Enterprise AI Analysis
A survey of the orienteering problem: model evolution, algorithmic advances, and future directions
Authors: Songhao Shen, Yufeng Zhou, Qin Leia, Zhibin Wua,*
Keywords: Orienteering Problem, Variants of the Orienteering Problem, Optimization Models, Solution Methodologies, State-of-the-Art Review
Abstract: The orienteering problem (OP) is a combinatorial optimization problem that seeks a path visiting a subset of locations to maximize collected rewards under a limited resource budget. This article presents a systematic PRISMA-based review of OP research published between 2017 and 2025, with a focus on models and methods that have shaped subsequent developments in the field. We introduce a component-based taxonomy that decomposes OP variants into time-, path-, node-, structure-, and information-based extensions. This framework unifies classical and emerging variants including stochastic, time-dependent, Dubins, Set, and multi-period OPs within a single structural perspective. We further categorize solution approaches into exact algorithms, heuristics and metaheuristics, and learning-based methods, with particular emphasis on matheuristics and recent advances in artificial intelligence, especially reinforcement learning and neural networks, which enhance scalability in large-scale and information-rich settings. Building on this unified view, we discuss how different components affect computational complexity and polyhedral properties and identify open challenges related to robustness, sustainability, and AI integration. The survey thus provides both a consolidated reference for existing OP research and a structured agenda for future theoretical and applied work.
Executive Impact
This analysis highlights critical advancements in Orienteering Problem (OP) research, driving efficiency and adaptability across complex logistics, resource allocation, and autonomous system operations.
The survey reveals a significant shift in OP modeling and solution methodologies from 2017-2025. Key developments include a novel component-based taxonomy that unifies diverse OP variants—from time- and path-based extensions to information-driven stochastic models. Methodologically, there's a clear trend towards hybrid exact and metaheuristic algorithms, with a growing emphasis on AI-driven approaches like reinforcement learning and neural networks to enhance scalability and real-time decision-making. These advancements provide robust frameworks for managing uncertainty and optimizing resource-constrained operations in dynamic environments, with emerging applications in UAV path planning, disaster relief, and intelligent urban logistics.
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Studies Analyzed (2017-2025)
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Nodes in Scalable Instances
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New Best-Known Solutions (BKS)
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Instances Solved to Optimality
Deep Analysis & Enterprise Applications
Select a topic to dive deeper, then explore the specific findings from the research, rebuilt as interactive, enterprise-focused modules.
Time-Based Extensions
These variants incorporate temporal factors such as time windows, time-dependent travel costs, and multi-period planning horizons. They are crucial for applications requiring scheduling and dynamic resource allocation, like urban logistics and satellite scheduling. Decisions are often embedded in time-expanded networks, requiring advanced algorithms to maintain feasibility and optimality over time.
Path-Based Extensions
Focusing on physical path characteristics, these extensions include arc, multi-path, Dubins, and drone-related OPs. They explicitly consider kinematic limits (e.g., turning radius), energy consumption, and geometric constraints. This shifts the optimization from abstract graph routing to hybrid formulations combining combinatorial choices with continuous motion planning, vital for UAVs and robotics.
Node-Based Extensions
These variants enrich vertex constraints beyond simple rewards, involving mandatory visits, capacity constraints, or Steiner OP structures. They address specific node requirements, often intersecting OP routing polytopes with knapsack- and assignment-type constraints. Applications include priority customer services and critical infrastructure inspection, where certain nodes are non-negotiable.
Structure-Based Extensions
Modifying the combinatorial structure of the vertex set itself, these include Set, Clustered, and Synchronized Team OPs. Decisions operate on clusters or multiple interacting routes, capturing group dependencies or simultaneous visit requirements. This aligns OP research with generalized routing and multi-route assignment problems, relevant for group-buying logistics and coordinated team operations.
Information-Acquisition-Based Extensions
These extensions model uncertainty and information acquisition, encompassing Stochastic, Dynamic, and Robust OPs. They focus on information quality, dynamic updates, or probabilistic data, where solutions are often formulated as policies rather than fixed routes. This is critical for adaptive planning in dynamic environments, such as disaster response and real-time logistics.
OP Taxonomy Breakdown
The proposed component-based taxonomy organizes Orienteering Problem variants into distinct categories, clarifying how structural changes impact computational properties and algorithm design.
Orienteering Problem
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Time-Based Extensions
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Path-Based Extensions
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Node-Based Extensions
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Structure-Based Extensions
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Information-Based Extensions
Stochastic & Time-Dependent OPs
Leading OP Variants for Real-time Adaptability
Recent research (2017-2025) highlights Time-Dependent and Stochastic OPs as dominant models for real-time adaptability, complemented by emerging variants like Dynamic and Set OPs.
| Category | Key Features |
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| Exact Algorithms |
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| Heuristics & Metaheuristics |
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| AI & Learning-Based Methods |
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UAV Path Planning with Dubins & Drone OPs
Problem: Optimizing unmanned aerial vehicle (UAV) routes for reconnaissance or data collection, considering kinematic constraints, energy consumption, and dynamic environments.
Solution: Path-based OP extensions like the Dubins Orienteering Problem (DOP) and Drone and Robot Orienteering Problems (DROP) are used. These models integrate motion primitives, curvature constraints, and geometric neighborhoods with advanced algorithms like VNS, Genetic Algorithms, and Branch-and-Cut to ensure efficient and feasible paths under budget and physical limits.
Impact: Enables robust UAV operations for environmental monitoring, disaster response, and surveillance, improving data acquisition efficiency and mission success rates in complex, real-world scenarios.
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Your AI Implementation Roadmap
A phased approach to integrate advanced Orienteering Problem solutions into your enterprise, ensuring robust and scalable deployment.
Phase 1: Discovery & Strategy Alignment
Understand existing routing/logistics challenges, data availability, and define precise objectives. Select optimal OP variants (e.g., Stochastic, Time-Dependent, Set) and initial performance metrics. Identify key stakeholders and success criteria.
Phase 2: Model Development & Pilot
Develop custom OP models incorporating specific constraints (e.g., time windows, capacities, multi-period), potentially integrating AI/ML for dynamic elements. Implement a pilot program with a subset of operations to validate the model and algorithms.
Phase 3: Integration & Optimization
Integrate the OP solution with existing enterprise systems (e.g., ERP, fleet management). Refine algorithms based on pilot results, focusing on scalability and robustness. Begin broader deployment with continuous monitoring and fine-tuning.
Phase 4: Advanced Capabilities & Sustained Value
Explore advanced features like real-time dynamic re-optimization, predictive analytics, and explainable AI (XAI). Expand to multi-agent or heterogeneous fleet scenarios. Establish a framework for continuous improvement and value realization from AI-driven OP solutions.
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