Prediction-Guided Combinatorial Optimization With Robustness Regularization
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Solution Overview
Problem
Existing combinatorial optimization methods, such as stochastic programming and robust optimization, face challenges in achieving desired robustness due to unknown distributions, difficulty in solving min-max problems, and the lack of unified solvers that handle both types effectively.
Innovation Solution
A method involving continuous relaxation and a prediction model to estimate instance parameters, combined with a regularization term to optimize robustness, is used to solve combinatorial optimization problems, allowing for the integration of expectation and min-max robust optimization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If stochastic programming or robust optimization is used for combinatorial optimization problems, then optimization capability is provided, but achieving desired robustness becomes difficult due to unknown distributions and difficulty in solving min-max problems
Solution Approach 1:
The patent introduces a prediction model as an intermediary component that estimates instance parameters from feature data. This mediator bridges the gap between available feature data and the unknown instance parameters required for robust optimization, allowing the system to achieve desired robustness without directly solving complex min-max problems with unknown distributions.
Solution Approach 2:
The patent transforms the optimization approach by changing parameters from directly optimizing under uncertainty to optimizing a prediction model that estimates uncertain parameters. The loss function is modified to include regularization terms that control robustness, converting the difficult min-max problem into a more tractable parameter estimation and optimization framework.
2Measurement precision
If a prediction model is used to estimate instance parameters, then optimization accuracy improves, but computational complexity increases due to integrating prediction and optimization
Solution Approach 1:
The patent merges the prediction model and optimization process into a unified framework. The prediction model and optimization objective function are integrated through a combined loss function that simultaneously performs parameter estimation and optimization, eliminating the need for separate prediction and optimization steps and reducing overall system complexity.
Solution Approach 2:
The patent creates a unified optimization framework that serves multiple functions: it performs instance parameter estimation, optimizes combinatorial decisions, and controls robustness all within a single optimization process. This multi-functional approach eliminates the need for separate dedicated components for each function.
3Reliability
If regularization term is added to control robustness, then solution robustness improves, but loss function complexity increases
Solution Approach 1:
The patent controls robustness by changing the regularization parameter in the loss function. By adjusting this parameter, the system can control the trade-off between optimization accuracy and robustness without fundamentally changing the loss function structure, maintaining relative simplicity while achieving robustness control.
Data Source
AI summary
There is provided a non-transitory computer-readable medium storing a calculation program for causing a computer to execute a process. The process includes using a prediction model learned using training data that associates feature data of an input target with an instance parameter of a target to be solved, and generating an estimate of the instance parameter corresponding to feature data, and searching for a solution for variables by using an objective function including variables for a combinatorial optimization problem and the estimate of the instance parameter, and a loss function including a regularization term that changes according to robustness of the variables.