Constraint-Aware Optimization Using Regression and Annealing
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Solution Overview
Problem
Existing optimization methods struggle with efficiently incorporating restrictions into cost functions, making it difficult to prevent implausible solutions and requiring complex penalty term representations.
Innovation Solution
An optimization method that includes a series of regression, optimization, and determination processes, with feedback loops and correction mechanisms to embed restrictions, using factorization machines and quantum/classical annealing to refine solutions based on threshold conditions and restrictions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If restrictions are transformed into penalty terms and added to the cost function, then implausible solutions can be prevented, but it becomes difficult to determine how to express the penalty term and increases calculation complexity
Solution Approach 1:
The patent divides the cost function into two separate components: the original cost function and a separate penalty function. The penalty function is constructed independently based on restriction conditions, and then added to the original cost function. This segmentation allows each function to be designed and optimized separately, reducing the complexity of determining the overall cost function structure.
Solution Approach 2:
The patent introduces a penalty function as an intermediary element that mediates between the original cost function and the restriction conditions. This penalty function serves as a bridge, translating restriction conditions into a form that can be integrated with the cost function without directly complicating the cost function's structure. The penalty function absorbs the complexity of restriction enforcement.
2Reliability
If penalty terms are added to the cost function to enforce restrictions, then solution constraints are satisfied, but calculation efficiency decreases
Solution Approach 1:
The patent performs preliminary classification of data into feasible and infeasible categories based on restriction conditions before the main optimization calculation. By pre-identifying and removing infeasible data points that would generate penalty terms, the actual optimization calculation operates on a reduced, pre-filtered dataset. This preliminary action eliminates unnecessary penalty term calculations during the main optimization process, thereby improving calculation efficiency while still ensuring restriction satisfaction.
Data Source
AI summary
This optimization method has a first regression process, a first optimization process, and a first determination process. The first regression process regresses a first function using a first training data group formed from combinations of an explanatory variable column and an objective variable. The first optimization process performs optimization of the first function and obtains a first explanatory variable column that is an optimal solution and a first predicted value obtained by substituting the first explanatory variable column into the first function. The first determination process determines whether a relationship between the first predicted value and a threshold value satisfies a condition. In a case in which the condition is not satisfied, a combination of the first explanatory variable column and the first predicted value is added to the first training data group as one of the combinations of the explanatory variable column and the objective variable.