Penalty Function Coefficient Tuning for Constrained Optimization
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Solution Overview
Problem
Existing methods for solving combinatorial optimization problems, such as binary quadratic programming, face challenges in determining appropriate constraint coefficients for penalty functions, leading to either insufficient constraint satisfaction or suboptimal solution quality.
Innovation Solution
A data processing apparatus and method that adjusts constraint coefficients based on the satisfaction status of constraints for stored solutions, using a penalty function to dynamically control the influence of constraints during the search process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If fixed constraint coefficients are used in the penalty function, then the evaluation function structure is simple, but constraint satisfaction is insufficient or solution quality becomes suboptimal
Solution Approach 1:
The patent applies dynamics by transforming fixed constraint coefficients into dynamic coefficients that automatically adjust based on constraint satisfaction status. The adjustment unit continuously modifies coefficients during the search process, enabling the evaluation function to adapt its structure in response to solution quality and constraint compliance, thereby resolving the contradiction between simplicity and reliability.
Solution Approach 2:
The patent implements feedback mechanisms where the satisfaction status of constraints is monitored and fed back to the adjustment unit. This feedback loop enables automatic modification of constraint coefficients based on actual constraint compliance, improving constraint satisfaction without requiring complex manual tuning of the evaluation function structure.
2Manufacturing precision
If constraint coefficients are manually tuned, then solution quality may improve, but the time and effort required increases significantly
Solution Approach 1:
The patent enables self-service by implementing an automatic adjustment unit that autonomously tunes constraint coefficients without human intervention. The system monitors constraint satisfaction status and automatically modifies coefficients to optimize solution quality, eliminating the time-consuming manual tuning process while maintaining high solution precision.
Solution Approach 2:
The patent applies parameter changes by dynamically modifying constraint coefficients based on real-time constraint satisfaction status. This automatic parameter adjustment allows the system to adapt to different problem instances and search stages, achieving high solution quality without manual intervention and significantly reducing the time required for coefficient tuning.
3Reliability
If constraint coefficients are increased to enforce constraints, then constraint satisfaction improves, but solution quality deteriorates due to suboptimal exploration
Solution Approach 1:
The patent resolves this contradiction through dynamic coefficient adjustment that adapts to the search process. Instead of uniformly increasing coefficients, the system selectively adjusts coefficients based on which specific constraints are violated and the current search stage, maintaining solution quality while improving constraint satisfaction through balanced, context-aware modifications.
Solution Approach 2:
The patent applies local quality by differentiating the adjustment of individual constraint coefficients based on their specific satisfaction status. Rather than applying a uniform increase to all constraints, the system selectively modifies only those coefficients corresponding to violated constraints, preserving solution quality while enforcing necessary constraints locally where needed.
Data Source
AI summary
A data processing apparatus includes a storage unit and a processing unit. The processing unit stores, in the storage unit, a solution found based on an evaluation function including a penalty function representing a constraint on a plurality of state variables and a constraint coefficient by which the penalty function is multiplied. The processing unit adjusts the constraint coefficient, based on the satisfaction status of the constraint for each of the plurality of solutions stored in the storage unit. The processing unit starts a search for a new solution based on the evaluation function including the adjusted constraint coefficient.