A Review of Urban Path Planning Algorithms in Intelligent Transportation Systems

Abstract

With the accelerating pace of urbanization and the increasing complexity of traffic systems, urban transportation faces growing challenges such as congestion, inefficiency, and environmental strain. Path planning algorithms—key components in intelligent transportation systems—have evolved from classical graph-based methods like Dijkstra and A* to modern approaches leveraging metaheuristics and deep learning. This paper systematically reviews the development of urban path planning algorithms, tracing their progression from foundational methods to state-of-the-art techniques such as Ant Colony Optimization, Probabilistic Roadmaps, and Rapidly Exploring Random Trees. Recent innovations, including improved genetic algorithms, hybrid A* variants, and reinforcement learning models, are analyzed in terms of adaptability, efficiency, and real-time performance. Furthermore, the review highlights ongoing challenges in scalability, dynamic adaptation, and algorithmic fairness, while discussing future directions that integrate technical innovation with policy and ethical considerations to support sustainable and equitable urban mobility.

1. Introduction

With the acceleration of global urbanization and the continuous growth of urban populations, urban transportation problems have become increasingly severe, including traffic congestion, resource waste, and environmental pollution. Especially in countries and regions with high urbanization rates, traffic congestion has become one of the main issues restricting economic development and affecting residents’ quality of life. Addressing urban transportation pressures through advanced technologies has become a shared priority for both academia and industry. As a key direction in transportation development, intelligent transportation systems (ITS) integrate technologies such as the Internet of Things (IoT), big data, and artificial intelligence to inject innovation into traditional transportation frameworks. ITSs aim to enable intelligent allocation and dynamic optimization of transportation resources, thereby improving road capacity, reducing energy consumption and environmental impact, and supporting sustainable urban development. Within these systems, path planning algorithms play a crucial role. Selecting an appropriate algorithm is further complicated by competing objectives and operational constraints in ITSs—balancing optimality with responsiveness, interpretability with learning capacity, and efficiency with equity—making a principled, context-aware comparison indispensable for practitioners.

Recent literature reviews have increasingly examined path planning in complex environments. For example, Kumar et al. offer a comprehensive classification of path-planning techniques spanning classical, heuristic, and model-based methods [1]. Reda et al. focus on path planning in autonomous driving systems specifically, analyzing challenges in perception, decision-making, and trajectory generation in urban contexts [2]. Moreover, the survey by Hu et al. (2025) reviews decision-making and planning methods for self-driving vehicles, combining knowledge-driven and data-driven paradigms [3]. These studies, however, tend to emphasize autonomous vehicles or robotics domains, with limited attention paid to large-scale urban transportation systems, and often neglect or rarely address cross-cutting issues such as algorithmic fairness, policy implications, and scalability under real-time ITS constraints.

To fill these gaps, our review synthesizes four methodological paradigms—graph-based, heuristic/metaheuristic, sampling-based, and learning-driven approaches. It also provides a cross-sectional comparison along four practical criteria: time complexity, dynamic adaptability, robustness, and high-dimensional scalability. By better understanding the strengths and limitations of different algorithms and their appropriate application scenarios, researchers can better select the algorithm that best suits their specific circumstances and conditions. This framing provides actionable guidance beyond prior surveys by linking algorithm capabilities to real-world ITS requirements and governance needs.

2. Basic Theory of Path Planning

Path planning seeks to identify the optimal route from a starting point to a target destination. It is typically categorized into single-vehicle and multi-vehicle planning, and with the advancement of transportation infrastructure and computational power, algorithms have evolved from static to dynamic and multi-objective approaches [4]. This section provides a concise overview of the fundamental path planning algorithms that serve as the theoretical foundation for later comparative analysis. Rather than reiterating well-known material, it aims to highlight the core logic and assumptions of classical approaches to better contextualize their subsequent improvements discussed in Section 3.

2.1. Dijkstra Algorithm

Early path planning research in the 1950s–1960s was grounded in graph theory and mathematical optimization, laying the foundation for modern navigation and network analysis. Among the earliest and most influential methods is the Dijkstra algorithm, proposed by Edsger W. Dijkstra in 1956, which remains one of the most widely used algorithms for determining the shortest path between a source node and all other nodes in a network [5]. The algorithm follows an iterative expansion process: starting from an initial node, it gradually explores neighboring nodes by always selecting the one with the smallest known distance from the source [6]. This greedy strategy ensures that local optimal decisions—choosing the shortest known path at each step—lead to a globally optimal solution when all edge weights are non-negative [7]. The overall iterative process of this algorithm is illustrated in Figure 1, which shows how the search frontier expands and updates as each node is finalized.

The algorithm’s key contribution lies in its balance between simplicity and mathematical rigor. It introduced a structured way to represent spatial relationships using weighted graphs, effectively transforming routing and navigation problems into solvable computational models. Its deterministic nature guarantees that the shortest path can be found without exhaustive search, which made it particularly valuable in early applications such as telecommunication networks and transportation systems [8].

However, despite its historical importance and theoretical elegance, the traditional Dijkstra algorithm has several well-known limitations. It assumes static and fully connected networks with non-negative edge weights, conditions that rarely hold in real-world transportation or robotic environments. When applied to large-scale or dynamic systems, the algorithm suffers from high computational cost and limited adaptability to changing conditions [9].

2.2. The Floyd–Warshall Algorithm

The Floyd–Warshall algorithm originates from two independent research efforts, proposed by Robert W. Floyd [10] and Stephen Warshall [11], respectively. Their results were eventually combined to form the Floyd–Warshall algorithm that is widely used today. Unlike the Dijkstra algorithm, the Floyd–Warshall algorithm is a multi-source shortest path algorithm, which means that it aims to find the shortest path between any two points in the study area at one time [12].

The core of this algorithm is to enumerate all possible starting points i, end points j and transit points k in turn through a triple loop and try to use node k as the intermediate node to optimize the shortest path from i to j in each iteration [13]. The algorithm starts by allowing the path to not contain any transit points, and gradually relaxes the restrictions, each time adding a new node k to the set that can be used as a transit, and updating the path length of all D[i][j] to the smaller value of the original path D[i][j] and the path D[i][k] + D[k][j] passing through k. This systematic dynamic programming iteration ensures that the shortest path between all point pairs is finally obtained. Similarly, when the graph is large in scale, the computational and storage resource requirements are extremely high, making the Floyd–Warshall algorithm unsuitable for large-scale sparse scenarios [14]. The time complexity of this algorithm could reach O(V³) [15].

In summary, the Dijkstra and Floyd–Warshall algorithms, as classical representatives of shortest path algorithms, are based on static and deterministic environments and are suitable for solving single-source or multi-source shortest path problems in many practical scenarios [16], laying an important foundation in the field of path planning [17].

2.3. A* Algorithm

From the 1960s to the 1980s, heuristic search methods began to play an increasingly important role in path planning. Among them, the A* algorithm, proposed by Peter Hart, Nils Nilsson, and Bertram Raphael in 1968, became one of the most influential and enduring approaches [18]. The core idea of A* lies in combining the actual travel cost from the starting point with a heuristic estimate of the remaining distance to the goal. By introducing this evaluation mechanism, A* effectively guides the search toward the destination, reducing unnecessary exploration compared with uniform-cost or blind search algorithms. The overall iterative process of A* is illustrated in Figure 2, which shows how the algorithm expands nodes based on their cumulative and estimated costs.

The strength of A* lies in its balance between efficiency and optimality. The algorithm expands nodes in order of their estimated total cost, ensuring that the first path reaching the goal is guaranteed to be optimal when the heuristic is admissible and consistent. Common heuristic measures, such as Manhattan or Euclidean distance, allow flexible adaptation to grid-based or spatial environments. This capability made A* particularly well-suited for early applications in robotics, gaming, and automated navigation, where computational resources were limited but real-time decisions were required.

However, A* also has notable limitations. Its performance is highly dependent on the accuracy and design of the heuristic function—an inappropriate heuristic can lead to excessive computation or even near-exhaustive search [19]. Moreover, like Dijkstra and Floyd–Warshall, A* assumes a static environment, making it less effective in dynamic or uncertain contexts [20]. Subsequent algorithms have thus sought to enhance A* through adaptive, incremental, and learning-based extensions to improve real-time performance and scalability.

2.4. Ant Colony Optimization Algorithm

Due to the rapid development of transportation infrastructure and the widespread adoption of electronic information technologies, the focus of path planning research has shifted from static to dynamic environments, with greater emphasis on solving real-time path updating problems in transportation networks. In 1991, Marco Dorigo and others proposed the Ant Colony Optimization (ACO) algorithm, which solves combinatorial optimization problems by simulating the mechanism by which ants release and perceive pheromones during foraging [21].

The core of the ACO Algorithm is reflected in its route selection probability formula [22]. The scenario of this formula is that when the kth ant is at node i, it needs to choose the next destination node from the current node i. The nodes that ant k has not visited are recorded in the set ${allowed}_k$ and the probability of ant k choosing to go j from i is calculated as (1)

$$P_{ij}^k\left(t\right)={\displaystyle \frac{[{{\tau }_{ij}\left(t\right)]}^{\alpha }\times [{{\eta }_{ij}\left(t\right)]}^{\beta }}{\sum _{l\in {allowed}_k}[{{\tau }_{ij}\left(t\right)]}^{\alpha }\times [{{\eta }_{ij}\left(t\right)]}^{\beta }}}ifj\in {allowed}_k,$$

(1)

where ${\tau }_{ij}\left(t\right)$ is the parameter indicating the pheromone concentration, a parameter controlled by pheromone, representing the pheromone concentration from node i to node j at time t. ${\eta }_{ij}\left(t\right)$ is the heuristic factor, usually defined as the inverse of the distance between two nodes, reflecting the attractiveness of the distance between node i and node j to the ant’s choice. α and β is used to control the influence of these two parameters. This formula reflects the simple principle that the denser the pheromone and the shorter the path, the more the ant tends to choose the path [23]. Each ant constructs a path probabilistically based on the heuristic information of the current pheromone concentration and path length. After each round of iteration, pheromones are left on the path, and the pheromones of excellent paths are accumulated. At the same time, the ACO algorithm also introduces a pheromone volatilization mechanism to prevent the algorithm from falling into a local optimum. After multiple rounds of iteration, the pheromone of the global shortest path is the densest and is gradually strengthened. It stops when there is no obvious improvement in the path within several rounds. Since pheromones ${\tau }_{ij}\left(t\right)$ and heuristic factors ${\eta }_{ij}\left(t\right)$ can be dynamically input, this enables dynamic path planning [24].

2.5. Probabilistic Roadmap Method

The introduction of randomization and sampling techniques has given rise to sampling path planning algorithms, which are developed for path planning in high-dimensional spaces and under complex constraints. The Probabilistic Roadmap Method (PRM) is a classic sampling path planning algorithm that randomly samples legal nodes (no collision points) in free space and tries to connect these points into obstacle-free paths, thereby constructing a “probabilistic path graph” [25]. On the probabilistic graph, traditional graph theory search algorithms (such as Dijkstra or A*) can be used to find the shortest path from the starting point to the end point [26].

PRM can be divided into two phases: the first is the offline composition stage, and the second is the online query phase using the probability graph. The graph search in the query phase of PRM relies on classical shortest-path algorithms such as Dijkstra or A*, which is not considered the algorithm’s innovation. The key contribution of PRM lies in the probabilistic construction of a roadmap in high-dimensional configuration space. In the graph construction phase of PRM, the algorithm first randomly samples many collision-free nodes in free space and uses them as vertices of the graph. Then, for each sampled point, it searches for several neighboring nodes and tries to connect them with a locally feasible path (such as a straight line). Only when the connection path is completely in free space, that is, without interference from obstacles, is a weighted edge added between the two nodes, and the weight is usually the Euclidean distance between the two points. After this series of operations, PRM constructs a sparse and connected graph structure (roadmap) in the high-dimensional configuration space, which approximately represents the feasible motion area of the system and provides a basis for subsequent path search [27].

In summary, PRM effectively transforms the continuous path planning problem into a graph search problem through probabilistic sampling and local connection, widely used for multiple queries in static environments [28].

2.6. Rapidly Exploring Random Trees

Rapidly Exploring Random Trees (RRT) is another sampling path planning algorithm, using an expanding random tree to quickly “explore” the entire free space from the starting point [29]. Differ from the two-phase PRM, the RRT is an online sampling algorithm that can perform exploration and composition at the same time.

The algorithm starts with a tree T, which initially contains only the root node (starting point). In each round of iteration, the algorithm randomly samples a target point in the entire configuration space, then searches for the existing node closest to the point in the current tree and then extends a fixed-length step from the node in the direction pointing to the target point to generate a new candidate node [30]. If the extended path has no collision in space, that is, it is completely in the feasible area, the new node is added to the tree and its parent node is recorded for subsequent path backtracking. By repeatedly sampling and expanding, RRT can quickly explore the feasible area in high-dimensional complex space in an adaptive manner. When the newly expanded node is close enough to the target point and the path from the node to the end point is also unobstructed, the algorithm considers that a feasible path has been successfully found, and the entire path can be restored by tracing the parent pointer of the node. If the end point cannot be connected within the set maximum number of iterations, the algorithm returns failure [31].

RRT’s “exploration while expanding” strategy makes it very suitable for dynamic environments and high-dimensional path problems, although the path it generates may not be optimal or smooth. The whole exploration process is shown in Figure 3 [32].

2.7. Vision–Language Models Based Method

While sampling-based algorithms such as PRM and RRT significantly improved the efficiency and scalability of classical path planning, they still rely primarily on geometric representations and lack the ability to interpret high-level semantic cues from real-world environments. To address this limitation, recent studies have begun to integrate Vision–Language Models (VLMs) into path planning frameworks, enabling algorithms to reason over both visual and linguistic information and thereby enhancing decision-making in complex urban contexts.

Representative examples include SignEye [33], which interprets traffic signs from first-person driving views using multi-modal vision–language transformers, and SignParser [34], which semantically parses regulatory signs into machine-readable descriptions for decision-level reasoning. Other VLM-driven frameworks demonstrate that language-grounded perception can improve the adaptability and robustness of traditional algorithms under complex urban scenarios [35]. These advances mark a new paradigm where rule-based algorithms and data-driven perception modules operate cooperatively—traditional path planners continue to provide mathematical rigor and optimality, while VLM-based interpretation enhances contextual intelligence and real-time responsiveness.

VLM-based methods expand the capability of traditional path planning by combining perception and reasoning, improving situational awareness and adaptability in unstructured environments. However, their deployment remains limited by computational cost, data requirements, and integration complexity when coupled with classical algorithms. Despite these challenges, the fusion of visual understanding and path reasoning marks an important step toward fully context-aware and human-aligned intelligent transportation systems.

3. Research Progress on Classical Algorithms

Entering the 21st century, as the core technology in the fields of artificial intelligence, intelligent transportation, autonomous driving, logistics distribution and mobile robots, path planning algorithms have attracted extensive attention worldwide. With the rapid development of big data, robotics, and artificial intelligence, path planning has become deeply integrated with technologies such as deep learning and reinforcement learning and has begun to focus on multi-objective optimization and multi-agent collaboration. This section reviews the major research breakthroughs and evolving paradigms that have extended or improved traditional algorithms, leading to more adaptive, efficient, and scalable solutions for modern urban mobility challenges.

To address the computational inefficiency of the conventional Dijkstra algorithm in large-scale or real-time applications such as car navigation, Noto and Hiroaki (2000) proposed an extended Dijkstra method that significantly reduces search time while maintaining near-optimal path quality [36]. Their approach introduces a bidirectional search strategy, in which the algorithm simultaneously expands from both the source and the destination nodes. This method restricts the concentric expansion typical of classical Dijkstra, effectively reducing the number of nodes evaluated by nearly half. Simulation results on large-scale grid networks demonstrated that the extended Dijkstra method could cut search time by up to 80% while preserving over 99% of the solution optimality. The authors further suggest hybridizing the method with genetic algorithms to handle even broader search spaces under time constraints, indicating strong potential for integration in real-time ITS applications.

To further enhance the applicability of Dijkstra’s algorithm in dynamic and multidimensional environments, Wang et al. (2019) proposed a three-dimensional extension tailored for multi-objective ship voyage optimization [37]. Unlike conventional two-dimensional implementation, this approach represents each node as a triplet (x,y,t), integrating both spatial coordinates and temporal information. By embedding navigational speed and route decisions into the graph structure, the algorithm effectively balances multiple objectives—such as fuel consumption, estimated time of arrival (ETA), and structural fatigue—within the shortest path computation. Experimental results demonstrated that the 3D Dijkstra algorithm achieved near-optimal routes while reducing fuel usage by approximately 5% compared to traditional methods, thereby validating its efficacy under real-world sea conditions. This extension exemplifies how classical graph-based methods can be adapted for high-dimensional, real-time decision-making problems in ITSs.

The research group of Duan Ran at the Institute for Interdisciplinary Information Sciences, Tsinghua University, proposed a new randomized algorithm to solve the Single-Source Shortest Path (SSSP) problem in undirected graphs with non-negative real weights. This algorithm breaks the traditional time complexity limit of Dijkstra-based methods of $O\left(m+nlogn\right)$ in the comparison-addition model, overcoming the sorting time barrier of the Dijkstra algorithm [38].

The research group of Xu An at the People’s Public Security University of China improved the Floyd algorithm, reducing the original computational complexity from $O\left(n^3\right)$ to $O\left({\displaystyle \frac{1}{2}}{n}^3\right)$, effectively decreasing computational cost and improving efficiency [39].

To improve the performance of the classical A* algorithm in mobile robot navigation, a modified version was proposed by František (2014), which incorporates heuristic enhancements and optimized node evaluation criteria to reduce computational complexity and improve path smoothness. Unlike traditional A* that may generate jagged or suboptimal paths in grid-based environments, the modified algorithm introduces a path smoothing mechanism and a dynamic weight factor for the heuristic function, thereby balancing path optimality and efficiency. Experimental simulations conducted in grid maps with static obstacles demonstrated that the modified A* algorithm yielded shorter and smoother paths with reduced computation time, indicating its suitability for real-time robotic applications in structured environments.

The research group of Wei Tong at Beihang University proposed an improved method based on genetic algorithms to address the issues of non-optimal path length and path discontinuity between successive planning results in conventional path planning algorithms. Insertion and deletion operators were introduced into conventional genetic operations, and the continuity of the planned path was incorporated into the fitness function to compute the fitness value of each candidate path and select the one with the highest fitness as the current optimal path. This research holds significant importance for realizing autonomous navigation of mobile robots [40].

The research group of Zhang Zhineng addressed the difficulty of existing local path planning methods in handling complex conditions such as multi-lane scenarios and dynamic obstacles. Based on the concept of discrete optimization, they improved the A* algorithm and integrated it with the Dynamic Window Approach to enhance the efficiency of path planning and the real-time performance of dynamic obstacle avoidance. This algorithm utilizes the property of uniform curvature variation in spline curves to generate a set of parameterized candidate path clusters in the s-ρ curve coordinate system. It simultaneously considers factors such as dynamic collision safety, static safety, and road occupancy rate to select the optimal path [41].

The research group of Zhang Rongxia at Shandong University of Science and Technology introduced the representative Deep Q-learning Network (DQN) algorithm, which performs well in path planning under complex dynamic environments. This deep learning algorithm has been widely applied in robotic arms, real-time scheduling strategies for electric vehicles, indoor and outdoor path planning, and unmanned aerial vehicles (UAVs), while it still faces problems such as difficulty in acquiring real-world samples and high costs [42]. From our discussion, the appeal of DQN lies in its adaptability to complex dynamics. However, we also find that its reliance on large-scale training data and the difficulty of transferring models from simulation to reality raise concerns about generalizability, interpretability, and long-term reliability in safety-critical systems.

The research group of Liu Chunxiao incorporated deep learning algorithms into autonomous driving path planning methods. They used robotic visual information and global path data to infer the required steering angle of the robot at the current moment, and by training and validating the core neural network in indoor scenarios, they evaluated metrics such as total path length and average curvature variation. Experimental results showed that this approach exhibited excellent local path generation capabilities in both simulation and real-world environments [43]. Still, thinking critically about this approach, I see that its dependence on annotated data and its vulnerability to sensor noise or adversarial conditions highlight the challenge of achieving robust and trustworthy deployment in real-world urban driving scenarios.

The University of California proposed a path planning algorithm named Bidirectional Target-Oriented Exploring Random Tree (BTO-RRT), which enables fast, optimized, smooth, and dynamically feasible path planning in point cloud environments. The BTO-RRT algorithm combines bidirectional expansion with a three-step optimization strategy and is capable of rapidly generating smooth and optimal paths in point cloud environments, with efficient obstacle detection capabilities [44]. Reflecting on this method, I find that although BTO-RRT achieves impressive efficiency and smoothness in point cloud environments, its reliance on intensive computation and the sensitivity to highly cluttered scenes suggest that real-time adaptability may remain a challenge when the environment is both dynamic and data-rich.

The research group of Alessandro Bonetti at the University of Modena and Reggio Emilia, building upon the traditional A* algorithm, proposed two improved path planning algorithms: Roadmap Hybrid A* and Waypoint Hybrid A*, which are suitable for car-like autonomous vehicles in logistics and industrial environments, particularly in narrow corridor scenarios. The Roadmap Hybrid A* algorithm combines the A* algorithm with a static roadmap search algorithm, featuring the flexibility of real-time obstacle monitoring, higher stability, and faster computation. The Waypoint Hybrid A* algorithm uses a topological map of the environment to generate waypoints, guiding the A* algorithm to reach the target pose, which can effectively reduce complexity and search time [45]. These improvements indeed enhance the practicality of A* in structured industrial settings. Yet, it cannot be ignored that their dependence on accurate maps and predefined waypoints seems to limit flexibility once the environment becomes highly dynamic or less predictable.

Mosab Diab and others at Delft University of Technology in the Netherlands, based on the traditional Artificial Potential Field (APF) method, proposed an improved algorithm for path planning in complex environments, addressing the limitations of traditional path planning. By introducing a bacterial point model, adaptive parameter tuning, and a segmented repulsive potential function, this research successfully overcomes the limitations of traditional APF methods in complex environments, improves navigation success rates and path planning efficiency, and provides new solutions for future autonomous navigation tasks such as drones and self-driving vehicles [46]. I recognize its ingenuity in overcoming several traditional APF limitations. Still, the need for careful parameter tuning and the lingering possibility of local minima make me question how seamlessly it can generalize across very complex urban settings.

The research group of Zachary Clawson at Cornell University in the United States proposed a bi-objective path planning algorithm, designed to simultaneously optimize two path planning objectives in complex environments. This algorithm achieves significant improvements over traditional path planning algorithms by expanding the state space and can efficiently generate optimal paths that satisfy multiple objectives in complex environments. It not only overcomes the limitations of scalarization methods but also has broad application potential in areas such as robotic navigation, UAV mission planning, and autonomous driving optimization in complex scenarios [47].

In summary, the advancements built upon classical algorithms have significantly improved computational efficiency, path smoothness, and adaptability to dynamic environments through hybridization, heuristic optimization, and learning-based strategies. However, despite these technical achievements, most works focus on optimizing individual algorithms rather than providing a systematic comparison across different paradigms. As a result, there remains a lack of analytical frameworks to guide the selection of appropriate algorithms under varying traffic conditions, objectives, and computational constraints. These unresolved issues highlight the need for comparative evaluation and cross-paradigm analysis, which form the basis of the discussion in the following section.

4. Discussion

With the rapid advancement of ITSs, a wide variety of path planning algorithms have been proposed and implemented to address different urban mobility challenges. While each algorithm offers unique advantages, a systematic comparison is essential to understand their respective strengths, limitations, and application suitability.

Path planning algorithms can be broadly categorized based on their underlying methodological paradigms, which reflect distinct approaches to solving optimization and decision-making problems. Graph-based search algorithms such as Dijkstra, Floyd–Warshall, and A* rely on deterministic traversal of predefined network structures. These methods are mathematically rigorous and guarantee optimality under static conditions but often struggle with scalability and responsiveness in dynamic environments [48]; Heuristic and metaheuristic algorithms, including ACO and GA, are inspired by natural phenomena and biological evolution. These approaches use iterative exploration and probabilistic strategies to identify near-optimal solutions in complex or changing scenarios. They are particularly effective in dynamic path planning tasks where traditional methods fail to adapt; Sampling-based methods, such as PRM and RRT, transform continuous high-dimensional motion planning into discrete graph search problems. PRM constructs a roadmap through random sampling in static space, while RRT incrementally explores the feasible configuration space online, making it suitable for real-time applications; Finally, learning-based algorithms, especially those leveraging deep reinforcement learning like Deep Q Networks (DQN), represent a new frontier. These data-driven methods can learn adaptive policies from experience, offering strong potential in uncertain, unstructured, or data-rich environments. However, they require extensive training data and raise concerns about generalization and interpretability [49].

Another meaningful way to classify path planning algorithms is by their functional roles in navigation tasks, particularly regarding their source–target structure and planning scope [50]. Single-source shortest path algorithms, such as Dijkstra and A*, are designed to compute the optimal path from one origin to all or specific destinations within a known network. These methods are foundational in route guidance systems and are suitable for scenarios with fixed origins. In contrast, multi-source or all-pairs shortest path algorithms, exemplified by the Floyd–Warshall algorithm, aim to compute shortest paths between all node pairs. Although comprehensive, such algorithms are computationally expensive and mainly used in offline global analysis. A further distinction can be made between global path planning and local or online path planning. Global planners, including PRM and classical Dijkstra, assume complete environmental knowledge and aim for overall optimality. Meanwhile, local planners like A*, RRT, or DQN operate under partial observability or in dynamically changing environments, continuously updating the route based on real-time input. Lastly, emerging needs in ITSs have led to multi-objective path planning algorithms, which optimize for more than one criterion—such as distance, time, energy consumption, or risk. Algorithms like bi-objective planning or improved ACO variants are used in traffic scenarios requiring trade-offs between competing objectives [51].

To provide a comprehensive understanding of the performance and applicability of the path planning algorithms discussed above, this section will end by conducting a comparative analysis based on four critical evaluation dimensions: time complexity, dynamic adaptability, robustness, and high-dimensional scalability. These dimensions are selected to reflect both theoretical and practical requirements in ITSs, particularly in the context of real-time urban mobility, uncertain environments, and computational resource constraints [52]. Time complexity directly reflects the algorithm’s computational efficiency, which is crucial for large-scale traffic networks or embedded systems with limited processing power. Floyd–Warshall and PRM have the highest time complexity and are suitable for offline computation. Dijkstra and A* have medium complexity and are often used for static path planning. RRT has a lower time complexity and is suitable for fast sampling. DQN has a high training time but a low inference time, making it suitable for real-time decision making. Dynamic adaptability evaluates whether an algorithm can adjust to changing traffic conditions, obstacles, or environmental inputs in real time. RRT and DQN can adapt to dynamic environments and are preferred for dynamic or learning systems. Other algorithms, such as Dijkstra, Floyd–Warshall, A*, and PRM, lack dynamic adaptability and are therefore suitable for static environments. Robustness assesses the algorithm’s ability to maintain reliable performance in the face of disturbances, data uncertainty, or incomplete information—an increasingly important factor in open, complex transportation systems. RRT is highly robust and can remain effective in complex environments. A*, Dijkstra, and DQN exhibit moderate robustness. Floyd–Warshall and PRM are less robust and are easily affected by obstacles or high-dimensional interference. High-dimensional scalability considers how well an algorithm generalizes to high-dimensional configuration spaces, such as those involved in autonomous vehicles, robotic fleets, or airspace navigation. RRT and PRM perform well in high-dimensional spaces and are suitable for drone or robot navigation. A* and DQN perform moderately well. Dijkstra and Floyd–Warshall lack scalability and are mainly suitable for low-dimensional graph structures. The comparison between these algorithms is summarized in

Table 1. Comparison Analysis Between Algorithms.

Algorithm	Dijkstra	Floyd–Warshall	A*
Time Complexity	Medium	High	Medium
Dynamic Adaptability	No	No	No
Robustness	Moderate	Low	Moderate
High-dimensional scalability	No	No	Moderate
Typical application	Static road network navigation	Offline network analysis	Grid map navigation

and

Table 2. Comparison Analysis Between Algorithms (continued).

Algorithm	PRM	RRT	DQN
Time Complexity	High	Low-Medium	High for training, low for inference
Dynamic Adaptability	No	Yes	Yes
Robustness	Low	High	Moderate
High-dimensional scalability	High	High	Moderate
Typical application	High-dimensional free space	UAV/robot navigation	Intelligent decision-making and control

.

In summary, the comparative analysis reveals that each algorithm exhibits distinct strengths and trade-offs across key dimensions such as time complexity, adaptability, robustness, and scalability. Classical methods offer interpretability and optimality but lack flexibility, while heuristic, sampling-based, and learning-driven approaches provide greater adaptability at the cost of complexity or transparency. The choice of algorithm should therefore align with the specific requirements and constraints of the intended urban transportation application.

5. Challenges and Prospects

In the 21st century, the field of path planning algorithms has made remarkable progress, with extensive applications in autonomous driving, mobile robotics, and intelligent transportation infrastructure. Despite breakthroughs in classical search algorithms, metaheuristics, and deep learning-based strategies, these algorithms still face several fundamental challenges in real-world deployment. Notably, generalizability across heterogeneous urban environments and robustness under dynamic and uncertain conditions remain limited. Computational inefficiency and scalability issues persist, especially in high-dimensional and time-sensitive tasks such as real-time navigation in congested cities or disaster-affected zones.

In addition to technical hurdles, policy-related challenges are increasingly shaping the trajectory of ITSs. Algorithmic decision-making raises concerns about fairness, transparency, data protection, and liability attribution—particularly as autonomous mobility systems gain autonomy in routing, risk assessment, and vehicle control. With the growing reliance on AI-driven path planning, there is a risk that algorithms may inadvertently reinforce social inequities, such as allocating longer travel times or reduced service quality to underserved populations. Recent research has emphasized the importance of embedding fairness constraints into transportation algorithms to ensure equitable outcomes across diverse user groups. For instance, Cohen argue that algorithmic equity should be treated as a fundamental design principle in transport systems, advocating for fairness-aware optimization that mitigates spatial and socio-economic biases [53]. Similarly, Faghri and Withers highlight the challenges of quantifying transportation equity, noting that traditional performance metrics often overlook distributional justice, thereby necessitating new frameworks to evaluate fairness in intelligent mobility [54]. Beyond metrics, Creutzig emphasize that machine learning–driven transport planning must integrate inclusivity to prevent systematic exclusion of vulnerable populations [55]. These studies collectively suggest that future path planning research must move beyond efficiency and robustness, to explicitly incorporate fairness-aware methodologies and participatory governance, ensuring that algorithmic advances support socially just and inclusive urban mobility. Moreover, data governance becomes essential when deploying AI-based mobility services, particularly in urban areas where sensors, connected vehicles, and edge computing continuously generate sensitive user data. Policies must define not only data ownership and access but also the permissible use of such data in real-time decision systems [56]. This is especially critical in smart cities where AI systems interact with public infrastructure and citizens at scale.

From a planning perspective, there is an urgent need for urban transport policies to explicitly integrate AI-based tools into strategic decision-making. For example, AI-enhanced path planning can be used to support congestion pricing, real-time fleet optimization, and adaptive traffic signal control—but only if regulatory structures permit data sharing and public–private cooperation. Without supportive institutional arrangements, even the most advanced algorithms may remain confined to simulations or isolated pilot projects. In parallel, integrating perception-based modules such as traffic sign detection, recognition, and interpretation into AI-driven planning frameworks can further enhance situational awareness and safety in autonomous driving systems. Such integration highlights the importance of aligning algorithmic innovation with policy, standardization, and data governance to ensure robust and reliable deployment in real-world urban environments.

Looking ahead, the evolution of path planning algorithms will likely follow four interrelated directions. The first is technological hybridization, integrating AI with digital twins, quantum computing, and next-generation networks to enable real-time urban optimization. The second is algorithmic sustainability, emphasizing energy-efficient and low-carbon routing aligned with climate goals. The third is ethical co-design, which promotes collaboration among engineers, data scientists, and policymakers to ensure social legitimacy. Finally, policy innovation—through regulatory sandboxes, open mobility data standards, and supportive governance—will be essential for safe and scalable implementation. Overall, future advancements will depend not only on technical progress but also on institutional foresight and policy responsiveness to achieve equitable and sustainable intelligent transportation.

6. Conclusions

This review has systematically examined the evolution and application of urban path planning algorithms within ITSs. From classical graph-based methods such as Dijkstra and Floyd–Warshall, to heuristic and metaheuristic approaches including A* and ACO, and further to sampling-based strategies like PRM and RRT, the field has undergone significant methodological diversification. More recently, learning-based techniques, particularly reinforcement learning and deep neural models, have opened new avenues for adaptive and real-time decision-making in complex traffic environments.

Through comparative analysis, we highlighted the trade-offs among these algorithms across key dimensions such as computational efficiency, robustness, adaptability, scalability, and fairness. Classical algorithms ensure interpretability and theoretical guarantees but face challenges in dynamic and high-dimensional contexts. Heuristic and sampling-based methods provide greater flexibility but often at the cost of optimality or computational burden. Learning-driven approaches show strong adaptability but raise concerns about data dependency, generalizability, and interpretability.

Looking ahead, the development of path planning algorithms must go beyond technical optimization to embrace broader societal goals. Future progress will depend on integrating fairness, transparency, and sustainability into algorithm design, ensuring that intelligent mobility solutions serve diverse urban populations equitably. Emerging technologies such as digital twins, 5G/6G networks, and quantum computing may further accelerate the scalability and responsiveness of urban path planning. However, the interplay between algorithmic innovation, regulatory frameworks, and ethical governance will be decisive in shaping the next generation of ITSs.

In conclusion, urban path planning algorithms are not only computational tools but also socio-technical instruments. Their future lies in harmonizing efficiency with inclusivity, adaptability with accountability, and innovation with sustainability—ultimately enabling resilient, fair, and intelligent urban mobility.