Non-Convex MINLP Graph Segmentation With Quantum Solvers
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Solution Overview
Problem
Conventional methods for solving non-convex mixed integer non-linear programming (MINLP) problems are time-consuming, require extensive experimentation, and are prone to human error due to the need for domain knowledge and manual intervention.
Innovation Solution
A method and system using quantum solvers that iteratively segment a non-linear, non-convex graph into sub-graphs based on vertical distance, assign binary variables to activate or deactivate segments, and utilize quantum solvers to optimize the objective function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional methods (AOA, COA) are used to solve MINLP problems, then the problems can be solved using traditional algorithms, but the solving time is excessive and multiple experimentation is required
Solution Approach 1:
The non-convex graph is segmented into multiple convex segments using an iterative algorithm that identifies seed points and divides the graph into manageable portions. This segmentation transforms the intractable MINLP problem into a series of solvable convex optimization problems, dramatically reducing solving time while maintaining solution accuracy.
Solution Approach 2:
The patent replaces classical computational mechanics with quantum mechanics by utilizing quantum solvers to solve the segmented optimization problems. Quantum algorithms provide exponential speedup for certain optimization problems, eliminating the excessive solving time associated with traditional methods.
2Ease of manufacture
If partial convexification technique is used with predictive feedback controller, then convex approximation of non-linear functions is produced, but pre-configured instructions and domain knowledge are required
Solution Approach 1:
The iterative segmentation algorithm automatically identifies seed points and divides the non-convex graph into convex segments without requiring pre-configured instructions or domain knowledge. The system serves itself by adaptively determining the segmentation strategy based on the problem characteristics, eliminating the need for manual pre-configuration.
Solution Approach 2:
The algorithm dynamically adjusts segmentation parameters during execution, changing the number and position of segments based on the vertical distance metric and error criteria. This adaptive parameter adjustment eliminates the need for fixed pre-configuration while maintaining ease of implementation.
3Manufacturing precision
If conventional methods are used to determine the number of segments, then segmentation can be performed, but immense experimentation time is required in hit and trial method
Solution Approach 1:
The algorithm employs feedback mechanisms where the vertical distance of each graph point from the segment line is computed and used to identify seed points for further segmentation. This feedback-driven approach automatically determines the optimal number of segments based on error criteria, eliminating the need for time-consuming hit-and-trial experimentation while maintaining segmentation precision.
4Reliability
If conventional methods require human intervention, then problems can be solved with domain knowledge, but human error is introduced
Solution Approach 1:
The complete automated workflow performs graph segmentation, quantum solver formulation, and optimization without human intervention. The system automatically computes vertical distances, identifies seed points, divides segments, and formulates quantum optimization problems, eliminating human error while maintaining ease of operation through full automation.
Solution Approach 2:
The patent introduces quantum solvers as an intermediary between the segmented graph representation and the final optimization solution. This intermediary automatically handles the complex optimization computations without human intervention, eliminating human error in the solution process while maintaining accessibility through standardized quantum computing interfaces.
Data Source
AI summary
Optimization problem aims to find a best optimal solution from feasible solutions The present disclosure provides optimization of non-convex problems using quantum solvers. Initially, the entire curve is considered as a single segment and the vertical distance of all points of the cure is determined. Then a point with maximum vertical distance is identified and the entire curve is segmented into two at this point. This step is repeated to get more such segments point until the maximum error distance in each segment falls below the threshold value. Now the objective function is broken down into its constituent parts, wherein each constituent part represents a separate segment. Each of these objective function segments are then assigned with a binary variable such that the binary variable allows to activate or deactivate the segments. Further, the objective function segments are fed to a quantum solver to get the optimal solution.