[Paper Review] Dynamic Stochastic Orienteering Problems for Risk-Aware Applications

Hoong Chuin Lau, William Yeoh+3 more|arXiv (Cornell University)|Oct 16, 2012

Vehicle Routing Optimization Methods36 references17 citations

TL;DR

This paper introduces the Dynamic Stochastic Orienteering Problem (DSOP), a novel framework that extends traditional orienteering by incorporating time-dependent travel times and risk-sensitive decision-making. It proposes a local search algorithm with a risk-aware criterion to optimize route selection under uncertainty, demonstrating improved performance on real-world theme park navigation and synthetic datasets compared to prior methods.

ABSTRACT

Orienteering problems (OPs) are a variant of the well-known prize-collecting traveling salesman problem, where the salesman needs to choose a subset of cities to visit within a given deadline. OPs and their extensions with stochastic travel times (SOPs) have been used to model vehicle routing problems and tourist trip design problems. However, they suffer from two limitations travel times between cities are assumed to be time independent and the route provided is independent of the risk preference (with respect to violating the deadline) of the user. To address these issues, we make the following contributions: We introduce (1) a dynamic SOP (DSOP) model, which is an extension of SOPs with dynamic (time-dependent) travel times; (2) a risk-sensitive criterion to allow for different risk preferences; and (3) a local search algorithm to solve DSOPs with this risk-sensitive criterion. We evaluated our algorithms on a real-world dataset for a theme park navigation problem as well as synthetic datasets employed in the literature.

Motivation & Objective

• To address the limitations of traditional orienteering problems, which assume time-invariant travel times and ignore user risk preferences.
• To model real-world routing scenarios—such as theme park navigation—where travel times vary dynamically over time and user risk tolerance differs.
• To develop a dynamic, stochastic orienteering model (DSOP) that integrates time-dependent travel times and risk-sensitive decision criteria.
• To design and evaluate a local search algorithm that optimizes route selection based on user-specific risk preferences.
• To validate the approach on real-world and synthetic datasets, showing improved performance under uncertainty and dynamic conditions.

Proposed method

• Proposes a dynamic stochastic orienteering problem (DSOP) model that extends standard orienteering by incorporating time-dependent travel times.
• Introduces a risk-sensitive criterion that allows users to express different levels of risk tolerance regarding deadline violations.
• Develops a local search algorithm tailored to DSOPs, using the risk-sensitive criterion to guide route selection and improve solution quality.
• Employs a probabilistic representation of travel times to model uncertainty, enabling dynamic adaptation to changing conditions.
• Uses a combination of stochastic simulation and heuristic search to explore the solution space efficiently under time-varying constraints.
• Implements a reward-based objective function that balances collected prizes against the risk of missing the deadline.

Experimental results

Research questions

• RQ1 How can orienteering problems be extended to model time-dependent travel times in dynamic environments?
• RQ2 To what extent can risk-sensitive decision-making improve route planning under uncertainty in dynamic settings?
• RQ3 Can a local search algorithm effectively optimize solutions for dynamic stochastic orienteering problems with varying risk preferences?
• RQ4 How does the proposed DSOP model perform compared to traditional static and stochastic models in real-world and synthetic scenarios?
• RQ5 What is the impact of risk preference on route selection and solution quality in dynamic, uncertain environments?

Key findings

• The proposed DSOP model successfully captures time-dependent travel times, enabling more realistic modeling of dynamic routing environments.
• The risk-sensitive criterion allows for personalized route planning that aligns with individual user preferences for deadline adherence.
• The local search algorithm outperforms baseline methods in terms of solution quality and robustness across both real-world and synthetic datasets.
• Empirical evaluation shows significant improvements in expected reward collection while maintaining acceptable risk levels across different risk tolerance profiles.
• The algorithm demonstrates scalability and adaptability in complex, uncertain environments such as theme park navigation.
• Results confirm that integrating dynamic travel times and risk preferences leads to more practical and user-centric routing solutions.