AI Formulation System for Narrowing Inequality Constraint Ranges
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Solution Overview
Problem
The introduction of auxiliary variables to encode inequality constraints in combinatorial optimization problems leads to an increase in the number of new variables, widening the solution space and making it difficult to solve the problem efficiently.
Innovation Solution
A formulation system that updates and transforms inequality constraints into equality constraints by reducing the range between upper and lower limit values using an auxiliary variable, thereby reducing the number of necessary binary variables.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If an auxiliary variable is introduced to formulate an inequality constraint, then the inequality constraint can be transformed into a solvable form, but the number of variables increases and the solution space becomes wider
Solution Approach 1:
The patent applies parameter changes by dynamically adjusting the upper and lower limit values of the inequality constraint during the solving process. By updating these boundary parameters to reduce the range between them, the patent transforms the constraint formulation to require fewer auxiliary variables while maintaining feasibility, thus resolving the contradiction between ease of formulation and variable complexity
Solution Approach 2:
The patent employs dynamics by making the constraint boundaries adaptive rather than static. The upper and lower limit values are updated iteratively during the solving process based on the current solution state, allowing the formulation to adapt and reduce the number of required auxiliary variables dynamically, thereby improving efficiency without sacrificing formulation ease
2Manufacturing precision
If the number of variables in the optimization problem increases, then the inequality constraint can be represented more accurately, but the solution space becomes wider and solving becomes more difficult
Solution Approach 1:
The patent changes the parameters of the inequality constraint (upper and lower limit values) during the solving process to reduce the range between them. This parameter update strategy maintains accurate constraint representation by adapting to the current solution state while reducing the solution space, thereby improving solving efficiency without sacrificing constraint accuracy
Solution Approach 2:
The patent extracts and removes redundant portions of the solution space by tightening the inequality constraint boundaries. By updating the limit values to eliminate unnecessary ranges, the patent maintains the essential constraint accuracy while reducing the overall solution space that needs to be searched, thus improving productivity
Data Source
AI summary
An artificial intelligence (AI) system includes an update unit and a transformation unit. The update unit updates at least one of an upper limit value and a lower limit value of an inequality constraint included in an optimization problem so as to reduce a range between the upper limit value and the lower limit value of the inequality constraint. The transformation unit transforms the updated inequality constraint into an equality constraint by using an auxiliary variable having a domain determined by the upper limit value and the lower limit value of the updated inequality constraint.