Online Inverse Optimization for Time-Varying Decision Constraints
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Solution Overview
Problem
Existing inverse optimization techniques struggle to handle time-varying optimization problems and recover both objectives and constraints in an online manner, particularly in complex decision-making scenarios like nurse scheduling, where data quality issues and temporal dependencies are prevalent.
Innovation Solution
An online probabilistic inverse optimization system that infers objectives and constraints using machine learning techniques, treating the problem as a maximum likelihood estimation, allowing for flexible adaptation to changing data and agent decisions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If standard inverse optimization techniques are used, then objectives can be recovered from agent decisions, but the techniques cannot handle time-varying optimization problems
Solution Approach 1:
The patent applies dynamics by making the objective function adaptive to changing conditions. The system transitions from static inverse optimization to a dynamic framework where objectives are continuously updated based on time-varying data, allowing the model to adapt to changing environmental conditions while maintaining recovery accuracy through probabilistic updates.
Solution Approach 2:
The patent changes parameters by introducing time-varying parameters into the objective function. Instead of fixed parameters, the system uses parameters that evolve over time, allowing the optimization problem to reflect real-world dynamics where conditions such as resource availability, costs, and constraints change continuously.
2Productivity
If offline inverse optimization is used, then complete objective recovery is possible, but it cannot learn from streaming data in real-time
Solution Approach 1:
The patent applies preliminary action by pre-processing streaming data to extract relevant features and maintaining a running model that is continuously updated. This allows the system to be prepared for real-time learning by establishing the probabilistic framework in advance, enabling immediate adaptation to new data while preserving temporal information through the sequential update mechanism.
Solution Approach 2:
The patent implements continuity of useful action by establishing a continuous learning process where the model is constantly updated with new streaming data. This continuous update mechanism ensures that the system maintains its learning capability over time, capturing temporal dependencies through the ongoing probabilistic inference process rather than discrete batch processing.
3Measurement precision
If complex constraints are included in nurse scheduling, then decision quality improves, but problem complexity increases significantly
Solution Approach 1:
The patent applies segmentation by dividing the complex nurse scheduling problem into manageable components. The system segments the objective function into multiple terms representing different constraints and preferences, allowing each component to be handled separately through probabilistic inference, thereby reducing overall problem complexity while maintaining comprehensive decision accuracy.
Solution Approach 2:
The patent introduces an intermediary probabilistic model that mediates between the complex constraints and the optimization process. This intermediary layer transforms complex hard constraints and soft preferences into a unified probabilistic framework, simplifying the optimization problem while preserving the nuanced decision-making requirements of nurse scheduling.
Data Source
AI summary
An online probabilistic inverse optimization system 10 is proposed for inferring objectives and constraints in an online fashion from changing problem data and corresponding agent decisions. The online probabilistic inverse optimization system 10 includes: a computing unit 11 which computes optimal solutions or decisions based on the forward optimization problem using the problem data that may include objectives, constraints and parameters; and a solving unit 12 which solves the inverse optimization problem using the agent decisions.