Auxiliary-Variable Function Transformation for Higher-Order Optimization
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Solution Overview
Problem
Existing combinatorial optimization problems face difficulties in handling higher-order forms when the evaluation function is given in quadratic form, making it challenging to effectively handle higher-order terms.
Innovation Solution
A transformation apparatus and method that utilize auxiliary variable constraints to transform an evaluation function into a higher-order form by introducing auxiliary variables and penalty terms, maintaining equivalence with the original function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If an evaluation function is given in quadratic form, then it is possible to make solution seeking more efficient, but it is difficult to handle an input of higher-order form
Solution Approach 1:
The patent introduces auxiliary variables as intermediary elements that bridge the gap between higher-order terms and the quadratic form requirement. These auxiliary variables act as mediators that transform the representation of higher-order interactions while maintaining the quadratic structure that the solver can efficiently process. The auxiliary variables enable the system to handle higher-order problems without sacrificing the efficiency benefits of quadratic form optimization.
2Adaptability or versatility
If auxiliary variables are introduced to handle higher-order terms, then higher-order forms can be handled, but the complexity of the evaluation function increases
Solution Approach 1:
The patent segments the higher-order evaluation function into multiple quadratic components by introducing auxiliary variables. Each auxiliary variable represents a specific higher-order interaction, allowing the complex higher-order function to be broken down into manageable quadratic segments. This segmentation maintains the overall functionality while making the problem tractable for quadratic solvers and reducing the apparent complexity at each processing stage.
Data Source
AI summary
A transformation apparatus includes: a selecting unit that selects an auxiliary variable constraint from a list of auxiliary variable constraints represented in a form in which a product of variables matches another variable; and a substituting unit that performs a substitution process based on the auxiliary variable constraint selected by the selecting unit and thereby transforms an evaluation function to be transformed represented by a polynomial with a plurality of variables into a higher-order evaluation function than the evaluation function.