Constraint Coefficient Tuning in Combinatorial Search
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Solution Overview
Problem
Existing combinatorial optimization systems face challenges in determining an appropriate constraint coefficient for balancing constraint satisfaction and solution quality, leading to difficulties in reaching optimal solutions.
Innovation Solution
A data processing apparatus and method that dynamically adjusts constraint coefficients by comparing solutions using different evaluation functions and determining whether constraints are satisfied, iteratively refining the search process to improve solution quality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If a fixed constraint coefficient is used in the evaluation function, then the search process is simple to implement, but the solution quality deteriorates due to inability to balance constraint satisfaction and objective function optimization
Solution Approach 1:
The constraint coefficient is changed from a fixed value to a dynamic value that varies during the search process. The coefficient is updated based on whether constraints are satisfied by obtained solutions, allowing the system to adaptively balance constraint satisfaction and objective function optimization throughout the search process
Solution Approach 2:
The evaluation function's constraint coefficient parameter is modified during the search process based on constraint satisfaction status. When constraints are violated, the coefficient is increased to penalize violations more heavily; when constraints are satisfied, the coefficient can be reduced to focus on objective function optimization
2Reliability
If the constraint coefficient is increased to enforce constraint satisfaction, then constraint compliance improves, but the search performance deteriorates due to overly restrictive search space
Solution Approach 1:
The constraint coefficient dynamically adjusts based on the satisfaction status of constraints during the search process. This dynamic adjustment allows the search to explore a broader space when constraints are not yet satisfied, while enforcing stricter compliance as the search progresses and solutions improve
Solution Approach 2:
The constraint coefficient is periodically updated at specific intervals or milestones during the search process, allowing the system to alternate between exploration phases (lower coefficient) and exploitation phases (higher coefficient), thereby maintaining both search performance and constraint satisfaction
3Manufacturing precision
If manual adjustment of constraint coefficient is performed, then solution quality can be optimized, but user intervention time increases
Solution Approach 1:
The system automatically determines and adjusts the constraint coefficient based on the constraint satisfaction status of obtained solutions, eliminating the need for manual user intervention. The algorithm self-regulates the coefficient to achieve optimal balance between constraint satisfaction and objective function optimization
Solution Approach 2:
The system uses feedback from constraint satisfaction checks to automatically adjust the constraint coefficient. The satisfaction status of constraints by obtained solutions feeds back into the evaluation function, creating a closed-loop control system that automatically optimizes the coefficient without user intervention
Data Source
AI summary
A storage unit stores first solutions each being a set of values of state variables. A processing unit obtains, from a search unit that searches for a solution based on a first evaluation function, a second solution obtained through search using an initial solution generated from the first solutions. The first evaluation function includes a constraint term indicating a violation degree of constraints on the state variables and a first constraint coefficient indicating a weight for the constraint term. The processing unit replaces any stored first solution with the second solution, depending on comparison between evaluation values of each first solution and the second solution, indicated by a second evaluation function obtained by replacing the first constraint coefficient with a second constraint coefficient, and determines the first constraint coefficient for next search, based on whether the constraints are satisfied by the second solution and/or other solutions obtained through searches.