Plan Analysis System Using Precomputed Upper Bounds
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Solution Overview
Problem
Existing methods for analyzing optimal plans require prior domain knowledge and are computationally expensive, making it difficult to quickly execute analysis without extensive calculation costs and user waiting time.
Innovation Solution
A plan analysis method that generates optimization patterns by combining constraints, calculates upper bounds based on evaluation indices, searches for executable solutions, and determines the presence of an optimal solution using a processor and memory-based system, allowing for quick analysis without requiring domain knowledge.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If sensitivity analysis is performed by perturbing input factors and solving optimization problems multiple times, then plan basis description accuracy is improved, but calculation cost and user waiting time increase significantly
Solution Approach 1:
The system pre-calculates and stores upper bound information for various constraint combinations before user queries. When a user asks about plan basis, the system retrieves pre-computed upper bounds and compares them with actual optimization results, avoiding repeated sensitivity analysis calculations and providing immediate explanations.
Solution Approach 2:
The system prepares cushioning data by computing upper bounds for different constraint scenarios in advance. These pre-computed upper bounds serve as a buffer that allows the system to quickly determine whether constraints are binding without performing costly re-optimization, thus cushioning against calculation time requirements.
2Productivity
If hierarchical relationship between input factors is used to reduce calculation combinations, then factor search efficiency is improved, but prior domain knowledge is required which general users lack
Solution Approach 1:
The system implements a universal upper bound calculation mechanism that works for any constraint combination without requiring domain-specific hierarchical knowledge. The upper bound computation is a general-purpose technique that can be applied to any optimization problem, making the system accessible to general users while maintaining efficiency.
Solution Approach 2:
The system changes the approach from hierarchical factor analysis to parameter-based upper bound computation. By computing upper bounds with modified constraint parameters, the system efficiently identifies binding constraints without requiring users to understand or define hierarchical relationships, thus maintaining efficiency while improving ease of use.
3Measurement precision
If optimization problems are solved multiple times for sensitivity analysis, then contribution degree of input factors is accurately determined, but computational cost increases
Solution Approach 1:
The system extracts only the essential information needed for sensitivity analysis by computing upper bounds for specific constraint combinations. Instead of solving full optimization problems multiple times, the system extracts upper bound values that are sufficient to determine constraint binding status and factor contribution degrees, significantly reducing computational cost while maintaining accuracy.
Solution Approach 2:
The system creates simplified copies of the optimization problem in the form of upper bound calculations. These upper bound problems are computationally cheaper copies that retain the essential information needed for sensitivity analysis, allowing the system to perform multiple analyses without the full computational cost of solving complete optimization problems repeatedly.
Data Source
AI summary
In a plan analysis method for analyzing an optimal plan in which an optimization target is optimized based on a plurality of constraints and evaluation indices, the plan analysis system generates a plurality of optimization patterns by combining constraints to be analyzed. Further, for each of the optimization patterns, an upper bound based on the evaluation indices when a condition corresponding to a focus state that a user pays attention to in the optimal plan is satisfied and the upper bound when the condition is not satisfied are calculated. Further, an executable solution for the optimization under each of the conditions is searched. Further, based on the upper bound and the executable solution, whether an optimal solution for the optimization is present under the conditions is determined.