Robust Path Determination in Stochastic Networks
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Solution Overview
Problem
Existing path determination algorithms in stochastic networks, such as traffic networks, are inefficient when faced with uncertain travel times, as they rely on accurate distribution functions which may not be available or reliable, leading to poor performance in real-world applications.
Innovation Solution
A robust optimization technique is employed to determine paths by modeling uncertain costs using reference points, upper bounds, and lower bounds, allowing for target-oriented robust optimization problems to be solved without requiring distribution information, ensuring robustness against uncertainty and optimizing travel time reliability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional shortest path algorithms are used in stochastic networks, then computational efficiency is improved, but reliability of the solution deteriorates due to uncertainty in travel times
Solution Approach 1:
The patent transforms the stochastic shortest path problem into a robust optimization problem by changing the parameter representation from probability distributions to uncertainty sets defined by nominal values and deviation bounds. This allows the use of efficient deterministic algorithms while guaranteeing solutions that satisfy travel time targets under uncertainty.
Solution Approach 2:
The patent uses a simplified uncertainty model that does not require complex distribution functions or extensive historical data. Instead, it uses readily available nominal travel times and reasonable deviation bounds, making the approach computationally inexpensive and easily applicable without needing expensive or difficult-to-obtain distribution information.
2Measurement precision
If distribution functions are used to model uncertainty, then measurement precision of travel time is improved, but device complexity increases due to difficulty in obtaining accurate distribution functions
Solution Approach 1:
The patent extracts only the essential information needed for robust path determination - nominal travel times and deviation bounds - while discarding the complex distribution function requirements. This simplification maintains measurement precision for travel time targets while eliminating the complexity of obtaining and working with accurate distribution functions.
3Ease of operation
If deterministic algorithms are used, then ease of operation is improved, but adaptability to stochastic environments deteriorates
Solution Approach 1:
The patent introduces dynamics by allowing the uncertainty parameters (deviation bounds) to be adjusted based on available information and user requirements. The robust optimization framework dynamically adapts to stochastic environments while maintaining the simplicity of deterministic algorithms, achieving both ease of operation and adaptability.
Data Source
AI summary
A technology for path determination using robust optimization is provided. In accordance with one aspect, a network graph of a network is generated. The network graph comprises nodes corresponding to points in the network, and edges which connect the nodes. Costs for each edge of the network are determined and modeled using reference point, upper bound and lower bound parameters. A user input which includes a source node, destination node, and cost target may be received from a client device. A resultant path connecting the source node and destination node are determined by solving a target-oriented robust optimization problem, which optimizes a cost of the resultant path based on the modeled costs of the edges. The resultant path is displayed on a user interface of the client device.