A Multi-Objective Path-Planning Approach for Multi-Scenario Urban Mobility Needs

Abstract

With the development of smart cities and intelligent transportation systems, path planning in multi-scenario urban mobility has become increasingly complex. Traditional path-planning approaches typically focus on a single optimization objective, limiting their applicability in complex urban traffic systems. This paper proposes a multi-objective vehicle path-planning approach tailored for diverse scenarios, addressing multi-objective optimization challenges within complex road networks. The proposed method simultaneously considers multiple objectives, including total distance, congestion distance, travel time, energy consumption, and safety, and incorporates a dynamic weight-adjustment mechanism. This allows the algorithm to provide optimal route choices across four application scenarios: urban commuting; energy-efficient driving; holiday travel; and nighttime travel. Experimental results indicate that the proposed multi-objective planning algorithm outperforms traditional single-objective algorithms by effectively meeting user demands in various scenarios, offering an efficient solution to multi-objective optimization challenges in diverse environments.

1. Introduction

The development of smart cities and intelligent transportation has made multi-objective path planning a key technology to meet the demands of efficient traffic management and personalized travel in urban environments. Intelligent transportation systems require path planning to support traffic management, autonomous driving, logistics, and public transportation in finding efficient routes that alleviate traffic congestion, enhance transportation efficiency, and reduce energy consumption. Consequently, real-time dynamic planning, multi-modal travel integration, personalized demand, and big data support are essential requirements for path planning in smart cities. In modern transportation systems, multi-objective path planning can provide customized travel solutions tailored to diverse user needs, enabling them to make optimal choices by balancing factors such as time, cost, comfort, and environmental impact. Additionally, multi-objective path planning offers a scientific basis for the design of public transportation systems, road layouts, and infrastructure planning. By considering the needs of different groups and environmental impacts, urban planners can allocate resources more effectively to improve accessibility and equity in urban transportation, reduce congestion, and mitigate environmental damage.

In recent years, path planning has achieved significant advances across various domains, including intelligent transportation, robotics, logistics management, and urban planning. Traditional algorithms, such as Dijkstra’s and A*, remain foundational; however, their applications are limited in complex and dynamic environments. Researchers have worked to optimize these algorithms to enhance computational efficiency and adaptability. For instance, Jin et al. proposed a multi-modal path-planning approach based on a multi-objective A* algorithm [1], meeting the complex requirements of multi-modal transportation. Akopov et al. applied real-coded genetic algorithms in simulation-based optimization for autonomous transportation systems, demonstrating higher accuracy in solving large-scale optimization problems [2]. Wu et al. introduced a 2.5D multi-objective path-planning method based on deep reinforcement learning, achieving an effective trade-off between distance and energy consumption for vehicles in off-road terrain environments [3]. Ren et al. integrated D* Lite with an improved A* algorithm to develop an incremental multi-objective path-planning algorithm [4], addressing efficiency issues in dynamic environments. Wang et al. presented a method that combines an improved A* algorithm with a multi-objective cellular genetic algorithm aimed at emergency resource allocation and path planning in natural disaster chains [5]. Bostelmann-Arp et al. developed a multi-objective evolutionary optimization approach for coverage path planning in precision agriculture, aiming to increase field coverage efficiency while reducing energy consumption [6]. Zhang et al., Huang et al., and Pu et al. employed the ant colony optimization algorithm [7,8,9], while Cui et al. used the artificial bee colony algorithm [10] to address the multi-objective path-planning challenges for mobile robots. Ntakolia et al. utilized the ant colony optimization algorithm to enhance each Pareto solution, evaluating the optimal solution using a Mamdani fuzzy inference system to achieve multi-objective path planning for unmanned surface vehicles [11]. Zhao et al. proposed an innovative path-planning framework for unmanned surface vessels, which integrates multi-objective optimization with a perceptual vector re-planning strategy [12]. Xin et al. utilized an improved genetic algorithm for path planning of unmanned surface vehicles, achieving an optimal balance between path length and time cost through a multi-domain inversion algorithm [13]. Li et al. developed a multi-objective path-planning method for unmanned aerial vehicle inspection in oilfields, enhancing the efficiency and reliability of route planning [14]. Salhi et al. designed a multi-objective optimization approach to balance connectivity quality and energy consumption in UAV path planning [15]. Zhang et al., Xu et al., and Yu et al. independently introduced novel multi-objective evolutionary algorithms with dual constraint-handling mechanisms [16], dimension exploration, differential evolution [17], and an adaptive evolutionary multi-objective estimation of distribution algorithm [18], respectively. These approaches yield both short and safe routes in UAV path-planning applications.

Single-objective optimization algorithms are limited in their ability to balance multiple conflicting objectives, making them less practical for path planning that requires comprehensive consideration of multiple factors. Multi-objective optimization provides a more comprehensive and flexible path-planning solution suited to diverse application scenarios and user requirements. However, optimizing multiple objectives simultaneously in path planning significantly increases the problem’s complexity. Current research lacks in-depth consideration of user-specific requirements for different driving scenarios within urban traffic systems [19,20,21].

This study employs a genetic algorithm to optimize the A* path-planning method and introduces a dynamic weight-adjustment mechanism. This mechanism enables multi-objective path planning to dynamically prioritize objectives based on specific scenarios and user requirements, thereby providing route options that better align with user preferences. This approach holds significant potential for enhancing the efficiency of transportation systems, reducing environmental pollution, and ensuring driving safety.

2. Preliminaries

To address the multi-objective optimization problem in urban path planning, this study focuses on minimizing five key objectives: total distance; congestion distance; total time; energy consumption; and risk index. These objectives are subject to various constraints, including maximum allowable time, congestion distance limits, energy consumption limits, and safety requirements. By combining the A* algorithm and the genetic algorithm and introducing a dynamic weight-adjustment mechanism, the proposed framework aims to provide efficient solutions to multi-objective optimization challenges. This section outlines the A* algorithm for multi-objective path planning, the genetic algorithm, and the dynamic weight-adjustment mechanism.

2.1. A* Path-Planning Algorithm

The A* algorithm is a heuristic search algorithm widely used in pathfinding and graph traversal. As a heuristic search algorithm, A* iteratively selects the optimal node and expands the search path to find the optimal route globally. By using a comprehensive cost evaluation function, the A* algorithm effectively reduces the number of intermediate nodes that need to be traversed, thus enhancing algorithm efficiency. The formula for the comprehensive cost evaluation function is as follows:

$$f(n)=g(n)+h(n)$$

(1)

where $f(n)$ represents the comprehensive priority of node $n$. $g(n)$ denotes the accumulated path cost from the start node to the current node $n$. $h(n)$ is the heuristic estimation function, which estimates the cost from node $n$ to the goal node.

Algorithm 1 illustrates the A* path-planning algorithm, a widely used approach for finding an optimal path from a start node to a goal node in a network graph. This algorithm initializes two sets, openSet and closeSet. The openSet contains nodes that are pending exploration, while the closeSet contains nodes that have already been explored.

In each iteration, the algorithm selects the node $n$ from openSet with the lowest priority. If $n$ is the goalNode, the algorithm traces back from goalNode through its parent nodes to construct and return the path from startNode to goalNode, successfully completing the search. If $n$ is not the goalNode, it is removed from openSet and added to closeSet, marking it as explored. The algorithm then examines each neighbor $m$ of $n$. If $m$ is already in closeSet, it is skipped, as it has already been explored. If $m$ is not in openSet, it is added to openSet, with its parent set to $n$, and its priority is calculated. The priority of $m$ combines the known cost from startNode to $m$ and the heuristic estimate from $m$ to goalNode, balancing exploration with an efficient path toward the goal.

This process repeats until openSet is empty (indicating that no path is found) or until the goalNode is reached, at which point, the path is returned. If no path is found after all nodes are explored, the algorithm returns a message, “Path not found”, signaling that no valid route exists between the start and goal nodes in the given network graph [22].

Algorithm 1: A* Algorithm

Inputs: Road network graph $G$, start node $n_{\mathrm{start}}$, goal node $n_{\mathrm{goal}}$ Outputs: $\mathrm{Path} \mathrm{from} n_{\mathrm{start}}$$\mathrm{to} n_{\mathrm{goal}}$, or “Path not found” Initialize: openSet and closeSet $\mathrm{Add} n_{\mathrm{start}}$ to openSet, with priority set to 0 while openSet is not empty do  $n\leftarrow$ node in openSet with the highest priority  if $n$ is $n_{\mathrm{goal}}$ then   return the path traced back from $n_{\mathrm{goal}}$ to $n_{\mathrm{start}}$  end if  Remove $n$ from openSet  Add $n$ to closeSet  for each neighbor node $m$ of $n$$m$ do   if $m$ is in closeSet then    Skip this neighbor node   end if   if $m$ is not in openSet then    Set $m$’s parent node as $n$    Calculate $m$’s priority    Add $m$ to openSet   end if  end for end while return “Path not found”

2.2. Genetic Algorithm

The genetic algorithm is an optimization algorithm based on natural selection and genetic mechanisms, suitable for solving complex global optimization problems. Its core idea is to simulate the process of biological evolution, gradually optimizing the fitness of candidate solutions through operations of “selection”, “crossover”, and “mutation”, leading the population toward the optimal solution [23,24,25]. The following outlines the specific steps of the genetic algorithm:

In the initial stage of the genetic algorithm, a random population is generated, where each individual $\alpha$ represents a vector encoding a specific solution. Each individual is evaluated based on a fitness function $f(\alpha )$, with the goal of maximizing the fitness function.

In each generation, the selection operation is responsible for selecting individuals with higher fitness from the current population, increasing the probability that these individuals will be passed on to the next generation. The selection process is typically based on proportional selection according to individual fitness, meaning that the probability $p_i$ of selecting an individual is positively correlated with its fitness, as given by the following formula:

$$p_i={\displaystyle \frac{f(x_i)}{{\displaystyle \sum _{j=1}^{N}f}(x_j)}}$$

(2)

where $f(x_i)$ represents the fitness of the $i$-th individual, and $N$ is the total number of individuals in the population. Through the selection operation, individuals with higher fitness are more likely to be retained, guiding the population toward regions of higher fitness.

The crossover operation is used to perform gene recombination within the population to generate new offspring. Typically, two individuals are selected for crossover, exchanging parts of their genes to create new individuals. Assuming a crossover point $k$, the offspring $x_{\mathrm{new}}$ generated from individuals $x_i$ and $x_j$ can be represented as

$$x_{\mathrm{new}}=(x_{i1},x_{i2},\dots ,x_{ik},x_{j(k+1)},\dots ,x_{jn})$$

(3)

The crossover operation increases the diversity of solutions and explores a broader solution space, thereby enhancing the global search capability.

Subsequently, the mutation operation randomly modifies certain genes of an individual with a certain probability, introducing new genetic variations to maintain population diversity and prevent premature convergence to local optima. For gene $x_{nk}$, the mutation operation can be expressed as

$$x^{\prime }nk=xnk+\delta , \mathrm{with} \mathrm{probability} \mu$$

(4)

where $\delta$ is a small random change, and $\mu$ is the mutation rate. The mutation operation increases the exploratory capability of the population, enabling the algorithm to escape local optima and increasing the probability of global convergence.

Through multiple iterations of the above “selection–crossover–mutation” process, the genetic algorithm continuously generates new generations of individuals, gradually improving the population’s fitness.

2.3. Dynamic Weight-Adjustment Mechanism

To adapt to the needs of different traffic scenarios, we have introduced a dynamic weight-adjustment mechanism based on real-world scenarios. This mechanism adjusts the weights in real time according to changes in the scenario and environment, enabling the path-planning process to meet diverse travel requirements. When assigning weights, we fully consider the potential correlations between different objectives. Generally, total time, congestion distance, and total distance are positively correlated. To avoid the amplification of such correlations affecting the optimization results, the dynamic adjustment mechanism reduces the weight proportions of strongly correlated objectives, ensuring the fairness of multi-objective optimization. The weights for multi-scenario urban mobility needs are shown in

Table 1. Weights for multi-scenario urban mobility needs.

Scenario	Total Distance	Congestion Distance	Total Time	Energy Consumption	Safety
Urban Commuting	0.1	0.2	0.6	0.05	0.05
Energy-Efficient Driving	0.2	0.1	0.1	0.5	0.1
Holiday Travel	0.25	0.25	0.2	0.15	0.15
Nighttime Travel	0.2	0.05	0.2	0.15	0.4

.

2.3.1. Urban Commuting

In urban commuting during peak hours, traffic congestion and commute time are the primary concerns for drivers. Therefore, the dynamic weight-adjustment mechanism assigns higher weights to travel time and congestion distance in the path planning, prioritizing routes that reduce traffic congestion. Through this strategy, path planning can provide efficient travel solutions under congested conditions, helping users avoid congested sections.

2.3.2. Energy-Efficient Driving

In the context of energy-efficient driving, especially for electric vehicles and low-carbon travel demands, energy consumption becomes the primary optimization target. In this scenario, the dynamic weight-adjustment mechanism increases the weight for the energy consumption objective and reduces the weights of other objectives, guiding the algorithm to favor low-energy routes, even if travel time is slightly extended. This strategy effectively reduces overall energy consumption, aligns with the demands for energy-efficient driving, and helps save energy while extending the range of electric vehicles.

2.3.3. Holiday Travel

Holiday travelers typically value comfort and efficiency during their journeys. Users tend to prioritize travel comfort over the shortest possible time. The dynamic weight-adjustment mechanism assigns higher weights to total distance and time, ensuring that trips are both comfortable and efficient.

2.3.4. Nighttime Travel

Safety and traffic efficiency are critical considerations for nighttime travel, particularly for rideshare drivers and emergency responders. The dynamic weight-adjustment mechanism increases the weights for safety and time, ensuring safe and efficient travel in high-risk environments.

3. Multi-Objective Path Planning

In multi-objective path planning, to optimize the driving experience and enhance path-planning efficiency across different scenarios, this study targets the optimization of five objectives across various application contexts. This section introduces the specific methods for optimizing objectives.

3.1. Optimization Objectives

This study adopts the weighted sum method as the core algorithm for multi-criteria decision analysis, primarily due to its low sensitivity to weight variations and low computational complexity, which make it highly applicable to path planning. In contrast, other multi-criteria decision analysis methods have certain limitations. For instance, the multiplicative convolution method may amplify interactions between objectives, reducing the robustness of the algorithm. Similarly, although the TOPSIS method performs well in ranking solutions, its computational cost increases significantly in high-dimensional objective scenarios. Therefore, considering these factors, the weighted sum method is the optimal choice for this study.

The goal of multi-objective path planning is to minimize a weighted comprehensive objective function $F_{\mathrm{total}}(p)$. The path $p$ is defined as a sequence of consecutive nodes $(n_1,n_2,\dots ,n_k)$, where each pair of nodes $(n_i,n_{i+1})$ forms an edge in the graph $G$. This function consists of multiple weighting factors and corresponding objective terms, each representing a different optimization requirement. Each weighting factor is dynamically adjusted during the path-planning process based on the demands of real-world scenarios, enabling multi-objective optimization of the path. To ensure comparability among the optimization objectives, each objective needs to be normalized. The normalization method is detailed in Formula (16). The mathematical model for this multi-objective path optimization problem is as follows:

$$\begin{array}{cc}{\min }_p{F}_{\mathrm{total}}(p)\hfill & =\alpha (t)\cdot f_{\mathrm{length}}(p)\hfill \\ & +\beta (t)\cdot f_{\mathrm{congestion}}(p)+\gamma (t)\cdot f_{\mathrm{time}}(p)\hfill \\ & +\delta (t)\cdot f_{\mathrm{energy}}(p)+ϵ(t)\cdot f_{\mathrm{risk}}(p)\hfill \end{array}$$

(5)

$$\mathrm{s}.\mathrm{t}.\hspace{1em}\left\{\begin{array}{l}{f}_{\mathrm{time}}(p)\le T_{\max }\hfill \\ f_{\mathrm{congestion}}(p)\le C_{\max }\hfill \\ f_{\mathrm{energy}}(p)\le E_{\max }\hfill \\ f_{\mathrm{risk}}(p)\le R_{\max }\hfill \end{array}\right.$$

(6)

$$\forall i\in \{1,2,\dots ,k-1\},\hspace{1em}(n_i,n_{i+1})\in E$$

(7)

where $\alpha (t)$, $\beta (t)$, $\gamma (t)$, $\delta (t)$, and $ϵ(t)$ are the weighting coefficients dynamically adjusted according to the scenario. $f_{\mathrm{length}}(p)$ represents the total length of path $p$; $f_{\mathrm{congestion}}(p)$ is the congestion length of path $p$; $f_{\mathrm{time}}(p)$ denotes the total time of path $p$; $f_{\mathrm{energy}}(p)$ represents the energy consumption of path $p$, and $f_{\mathrm{risk}}(p)$ is the risk index of path $p$.

Equation (6) describes the constraints of this optimization problem. The path must be composed of consecutive nodes from the start to the destination, meaning that there is an edge between each pair of adjacent nodes $n_i$ and $n_{i+1}$ in graph $G$. The total travel time $f_{\mathrm{time}}(p)$ has an upper limit $T_{\max }$, representing the maximum acceptable travel time. The congestion length $f_{\mathrm{congestion}}(p)$ has an upper limit $C_{\max }$ to avoid paths passing through severely congested areas. The energy consumption $f_{\mathrm{energy}}(p)$ has an upper limit $E_{\max }$, meeting the demand for energy conservation. The risk index $f_{\mathrm{risk}}(p)$ has an upper limit $R_{\max }$ to ensure driving safety.

Equation (7) describes the decision variable constraints of the optimization problem. The decision variable is the feasibility constraint of the path: the path must consist of consecutive nodes from the start to the end, with an edge connecting each pair of adjacent nodes $n_i$ and $n_{i+1}$. $k$ represents the total number of nodes in the path, and $(n_i,n_{i+1})\in E$ indicates that there is an edge between node $n_i$ and node $n_{i+1}$.

This study selects five optimization objectives: total distance; congestion distance; time; energy consumption; and risk index. These objectives comprehensively assess the feasibility of each path based on the actual needs of users. Each optimization objective is described in detail below.

• Total Distance

The total distance of the path is defined as the cumulative length from the starting point to the endpoint. Given a path node sequence $n_1,n_2,\dots ,n_k$, where $k$ is the number of nodes in the path, the total distance $f_{\mathrm{length}}(p)$ of the path is expressed as

$$f_{\mathrm{length}}(p)={\displaystyle \sum _{i=1}^{k-1}d}(n_i,n_{i+1})$$

(8)

where $d(n_i,n_{i+1})$ represents the distance between nodes $n_i$ and $n_{i+1}$;

2.

Congestion Distance

The congestion distance refers to the cumulative length of all congested segments in the path and is used to assess the traffic condition of the path. Congestion status is determined by the “congestion tag” in the path. The congestion distance $f_{\mathrm{congestion}}(p)$ of the path is defined as follows:

$$f_{\mathrm{congestion}}(p)={\displaystyle \sum _{i=1}^{k-1}\left\{\begin{array}{l}d(n_i,n_{i+1}),\mathrm{if} \mathrm{congestion}(n_i,n_{i+1})>0\\ 0,\mathrm{otherwise}\end{array}\right.}$$

(9)

where $\mathrm{congestion}(n_i,n_{i+1})$ is the congestion value of edge $(n_i,n_{i+1})$. If the congestion value is greater than zero, the segment distance is included in the cumulative congestion distance;

3.

Total Time

The total time $f_{\mathrm{time}}(p)$ of the path comprises the driving time and the waiting time at red lights. In this study, the average vehicle speed is set to $v$ = 60 km/h, and the red light waiting time is assumed to be 1 min per stop. The total time can be expressed as

$$f_{\mathrm{time}}(p)={\displaystyle \frac{f_{\mathrm{length}}(p)}{v}}+r\cdot t_r$$

(10)

where $f_{\mathrm{length}}(p)$ is the total length of the path; $r$ is the number of red lights along the path, and $t_r$ is the waiting time per red light;

4.

Energy Consumption

Based on the phenomenon of increased energy consumption under congested conditions, this study evaluates energy consumption according to the congestion status of the path. Due to frequent acceleration, deceleration, and idling, vehicles experience additional energy consumption. The value of 20% is used as an average to represent the extra impact of congestion on energy consumption. The total energy consumption $f_{\mathrm{energy}}(p)$ of the path can be represented as

$$f_{\mathrm{energy}}(p)={\displaystyle \sum _{i=1}^{k-1}e}(n_i,n_{i+1})$$

(11)

where $e(n_i,n_{i+1})$ denotes the unit energy consumption from node $n_i$ to node $n_{i+1}$, defined as

$$e(n_i,n_{i+1})=d(n_i,n_{i+1})\times \left\{\begin{array}{ll}1.2,\hfill & \mathrm{if}\mathrm{congestion}(n_i,n_{i+1})>0\hfill \\ 1,\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(12)

When a segment of the path is congested, the energy consumption increases by 20% due to congestion; otherwise, it is calculated at the normal rate;

5.

Risk Index;

6.

In this study, the risk index is measured by the sum of the “road type score” and “traffic flow score”. The risk index $f_{\mathrm{risk}}(p)$ of the path is calculated as

$$f_{\mathrm{risk}}(p)={\displaystyle \frac{d(n_i,n_{i+1})}{f_{\mathrm{length}}}}{\displaystyle \sum _{i=1}^{k-1}(\mathrm{RL}(}{n}_i,n_{i+1})+\mathrm{TL}(n_i,n_{i+1}))$$

(13)

where $\mathrm{RL}(n_i,n_{i+1})$ represents the road type score from node $n_i$ to node $n_{i+1}$; $\mathrm{TL}(n_i,n_{i+1})$ represents the traffic flow score from node $n_i$ to node $n_{i+1}$; $d(n_i,n_{i+1})$ is the length of the edge from node $n_i$ to node $n_{i+1}$, and $f_{\mathrm{length}}(p)$ is the total length of the path. The road type score is as follows:

$$\mathrm{RL}(n_i,n_{i+1})=\left\{\begin{array}{ll}5,\hfill & \mathrm{Highway}\hfill \\ 4,\hfill & \mathrm{Urban} \mathrm{Main} \mathrm{Road}\hfill \\ 3,\hfill & \mathrm{Urban} \mathrm{Sec}\mathrm{ondary} \mathrm{Road}\hfill \\ 2,\hfill & \mathrm{Rural} \mathrm{Road}, \mathrm{Alley}, \mathrm{Side} \mathrm{Road}\hfill \\ 1,\hfill & \mathrm{Other}\hfill \end{array}\right.$$

(14)

The traffic flow score is as follows:

$$\mathrm{TL}(n_i,n_{i+1})=\left\{\begin{array}{l}1,\ge 2000\mathrm{vehicles}/\mathrm{day}\\ 3,500~2000 \mathrm{vehicles}/\mathrm{day}\\ 5,\le 500 \mathrm{vehicles}/\mathrm{day}\end{array}\right.$$

(15)

The risk index comprehensively considers the impact of road type and traffic flow on the safety of the path. A higher score indicates a greater potential risk associated with the road. When optimizing the path, the system tends to favor paths with a lower risk index to enhance overall safety.

The selection of the above optimization objectives aims to comprehensively evaluate path quality from multiple dimensions, meeting the diverse requirements of vehicle path planning in intelligent transportation systems. The importance of each optimization objective varies across different scenarios. Through the dynamic weight-adjustment mechanism, the system can provide optimized path selections tailored to each specific scenario.

3.2. Optimization Method

In this experiment, a genetic algorithm is used for multi-objective optimization of path planning. The genetic algorithm is an evolutionary algorithm based on the principles of natural selection and genetics, evolving a population of paths through selection, crossover, and mutation operations to approximate the optimal solution in a multi-objective space. In the genetic algorithm optimization for multi-objective path planning, the diversity and rationality of the initial population are key factors influencing the final optimization effect. To generate an initial population that is both diverse and feasible, this study uses the A* algorithm to generate a set of feasible paths from the start node to the goal node. To avoid excessive concentration or convergence of the generated paths, a dynamic avoidance point strategy is introduced, which enhances the diversity of each path in the population while maintaining feasibility. This approach allows a more comprehensive coverage of the search space, facilitating crossover and mutation operations in subsequent genetic processing. For each generated path, the values of each objective attribute are calculated, which will be used in the subsequent multi-objective optimization process.

Algorithm 2 describes the process of generating an initial population of paths. First, it accepts the road network graph $G$, the start node $n_{\mathrm{start}}$, the end node $n_{\mathrm{end}}$, and the number of candidate paths $M$ as inputs. To enhance path diversity, the algorithm temporarily removes nodes from the avoidance set $P_{\mathrm{avoid}}$ during each path generation to ensure that the generated paths are not completely identical. In each iteration, the algorithm uses the A* algorithm to search for the optimal path $b_k$ from the start node to the end node in the road network graph. Then, the generated path $b_k$ is added to the candidate path set $P$, and a node from path $b_k$ is selected and added to the avoidance set $P_{\mathrm{avoid}}$ to prevent this node from being included in subsequent path generations. After the path generation is completed, the nodes in $P_{\mathrm{avoid}}$ are restored to the road network graph $G$ to ensure the integrity of the graph for the next path generation. Finally, the algorithm returns the initial population $P$, which contains $M$ paths.

Algorithm 2: A* Initial Path Generation

Input: $G$: Road network graph, $n_{\mathrm{start}}$: Start node, $n_{\mathrm{end}}$: End node, $M$: Number of candidate paths to generate in the population Output: $P$: Set of candidate paths in the initial population Initialize population count: population $\leftarrow 0$ $P\leftarrow \varnothing$ $P_{\mathrm{avoid}}\leftarrow \varnothing$ for each $k=(1,\dots ,M)$ do   Temporarily remove nodes in $P_{\mathrm{avoid}}$ from $G$   Use the A* algorithm in $G$ to search for the optimal path $b_k$ from $n_{\mathrm{start}}$ to $n_{\mathrm{end}}$   Add the generated path $b_k$ to the path set $P$   Select a node from $b_k$ and add it to $P_{\mathrm{avoid}}$   Restore nodes in $P_{\mathrm{avoid}}$ to $G$ end for return $P$

Algorithm 3 describes the process of using a genetic algorithm on the road network graph $G$ to find the optimal path from the start node $n_{\mathrm{start}}$ to the end node $n_{\mathrm{end}}$. Unlike traditional genetic algorithms that rely on fixed weights, Algorithm 3 employs dynamic weights $\alpha (t)$, $\beta (t)$, $\gamma (t)$, $\delta (t)$, and $ϵ(t)$, allowing the algorithm to adapt to varying optimization priorities. In addition, the use of the A* algorithm ensures that paths generated during mutation remain valid and connected. The algorithm begins by generating an initial population of paths. For each path $b_k$, its cost is calculated as the weighted sum of multiple objectives, including path length, congestion, time, energy consumption, and risk. The paths are then sorted by their costs, and the lowest-cost half is selected as parents for reproduction.

Next, the selected paths are shuffled and paired for crossover operations. For each pair of parent paths, path1 and path2, a random crossover point $c$ along the path length is selected. Two child paths are created by combining the first half of path1 with the second half of path2 to form child1 and the first half of path2 with the second half of path1 to form child2. These child paths are added to the new population $P_{\mathrm{new}}$ to increase diversity.

Subsequently, each path in $P_{\mathrm{new}}$ undergoes a mutation operation with a certain probability. If a mutation occurs, a random node $m$ in the path is selected as the mutation point, and a new node connected to $m$ is selected as the insertion node. If the new node is not adjacent to the next node in the path, the A* algorithm is used to generate a sub-path (referred to as “pathlink”) connecting the insertion node to the subsequent node in the original path, ensuring the connectivity and validity of the path. After each iteration, the path $B$ with the minimum cost in the population is selected. If $B$’s cost is lower than the global minimum cost $\mathrm{minCost}$, $B$ is marked as the global best path, referred to as “globalBest”. The algorithm continues until the maximum number of iterations $T$ is reached, at which point, it outputs the globalBest path.

This algorithm ensures diversity in the optimized paths through crossover and mutation operations, enabling the generation of solutions that satisfy multi-objective constraints. It ensures the generated paths meet the required targets while exhibiting optimal trade-offs and characteristics.

Algorithm 3: Path Optimization Algorithm

Inputs: Road network graph $G$, start node $n_{\mathrm{start}}$, end node $n_{\mathrm{end}}$, initial population size $N$, maximum iterations $T$, mutation rate $k$. Output: $B$: Optimal path after crossover and mutation. $globalBest\leftarrow \mathrm{None}$  $minCost\leftarrow \infty$ for each candidate path $b_k$ in the initial population $P$ do   $cost$$\leftarrow$$\alpha (t)\cdot f_{\mathrm{length}}(b_k)+\beta (t)\cdot f_{\mathrm{congestion}}(b_k)$$+\gamma (t)\cdot f_{\mathrm{time}}(b_k)+\delta (t)\cdot f_{\mathrm{energy}}(b_k)+ϵ(t)\cdot f_{\mathrm{risk}}(b_k)$ end for $selected$ $\leftarrow$ Select top $N/2$ paths based on $cost$ $P_{\mathrm{new}}\leftarrow \varnothing$ for each pair of paths (path1, path2) in $selected$ do   Select random crossover point $c$   child1 $\leftarrow$ path1[0:c] + path2[c+1:]   child2 $\leftarrow$ path2[0:c] + path1[c+1:]   Add child1 and child2 to $P_{\mathrm{new}}$ end for for each path in $P_{\mathrm{new}}$ do   if random probability < mutation rate     Select path[m] as mutation point     Select new node connected to path[m] and insert after path[m]     if path[m+1] and new node are not directly connected     Generate $pathlink$ $\leftarrow$A*search (G, new node, path[m+1])     Insert $pathlink$ into path   end if  end if end for $B\leftarrow$ Select the path with the minimum $cost$ in $P_{\mathrm{new}}$ if $cost(B)<minCost$   $globalBest\leftarrow B$   $minCost\leftarrow cost(B)$ end if $generation\leftarrow generation+1$ if $generation\ge T$   return $globalBest$ end if.

4. Experimental Design

This study adopts a multi-objective optimization approach for path planning by combining the A* algorithm with a genetic algorithm and applying weighted objectives to achieve optimal solutions. This section provides a detailed explanation of this experimental scheme for multi-objective path planning. The specific experimental scheme is shown in Figure 1.

This study uses open-source road network data obtained from OpenStreetMap [26]. The road network data are converted into a graph structure, and graph search algorithms are applied for path planning. Each intersection is treated as a node, and the segments between adjacent intersections serve as edges. The node information includes geographic coordinates and other details, while edges represent road segments and contain attributes such as length and road type. Additionally, to better simulate real traffic conditions, this study introduces randomly generated traffic lights and congestion attributes in the experimental design. Traffic light attributes include red and green signals, simulating the signal control characteristics of real-world traffic intersections. Furthermore, each edge is randomly assigned a congestion attribute to mimic the impact of varying vehicle densities on traffic speed, making path planning more aligned with actual requirements.

In this experiment, an initial population is generated using Algorithm 1, consisting of paths with the same start and end points but different routes. To evaluate the quality of each path individual, a comprehensive fitness function is designed. The fitness function is based on the weighted sum of the following five optimization objectives: total path length, length of congested segments, total time, energy consumption, and safety. To avoid the influence of scale differences between the various objectives on optimization and to make each objective comparable in fitness calculations, each objective is normalized. This normalization ensures that indicators with different units have a consistent basis for comparison. Let $x$ be the raw value of a certain objective, and let $x_{\min }$ and $x_{\max }$ be the minimum and maximum values of this objective within the current population, respectively. The normalized value $x_{\mathrm{norm}}$ is calculated as follows:

$$x_{\mathrm{norm}}={\displaystyle \frac{x-x_{\min }}{x_{\max }-x_{\min }}}$$

(16)

Through this normalization, the range of each objective is unified within the interval [0, 1], ensuring a balanced influence of different objectives on fitness during the optimization process. The normalized initial population data are then processed by Algorithm 2, where continuous crossover and mutation operations are applied to find the optimal path under multi-objective constraints.

5. Discussion

The performance of the multi-objective path-planning algorithm is presented across different experimental scenarios, with a detailed analysis of each experimental result. By comparing the optimization effectiveness of paths generated by different algorithms, the effectiveness of the proposed method is verified.

This experiment selected road network data within Wuhan as the study area, setting two geographical coordinates within Wuhan as the start and end points for path planning, with latitude and longitude coordinates of (114.2547391, 30.632697) and (114.3286448, 30.3069509), respectively. The geographic area of this experiment covers various road types, including highways, main roads, secondary roads, and residential roads, allowing the influence of different road types on various indicators to be reflected, thereby providing a more comprehensive test of the algorithm’s performance in multi-objective trade-offs.

In this experiment, 10 initial paths were generated using the A* algorithm with dynamic avoidance points, and optimized paths were selected using the multi-objective optimization algorithm. In different scenarios, the requirements and focus of path planning vary. Therefore, to evaluate the effectiveness of the algorithm in the multi-objective optimization process, we compared the changes in each indicator between the optimized paths and the initial population and conducted statistical analysis, as shown in

Table 2. Result of the multi-objective path-planning approach.

Scenario	Path Type	Total Length (km)	Congestion Length (km)	Total Time (hours)	Risk Index	Energy Consumption	Weighted Cost
Urban Commuting	Initial Population 5	75.5	7.657	1.258	4.674	77,030.846	0.276
	Initial Population 1	74.517	7.318	1.242	4.605	75,980.633	0.21
	Initial Population 2	70.533	8.113	1.176	4.93	72,155.424	0.079
	Optimized Path	69.442	4.077	1.391	4.623	70,257.355	0.075
Energy-Efficient Driving	Initial Population 5	75.5	7.657	1.258	4.674	77,030.846	0.269
	Initial Population 1	74.517	7.318	1.242	4.605	75,980.633	0.204
	Initial Population 2	70.533	8.113	1.176	4.93	72,155.424	0.075
	Optimized Path	65.458	4.872	1.474	4.974	66,432.146	−0.192
Holiday Travel	Initial Population 7	76.499	9.229	1.275	4.608	78,344.574	0.410
	Initial Population 5	75.500	7.657	1.258	4.674	77,030.846	0.393
	Initial Population 1	74.517	7.318	1.242	4.605	75,980.633	0.304
	Optimized Path	73.622	12.218	1.560	4.136	76,066.184	0.196
Nighttime Trave	Initial Population 7	76.499	9.229	1.275	4.608	78,344.574	0.420
	Initial Population 1	74.517	7.318	1.242	4.605	75,980.633	0.355
	Initial Population 10	83.014	16.924	1.384	4.361	86,398.536	0.350
	Optimized Path	70.99	8.955	1.483	4.095	72,781.000	−0.133

. The path maps for each scenario are shown in Figure 2, where the red curve represents the optimized path, and the other colored curves represent the paths from the initial population.

From the distribution of paths in each scenario shown in Figure 2, it can be observed that the dynamic avoidance point strategy significantly enhances the diversity of the population, providing a broad search space for the genetic algorithm. Table 2 presents the weighted cost and the three lowest-cost initial population paths, along with the optimized path for each scenario. In the “Urban Commuting” scenario, the optimized path has a total length of approximately 69 km, significantly shorter than the paths in the initial population. The total time of the optimized path is also lower than that of the initial population paths, meeting the primary requirement for speed and smooth traffic flow during peak hours. In the “Energy-Efficient Driving” scenario, the energy consumption of the optimized path is significantly lower than the average energy consumption level of the initial population, with fewer congested segments, further reducing energy usage. In the “Holiday Travel” scenario, the optimized path exhibits excellent performance in terms of total length, risk index, and energy consumption, balancing the trip’s cost-effectiveness with driving safety. In the “nighttime travel” scenario, the optimized path performs well in terms of risk index and path length, ensuring safety while reducing congested segments.

To further demonstrate the multi-objective optimization advantages of this algorithm in path-planning tasks, we designed a set of comparative experiments. Using the same initial path population, we compared the performance of our algorithm with single-objective optimization algorithms. The single-objective optimization algorithms selected were simulated annealing [27] and a greedy algorithm [28].

Table 3. Comparison results with other optimization methods.

Path Type	Total Length	Congestion Length	Total Time	Risk Index	Energy Consumption	Execution Time (s)
Genetic Algorithm Multi-Objective Optimization (Urban Commuting)	69.442	4.077	1.391	4.623	70,257.355	144.33
Genetic Algorithm Multi-Objective Optimization (Energy-Efficient Driving)	65.458	4.872	1.474	4.974	66,432.146	152.21
Genetic Algorithm Multi-Objective Optimization (Holiday Travel)	69.532	4.077	1.409	4.621	70,347.685	148.17
Genetic Algorithm Multi-Objective Optimization (Nighttime Travel)	73.63	12.218	1.56	4.174	76,073.595	140.94
Simulated Annealing Single-Objective Optimization	75.493	8.199	1.258	4.691	77,133.551	173.14
Greedy Algorithm Single-Objective Optimization	75.117	8.199	1.251	4.701	76,756.651	165.49

summarizes the optimization results of each algorithm.

From the experimental results, while our algorithm shows a slight disadvantage in the total travel time of the paths, it exhibits significant advantages in multiple dimensions, including path length, congestion avoidance, energy consumption control, and safety. First, the total length and congestion length in each scenario for our algorithm are almost universally lower than those of the single-objective optimization algorithms, indicating that multi-objective optimization can more efficiently avoid congested areas and find shorter paths. Second, the energy-saving effect of the multi-objective optimization algorithm is significantly better than that of the single-objective algorithms, making it an ideal choice for environmentally conscious users and those with long-distance driving needs. Additionally, the risk index of the paths planned by our algorithm is generally lower than that of the single-objective optimization algorithms, effectively enhancing the safety of users during driving. Finally, despite balancing multiple objectives, our algorithm demonstrates a shorter execution time compared to other methods like simulated annealing and greedy algorithms, highlighting its efficiency and practicality in real-world applications.

This fully demonstrates the effectiveness and superiority of our algorithm in meeting diverse path-planning requirements, providing an ideal path-planning solution for future real-world applications.

6. Conclusions

This study proposes a multi-objective path-planning method for vehicles in urban transportation tailored for various scenarios. The method introduces a dynamic weight-adjustment mechanism to accommodate the requirements of different traffic scenarios. Experiments conducted on the road network data from OpenStreetMap validate the effectiveness of this approach in meeting the demands of various scenarios, including urban commuting, energy-efficient driving, holiday travel, and nighttime travel. Compared with traditional single-objective optimization algorithms, the proposed method balances multiple conflicting objectives in path planning, resulting in more reasonable routes. This study provides a practical solution to the problem of multi-scenario, multi-objective path planning and demonstrates strong potential for application in urban transportation system optimization. As traffic networks expand and demands become more diverse, future research could further enhance the computational efficiency of the algorithm and introduce additional constraints to improve its applicability in real-time traffic environments. This study highlights the flexibility of the proposed method in addressing diverse traffic conditions, paving the way for its integration and application in intelligent transportation systems. Future research should explore the application of this method in more complex and dynamic traffic networks, such as multi-modal transportation systems or scenarios with highly variable traffic flow. Additionally, efforts could be made to further enhance the algorithm’s real-time computational performance and incorporate more optimization objectives or constraints to expand its practical applicability.