Adaptive Simplex Pricing for Fewer Linear Programming Iterations
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Solution Overview
Problem
The simplex method for solving linear programming problems is inefficient due to its complex iterative operations, leading to low computing device efficiency.
Innovation Solution
An objective function solving method that dynamically updates pricing strategies in the simplex method based on objective improvements, basis exchange degeneracy, and execution duration proportion to optimize each iterative operation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the simplex method is used to solve linear programming problems, then the problem can be resolved systematically, but the computing device efficiency is low due to complex iterative operations
Solution Approach 1:
The patent applies dynamics by making the pricing strategy adjustable and adaptive throughout the simplex method iterations. Instead of using a fixed pricing strategy, the system dynamically selects different pricing strategies (Dantzig, Devex, or Steepest-edge) based on real-time evaluation of objective improvement and basis exchange degeneracy metrics, thereby optimizing computing efficiency while maintaining systematic problem resolution
Solution Approach 2:
The patent implements parameter changes by modifying the pricing strategy parameter during the solving process. The system evaluates two key parameters (objective improvement and basis exchange degeneracy) after each iteration and changes the pricing strategy parameter accordingly, selecting from multiple available strategies to improve overall solving efficiency while preserving the systematic approach
2Ease of manufacture
If a fixed pricing strategy is used in the simplex method, then the implementation is simple, but the number of iterative operations is large leading to low efficiency
Solution Approach 1:
The system transitions from a static pricing strategy to a dynamic one by continuously evaluating performance metrics and adapting the strategy selection. This allows the system to maintain implementation simplicity through automated decision-making while significantly improving solving efficiency by selecting optimal strategies for different problem states
Solution Approach 2:
The patent implements feedback mechanisms by evaluating objective improvement and basis exchange degeneracy after each iteration, then using this feedback to inform the next pricing strategy selection. This closed-loop approach enables the system to learn from previous iterations and adjust accordingly, reducing the total number of iterations needed while keeping the implementation straightforward through rule-based decision logic
3Productivity
If the pricing strategy is updated frequently based on objective improvement, then the solving efficiency improves, but the complexity of the solving process increases
Solution Approach 1:
The patent manages complexity by changing only one key parameter (pricing strategy) based on two evaluated metrics, rather than modifying multiple aspects of the solving process. This focused parameter change approach improves solving efficiency while controlling overall process complexity through a structured decision framework
Data Source
AI summary
The application disclose an objective function solving method and apparatus, and a computing device cluster, and belong to the field of cloud computing technologies. The method includes: receiving a solving requirement input, where the solving requirement includes an objective function, a decision variable, and a constraint condition; determining, based on the solving requirement, a simplex method as a solving method, to solve the objective function; in a process of solving the objective function using the simplex method, after solving the objective function according to a first pricing strategy using the simplex method, determining, based on an objective improvement on the objective function by the current solving in the simplex method, a second pricing strategy for solving the objective function in a next iteration; and solving the objective function according to the second pricing strategy. According to this application, objective function solving efficiency can be improved.