Non-Convex MINLP Optimization Using Quantum Solver Segmentation
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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 to determine the number of segments in a hit-and-trial method.
Innovation Solution
A method and system using quantum solvers that iteratively segment a non-linear, non-convex graph into smaller segments 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 like outer approximation algorithm or predictive feedback controller are used to solve MINLP problems, then the problems can be approached with traditional computational tools, but the methods require extensive experimentation, domain knowledge, and manual intervention to determine the number of segments, resulting in significant loss of time and human error
Solution Approach 1:
The system automatically determines the number of segments required for convexification by analyzing the non-convex MINLP problem structure itself, without requiring external domain knowledge or manual intervention. The quantum solver autonomously identifies segmentation requirements and executes the convexification process, eliminating the need for human experts to perform hit-and-trial experimentation to determine segment counts.
2Ease of manufacture
If conventional methods require preconfigured instructions and domain knowledge to perform partial convexification, then the approach can be systematically applied, but the requirement for prior domain knowledge increases the complexity of operation and limits accessibility
Solution Approach 1:
The quantum-based system performs partial convexification autonomously by evaluating the problem structure and automatically determining the necessary segmentation. The quantum solver inherently understands when and how to segment the non-convex problem without requiring preconfigured instructions or domain knowledge from the user, making the method both broadly applicable and easy to operate.
3Adaptability or versatility
If hit-and-trial method is used to determine the optimal number of segments, then flexibility in finding solutions is maintained, but the immense experimentation time required significantly reduces productivity
Solution Approach 1:
The quantum solver employs feedback mechanisms where the quantum state evolution provides information about the problem structure and optimal segmentation requirements. The system continuously monitors the quantum state during evolution and uses this feedback to determine when sufficient segmentation has been achieved, eliminating the need for extensive hit-and-trial experimentation while maintaining solution flexibility.
4Reliability
If manual intervention is required in conventional methods to determine segments, then human expertise can guide the process, but human error increases and the process becomes less reliable
Solution Approach 1:
The quantum-based system completely automates the segmentation determination process, with the quantum solver autonomously analyzing the non-convex problem structure and identifying the optimal number of segments. This self-service approach eliminates human intervention entirely, removing the source of human error while maintaining high reliability through the quantum computational process's inherent consistency and repeatability.
Data Source
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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.