achieve high accuracy while reducing the number of sampling times required.
Data Source
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AI summary
An arithmetic program causes a computer to execute a process including: when arithmetic processing is repeatedly performed in which an Ising model is created based on a training data group, a first recommended point that corresponds to a first set number is retrieved for the Ising model, a second recommended point that corresponds to a second set number is retrieved for the training data group by genetic algorithm, and each set of the first recommended point and a first evaluation value of the first recommended point and the second recommended point and a second evaluation value of the second recommended point is added to the training data group as training data, generating an integer array of a plurality of types as an initial point of each piece of the training data of the training data group; searching for the first recommended point by providing a constraint in which, when the first recommended point is retrieved, an index of a variable in the integer array is set to i and an index that represents a type of the variable is set to j for each piece of the training data, a case of i = j in the integer array in a matrix of i and j is set to 1 and another case is set to 0 to perform conversion into a bit array of i and j, and only one variable in each row is 1 in the matrix; and applying the genetic algorithm to a format of the integer array when the second recommended point is retrieved.