[Paper Review] Scenic Routes Now: Efficiently Solving the Time-Dependent Arc Orienteering Problem

Gregor Jossé, Ying Lü+5 more|arXiv (Cornell University)|Sep 27, 2016

Mobile Crowdsensing and Crowdsourcing42 references3 citations

TL;DR

This paper introduces the Twofold Time-Dependent Arc Orienteering Problem (2TD-AOP), modeling both time-dependent travel times and time-dependent value gains in large road networks. It proposes an efficient approximate dynamic programming solution that significantly outperforms optimal methods in speed while producing valid, high-value paths, validated on real-world data with substantial gains from time-dependent value modeling.

ABSTRACT

This paper extends the Arc Orienteering Problem (AOP) to large road networks with time-dependent travel times and time-dependent value gain, termed Twofold Time-Dependent AOP or 2TD-AOP for short. In its original definition, the NP-hard Orienteering Problem (OP) asks to find a path from a source to a destination maximizing the accumulated value while not exceeding a cost budget. Variations of the OP and AOP have many practical applications such as mobile crowdsourcing tasks (e.g., repairing and maintenance or dispatching field workers), diverse logistics problems (e.g., crowd control or controlling wildfires) as well as several tourist guidance problems (e.g., generating trip recommendations or navigating through theme parks). In the proposed 2TD-AOP, travel times and value functions are assumed to be time-dependent. The dynamic values model, for instance, varying rewards in crowdsourcing tasks or varying urgency levels in damage control tasks. We discuss this novel problem, prove the benefit of time-dependence empirically and present an efficient approximative solution, optimized for fast response systems. Our approach is the first time-dependent variant of the AOP to be evaluated on a large scale, fine-grained, real-world road network. We show that optimal solutions are infeasible and solutions to the static problem are often invalid. We propose an approximate dynamic programming solution which produces valid paths and is orders of magnitude faster than any optimal solution.

Motivation & Objective

• To address the limitations of static models in real-world route planning by incorporating time-dependent travel times and value gains.
• To model dynamic value functions that reflect varying rewards (e.g., scenic views, urgency) at different times of day.
• To develop a scalable, efficient solution for the NP-hard 2TD-AOP on large, fine-grained road networks.
• To empirically demonstrate the superiority of time-dependent value modeling over static averaging.
• To provide a fast, approximate algorithm suitable for real-time systems in applications like tourist navigation and field operations.

Proposed method

• Extends the Arc Orienteering Problem (AOP) to include time-dependent travel times and time-dependent arc values, forming the 2TD-AOP.
• Uses a modified time-dependent Dijkstra algorithm (FWR) to compute forward-reachable vertices within a time budget from the source.
• Employs a backward-reachability algorithm (BWR) to compute latest departure times from the destination, using time-window linear scanning and epsilon correction for boundary precision.
• Applies pruning techniques based on intersection of forward and backward reachable regions to reduce search space.
• Develops an approximate dynamic programming approach that balances value collection and time budget constraints using time-dependent arc value functions.
• Optimizes for fast response by avoiding exact optimal solutions, which are infeasible on large networks.

Experimental results

Research questions

• RQ1 How does modeling time-dependent values improve solution quality in route planning compared to static value assumptions?
• RQ2 What is the performance gain of using time-dependent value functions in real-world road networks with dynamic traffic and variable rewards?
• RQ3 Can an efficient, approximate algorithm outperform exact optimal solutions in runtime while maintaining solution validity and quality?
• RQ4 How do time-dependent travel times and values jointly affect path selection in large-scale road networks?
• RQ5 What is the impact of pruning based on forward and backward reachability on solution efficiency?

Key findings

• Optimal solutions to the 2TD-AOP are infeasible on large-scale road networks due to computational complexity.
• Solutions based on static value assumptions are often invalid, as they fail to capture peak value periods.
• The proposed approximate dynamic programming solution is orders of magnitude faster than optimal methods while still producing valid, high-value paths.
• Time-dependent value modeling leads to significant improvements in solution quality, especially for scenic route planning with diurnal value variations.
• The FWR and BWR algorithms effectively compute reachable regions, enabling efficient pruning and scalable solution computation.
• Empirical evaluation on real-world road networks confirms that time-dependent value functions yield better results than averaged static values.