Machine Learning With Continuous Relaxation for Diverse Discrete Solutions
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Solution Overview
Problem
Existing combinatorial optimization methods, such as those using Ising machines and continuous relaxation simulated annealing, struggle to efficiently find multiple solutions due to issues with penalty coefficients and local solutions, leading to inefficiencies and limited solution diversity.
Innovation Solution
A machine learning program that trains a model using a cost function where discrete variables are relaxed to continuous matrices, allowing for simultaneous optimization with multiple penalty coefficients and Bayesian optimization of these coefficients to obtain a plurality of solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If continuous relaxation solving method is used to search for optimum solution, then search efficiency is improved, but ability to obtain multiple solutions deteriorates
Solution Approach 1:
The patent segments the optimization process by introducing multiple penalty coefficients (λ1, λ2, ..., λk) that divide the search space into different regions. Each penalty coefficient guides the search toward different types of solutions, enabling the system to obtain multiple diverse solutions while maintaining search efficiency through the continuous relaxation framework.
2Manufacturing precision
If penalty coefficient method is used in combinatorial optimization, then solution accuracy is improved, but reliance on penalty coefficients increases and solution diversity decreases
Solution Approach 1:
The patent dynamically adjusts penalty coefficients during the training process. By varying penalty coefficients across different training iterations and using multiple penalty coefficients simultaneously, the system maintains solution accuracy while exploring diverse solution spaces, thus reducing reliance on any single penalty coefficient value and increasing solution diversity.
Solution Approach 2:
The patent changes the parameter values of penalty coefficients during the optimization process. By using multiple different penalty coefficient values (λ1, λ2, ..., λk) and adjusting them dynamically, the system achieves both accurate solutions and diverse solution sets, overcoming the limitation of fixed penalty coefficient methods.
3Device complexity
If discrete variables are relaxed to continuous matrix, then optimization process is simplified, but obtaining discrete solutions becomes difficult
Solution Approach 1:
The patent performs preliminary relaxation of discrete variables to continuous matrices to simplify the optimization process. Then, in a subsequent step, it applies discrete rounding techniques to convert the continuous solutions back to discrete solutions. This two-stage approach maintains the simplicity of continuous optimization while ensuring high-quality discrete solutions are obtained.
Data Source
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AI summary
A machine learning program for causing a computer to execute a process includes training a machine learning model by machine learning that uses a cost function in which each element of a matrix obtained by relaxing a discrete variable to be optimized to a continuous matrix becomes a discrete optimization problem as a cost function in a search process that performs a search by adopting continuous relaxation into the discrete optimization problem.