Bezier Simplex Model for Pareto Front Solution Selection
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Solution Overview
Problem
Users face difficulties in selecting desired solutions from a Pareto front in multi-objective optimization problems, especially when the number of objective functions is three or more, as visualizing and specifying all evaluation values becomes complex.
Innovation Solution
A Bezier simplex model is fitted to the graph data of solutions and evaluation values, allowing for the generation of data points that correspond to each other, enabling users to input conditions and easily select solutions based on these data points.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If a Bezier simplex model is fitted to graph data of solutions and evaluation values, then the visualization of Pareto front is improved and solution selection is simplified, but the computational complexity and mathematical processing required increases
Solution Approach 1:
The system performs preliminary fitting of Bezier simplex models to the graph data of solutions and evaluation values before the user needs to select solutions. This pre-processing creates a structured mathematical representation that simplifies subsequent user interactions and solution filtering operations.
Solution Approach 2:
The Bezier simplex model acts as an intermediary between the raw optimization data and the user's selection criteria. By fitting these mathematical models to the graph data, the system creates a simplified intermediate representation that makes it easier to query and filter solutions based on user-specified conditions.
2Adaptability or versatility
If the number of objective functions is three or more, then the comprehensiveness of optimization coverage is improved, but the difficulty of visualizing and specifying all evaluation values increases
Solution Approach 1:
The system uses Bezier simplex models to represent the Pareto front in a mathematical space that can accommodate three or more objective functions. This approach transforms the visualization problem from directly displaying high-dimensional data to using parametric mathematical models that can be queried and filtered without requiring direct visualization of all dimensions.
Data Source
AI summary
A non-transitory computer-readable recording medium storing an output program for causing a computer to execute a process, the process includes acquiring first graph data related to solutions over a Pareto front and second graph data related to a plurality of evaluation values corresponding to the solutions, fitting a Bezier simplex to each of the acquired first graph data and the acquired second graph data, generating a plurality of data points that corresponds to each other over a Bezier simplex fitted to each of the first graph data and the second graph data, receiving input of a condition that indicates a range of each of the plurality of evaluation values, and outputting solutions indicated by data points over a Bezier simplex fitted to the first graph data, the data points corresponding to data points over a Bezier simplex fitted to the second graph data selected based on the received condition.