1 Introduction

Unmanned aerial vehicles (UAVs) have emerged as important tools in many industrial fields, such as military operations (Tahir et al. 2019; Yin et al. 2021), surveillance (Stolfi et al. 2020; Savkin and Huang 2022), agriculture (Del Cerro et al. 2021; Salam et al. 2021), search and rescue (Yang et al. 2020b; Ribeiro et al. 2022), environmental monitoring (Wang et al. 2021; Wang et al. 2021), and berth management and ship monitoring (Li et al. 2024). UAV path planning is a crucial problem in UAV technology, which aims to find the optimal flight path from the start point to the destination point for each aerial vehicle (Zhang et al. 2020). Due to the dynamic nature of the environment, the limited energy and resources of UAVs, and the requirement for real-time decision-making, the UAV path planning task becomes more challenging as the application scenario grows more complex. Conventional path planning strategies for UAVs, such as mathematical optimization techniques and deterministic optimization algorithms, are computationally intensive and are hard to efficiently solve UAV path planning tasks in more complex environments (Zhao et al. 2018; Puente-Castro et al. 2022).

Evolutionary computation (EC) is a nature-inspired optimization tool (Zhan et al. 2021, 2023; Jiang et al. 2023a), that imitates the principles of biological evolution and the social behavior of organisms. EC has powerful global search capability and robustness based on the principle of “survival of the fittest” (Zhan et al. 2022b). Also, EC does not require a precise mathematical model of the optimization problem and can obtain the optimal or suboptimal solution in an acceptable time. Due to these advantages, EC has been successfully applied to a wide range of optimization problems in real-world applications and achieved promising performance (Li et al. 2022c; Zhan et al. 2022a; Chen et al. 2022).

To date, numerous EC algorithms have emerged in the research field of UAV path planning and achieved considerable success (Yang et al. 2014; Jamshidi et al. 2020; Wang et al. 2022b). Compared with the other existing studies using learning-based algorithms to find the path, the EC algorithms have better adaptability and flexibility and are easier to implement and use (Puente-Castro et al. 2022; Luo et al. 2024). For example, although learning-based techniques like deep learning and reinforcement learning can be quite effective, they often require extensive training data and computational resources (Zhang et al. 2024; Tang et al. 2024). Also, they might need retraining or fine-tuning when the environment changes significantly. Meanwhile, EC algorithms can easily incorporate different constraints and dynamic environments without significant changes to the core algorithm.

To better show the development of studies on EC for UAV path planning in recent years, Fig. 1 summarizes the trend of the number of publications about EC for UAV path planning from 2013 to 2023 in three relatively well-known databases, which are Google Scholar, Web of Science, and IEEE Xplore. The search strategies in their corresponding search engines are summarized as follows: (1) Google Scholar: “evolutionary” AND “UAV path planning”. (2) Web of Science: evolutionary (Topic) and UAV path planning (Topic). (3) IEEE Xplore: (“All Metadata”: evolutionary) AND (“All Metadata”: UAV path planning). As can be seen in Fig. 1, the number of publications on EC for UAV path planning has dramatically increased since 2020, and the researchers’ interest in EC for UAV path planning increases every year.

Fig. 1
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The number of publications about EC for UAV path planning from 2013 to 2023 in different databases

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Although some surveys have been proposed to summarize the existing studies of EC for UAV path planning (Zhao et al. 2018; Yahia and Mohammed 2023), they merely classified the existing studies based on the categories of the EC algorithms rather than the application scenarios. Therefore, a systematic review of existing studies is necessary for the further development of EC for UAV path planning. It is crucial to review the related research and literature for enhancing the research on EC for UAV path planning. This paper presents a comprehensive survey to show the success achieved by EC in UAV path planning for different complex application scenarios and to discuss how to design more effective EC algorithms to handle this problem in increasingly complex environments.

The main contents of this survey are listed as follows:

  1. (1)

    First, this survey describes the basic definitions and concepts of the UAV path planning problem and several categories of EC algorithms.

  2. (2)

    Second, a taxonomy is designed and proposed based on the complex properties of various application scenarios, to conduct a thorough review of the pertinent studies of EC for UAV path planning. The taxonomy covers three different aspects of application scenarios in existing studies, which are complex search space, complex time control, and complex optimization objectives. This taxonomy can be useful to gain a deeper understanding of how well the EC algorithm handles UAV path planning in various complex application scenarios.

  3. (3)

    Third, this paper discusses the potential future research directions to enlighten new ideas on EC for UAV path planning, based on the reviews of various relevant studies.

The rest of this paper is organized as follows: Section 2 gives the preliminaries of this paper, including the concepts of UAV path planning, EC, and the description of the taxonomy. Sections 3 to 5 introduce three categories of related studies of EC for UAV path planning according to the taxonomy. Section 6 discusses several potential future research directions. Section 7 draws the conclusions of this paper.

2 Preliminaries

2.1 UAV path planning

Modern UAV applications rely heavily on UAV path planning (Li et al. 2022a). The goal of UAV path planning is to plan and find the optimal flight path of single or multiple UAVs using effective algorithms and techniques. Effective UAV path planning is crucial for UAV research and development as it can increase mission success, efficiency, and safety (Xiao et al. 2018; Savkin and Huang 2019). Numerous real-world application scenarios, including military operations, surveillance, agriculture, search and rescue, and environmental monitoring, have involved various UAV path planning tasks.

In the UAV path planning task, some important factors such as obstacle avoidance, mission objectives, and energy consumption should be considered by the path planning algorithms. To address the aforementioned factors, various traditional techniques have been proposed to solve UAV path planning tasks (Zhao et al. 2018). However, with the rapid development of UAV technology, UAVs are required to perform missions in increasingly complex environments. Traditional algorithms have difficulty in solving the UAV path planning problem in a more complex environment because the task of UAV path planning is more difficult in complex environments. As an effective meta-heuristic optimization tool, EC has achieved considerable success in solving the UAV path planning problem in a more complex environment.

2.2 EC

Evolutionary computation is a nature-inspired optimization tool. Due to their promising search capacity, EC algorithms have recently demonstrated considerable success in addressing a range of real-world optimization problems (Xu et al. 2024). The two principal branches of EC algorithms are evolutionary algorithms (EAs) and swarm intelligence (SI). The EA emulates the process of biological evolution, whereby superior solutions are selected and inferior ones are rejected, thereby guiding the entire population toward the global optimum. Genetic algorithm (GA) (Holland 1992; Wu et al. 2021; Liu et al. 2023a; Yang et al. 2023b) and differential evolution (DE) (Storn and Price 1997; Zhan et al. 2020; Jiang et al. 2023b; Wang et al. 2023) are two typical EAs. SI is inspired by the social behavior of organisms to update the candidate solutions to search for the optimal solution. Typical SI includes particle swarm optimization (PSO) (Kennedy and Eberhart 1995; Wang et al. 2020; Jian et al. 2021; Yang et al. 2023a) and ant colony optimization (ACO) (Dorigo and Gambardella 1997; Zhang et al. 2022; Shi et al. 2022; Wang et al. 2022a).

The general process of a typical EC algorithm contains four operations, which are initialization, fitness evaluation, solution evolution, and selection. First, in initialization, the candidate solutions are generated at random. To bring solutions closer to the global optimum, the fitness evaluation, solution evolution, and selection operations are then iteratively carried out. The fitness evaluation operation evaluates the fitness of each candidate solution based on how well it meets the problem objectives. The solution evolution operation, such as crossover and mutation, is executed to produce new offspring from the parental solution and update the population. Based on fitness, the selection operation chooses elite solutions among the parental solutions and offspring, with fitter solutions having a higher chance of being chosen.

Compared to other prevalent approaches, particularly learning-based algorithms such as reinforcement learning and neural networks, EC algorithms demonstrate significant robustness and efficiency in exploring large and complex search spaces without requiring a precise mathematical model of the problem (Puente-Castro et al. 2022; Luo et al. 2024). Reinforcement learning and neural networks excel in adapting to dynamic environments and learning from extensive datasets, enabling them to make data-driven decisions and optimize performance over time (Zhang et al. 2024; Tang et al. 2024). However, these methods often necessitate extensive training periods and can struggle with generalizing to new, unseen scenarios, limiting their applicability in rapidly changing or unpredictable environments. In contrast, EC has demonstrated the ability to provide competitive results with considerably less computational overhead. These algorithms are inherently flexible and can efficiently handle complex optimization tasks, making them well-suited for complex UAV path planning scenarios. EC algorithms leverage the principles of natural evolution and social behaviors, allowing them to adapt and find near-optimal solutions in diverse and challenging environments without the extensive data and training requirements typical of reinforcement learning and neural networks.

2.3 Taxonomy

The taxonomy of the existing studies on EC for UAV path planning is shown in Fig. 2. Previous surveys on EC for UAV path planning have primarily categorized these studies based on the types of EC algorithms. These algorithms can be broadly divided into two main branches: EA and SI. Typical EAs include GA and DE, while prominent SI algorithms include PSO and ACO. In contrast, this article categorizes existing studies based on the properties of application scenarios in UAV path planning. The complex properties of real-world application scenarios of UAV path planning can be classified from three aspects, which are the complex search space, complex time control, and complex optimization objectives. To be specific, the first part, i.e., the EC algorithms for UAV path planning with complex search space, includes two sub-categories, which are UAV path planning in constrained search space and UAV path planning in large-scale search space. The second part, i.e., the EC algorithms for solving UAV path planning tasks with complex time control, includes two sub-categories, which are dynamic UAV path planning and multi-UAV concurrent path planning. The third part, i.e., the EC algorithms for solving UAV path planning tasks with complex optimization objectives, includes two sub-categories, which are UAV path planning with expensive fitness evaluation and multi-objective path planning.

Fig. 2
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The illustration of the taxonomy based on the categories of EC algorithms and properties of UAV path planning

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3 EC For UAV path planning in complex search space

With the developments in UAVs, the path planning tasks of UAVs become more complex. In some real-world application scenarios, there are some additional complex properties in the search space. For example, the search space of the UAV path planning tasks has many constrained regions, or the search space is relatively large. It results in two different kinds of difficult UAV path planning tasks, namely the UAV path planning in constrained search space and the UAV path planning in large-scale search space. The complex properties in the search space pose great challenges to traditional methods. Due to the great potential of the EC algorithm in dealing with constrained optimization problems and large-scale optimization problems (Zhan et al. 2021), many relevant studies devoted to the use of EC algorithms to effectively solve UAV path planning tasks in constrained search space and large-scale search space (Chen et al. 2017; Yahia and Mohammed 2023).

3.1 UAV path planning in constrained search space

In real-world applications, the search space of each UAV can contain several forbidden flying areas and obstacles, which are constrained regions to each UAV. Also, when dealing with the path planning task for multiple UAVs, each UAV should avoid collision with other UAVs, and thus the surrounding region of each UAV is a constrained region to the other UAVs. Since the UAVs can not pass through these constrained areas, the UAV path planning task with constrained search space is more challenging.

Due to the deficiencies of the traditional deterministic algorithms in solving the UAV path planning task with constrained search space, many studies devoted to using EC algorithms to effectively solve this problem. These EC-based UAV path planners in constrained search space can be divided into two categories, including EC algorithms with several constraint handling strategies and EC algorithms with several novel evolutionary operations.

The first category of studies is the EC algorithms with several constraint handling strategies, which can avoid stepping into the constrained region to effectively solve the constrained path planning problem of UAVs. For example, Shen et al. (2021) proposed an EA based on multi-level constraint processing (ANSGA-III-PPS). In this work, the path planning task of each UAV was transformed into a multi-objective optimization problem in a 3D-constrained search space. To efficiently manage the constraints in the search space and create the ideal path, ANSGA-III-PPS developed an adaptive constraint processing technique. The research enriches UAV path planning and addresses various challenges in path optimization. To deal with UAV path planning in disaster scenarios, Yu et al. (2020) suggested an adaptive selection mutation constraint DE (ASMCDE), where the constraint violation rate was employed to help evaluate the paths. Although the limitations of ASMCDE in handling complex and dynamic disaster environments are not explicitly addressed, leaving room for further research and development, this paper demonstrates the competitiveness and suitability of EC algorithms for UAV path planning problems in disaster scenarios. B-spline curves are used in the new quantum-inspired monarch butterfly optimization (QMBO) algorithm created by Yi et al. (2020) to produce a smooth and constraint-free path. QMBO divides the population into two subpopulations and updates individuals using MBO and quantum computation theory simultaneously, leading to improved performance in finding optimal paths. Ding et al. (2022) transformed the problem of UAV path planning into a Dubins traveling salesman problem with dynamic neighborhoods and introduced a novel encoding scheme and decoding scheme, which can enhance population diversity and achieve rapid decoding. This work utilized the memetic algorithm (MA) to find the optimal solution and the feasibility of each path is calculated via the degree of constraint violation. Wang et al. (2016) designed an improved bat algorithm (IBA), where the B-spline curves are also used to generate more feasible paths.

The second category of studies is the EC algorithms with several novel evolutionary operations, aiming at enhancing the effectiveness of EC algorithms in constrained search space. For example, Cakir (2015) modeled the UAV path planning problem as a traveling salesman problem and used a GA to construct paths in a 2D search space with constrained regions. The experimental results showed that the GA-based planner may provide safe routes for independent single UAVs by avoiding prohibited areas in the 2D environment. However, the effect of algorithm design on the solution quality is not taken into account in this study. Ahmadi et al. (2018) proposed an action-based encoding GA (ABEGA) and a node-based encoding GA (NBEGA) to generate the optimal paths in the constrained search space in the offline mode. The simulation showed that the suggested techniques, particularly ABE, may produce workable routes that maximize coverage while adhering to operational constraints. Nevertheless, this study only considers the path planning problem in static environments, and the current UAV may required to handle dynamic obstacles. Yang et al. (2015) proposed a JADE-based path planner for solving constrained UAV path planning problems. In this work, a 3D coordinate system is adopted to limit the search space by requiring waypoints to increase monotonically along a single axis. Rather than optimizing the path as a whole at once, the suggested JADE-based path planner evolves each waypoint along the path independently, which enables more efficient UAV path planning by leveraging good waypoint positions across the population. Zhang and Duan (2015) considered multiple constraints in the search space and proposed a DE with level comparison (DELC) algorithm to deal with the constrained UAV path planning problem. The numerical experiments verified that the proposed algorithm performs better than the compared penalty function-based methods in terms of solution quality and constraint-handling ability. The method is tailored for UAV route planning in a fixed environment with known obstacles and threats and its applicability to dynamic or uncertain environments might be limited. Aiming at effectively solving the UAV path planning in the curvature-constrained search space, Xu et al. (2018) proposed a DE with a receding horizon control (DE-RHC) algorithm. The detection range of each UAV is restricted to a sector area within the view of the UAV. Sun et al. (2016) applied the UAVs as the receivers to receive the echo transmitted by the geosynchronous synthetic aperture radar and proposed a constrained adaptive multi-objective DE (CA-MODE) algorithm to find the optimal paths. The optimal path of each UAV is required to achieve a trade-off between the safe rate and the path distance in this application scenario.

3.2 UAV path planning in large-scale search space

In some real-world application scenarios, the UAVs are required to find the optimal paths in a very large search space (Arantes et al. 2015; Tan et al. 2019; Betalo et al. 2021). The UAV path planning in such a case is called the UAV path planning in large-scale search space. This kind of problem poses a significant challenge to the EC algorithms, as the large search space contains more obstacles and forbidden areas and requires UAVs to plan longer routes with multiple waypoints. Also, the UAV path planning in large-scale search space can consume much time to get an optimal path. To solve this kind of problem, EC algorithms should either have good global search capacity or contain specific large-scale search space handling strategies.

In recent years, many EC algorithms aiming at effectively solving the UAV path planning problems in large-scale search space have been proposed in the existing literature. As the UAV path planning problems in large-scale search space lead to extra computational complexity to EC algorithms, most of the current works aim to quickly find the optimal path. They can be categorized into two categories, which are convergence-accelerate-based EC algorithms and parallel-based EC algorithms.

Firstly, the studies on convergence-accelerate-based EC algorithms are surveyed. To enhance the convergence speed, Hohmann et al. (2022) applied a bidirectional Dijkstra algorithm to generate relatively good initial paths. The initialization strategies were hybrid with several multi-objective EC algorithms including the covariance matrix adaptation evolution strategy, non-dominated sorting GA, and Broyden-Fletcher-Goldfarb-Shanno algorithm, resulting in the H.CMA-ES, H.NSGA-II, and H.BFGS algorithms, respectively. To address the UAV path planning problem in military reconnaissance missions, Liu et al. (2022b) proposed an EA with deep reinforcement learning (EA-DRL), which was able to effectively plan the optimal path in large-scale search space via inheriting both the global search capacity of the EA and the excellent generalization capacity of the deep reinforcement learning. Zhao et al. (2017) proposed a discrete mapping DE (DMDE), where the discrete mapping and inverse mapping rules and a hybrid differential strategy with a dynamic crossover rate were designed to enhance the global search ability to enhance the performance of DMDE in large-scale UAV path planning problems. The path planning task for UAVs was turned into a large-scale optimization problem by Jarray et al. (2022a) and a parallel cooperative coevolutionary grey wolf optimizer (PCCGWO) was created to solve it. The approach guarantees fair and accurate comparisons by making the flying mission more complicated by adding a variety of additional situations.

Second, the studies on parallel-based EC algorithms are described. Yang et al. (2016) designed a separately evolving waypoints framework, which was based on the EA and can effectively solve large-scale problems. In this study, the separately evolving waypoints framework and a negatively correlated search strategy were combined to propose the SEW-NCS-C algorithm, which achieved more promising performance than the compared EC algorithms. Turker et al. (2016) implemented the simulated annealing (SA) algorithm in parallel. The proposed method was also redesigned for GPU acceleration, resulting in significant increases in computing performance. To reduce the time consumption, Cekmez et al. (2018) proposed a multi-colony ant optimization (MCAO) and executed MCAO on GPU in parallel. By utilizing CUDA for parallel computing, the algorithm achieves good improvements in fast convergence for path planning problems of multiple UAVs.

3.3 Summarization and discussion

This section gives a summarization and discussion of the existing studies of EC for UAV path planning with complex search space. Table 1 presents an overview of the recent EC algorithms designed for UAV path planning with complex search space. Based on the information in Table 1, several key conclusions can be drawn.

Table 1 The summarization of the existing studies of EC for UAV path planning with complex search space
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First, in most application scenarios of UAV path planning, the search space is inherently constrained. This constraint is primarily due to the presence of numerous obstacles and forbidden areas within the search space of UAV path planning. These constraints guarantee that the problem model closely resembles real-world UAV route planning problems, in which UAVs have to follow regulations, avoid no-fly zones, and navigate through urban environments. The problem becomes more realistic to real-world situations when these constraints are incorporated into the search space, which increases the relevance and application of the study findings.

Second, most EC algorithms developed for constrained UAV path planning incorporate one or more constraint-handling strategies. These strategies enable the algorithms to efficiently navigate complex environments while adhering to the specified constraints, often resulting in improved performance. However, some constraint-handling methods may over-constrain the search space, which can limit the exploration capability of the algorithm. They might exclude feasible solutions that slightly violate certain constraints but offer better overall paths.

Third, when addressing UAV path planning tasks in large-scale search spaces, the existing methods usually implement specific strategies to reduce computational complexity. In large-scale environments, the search space can be vast and highly complex, where the algorithms are hard to find optimal paths within a reasonable time frame. To tackle this, researchers have developed advanced global search techniques and parallel processing approaches, enhancing the algorithms’ capability to explore the search space comprehensively while maintaining computational efficiency. However, the parallel processing technique requires synchronization between different processing units and can pose an extra cost to the computational resources.

4 EC for UAV path planning in complex time control

There are some additional complex properties in the time control aspect for some real-world UAV path planning tasks. Two significant subproblems, referred to as dynamic UAV path planning and multi-UAV concurrent path planning, are derived from the complex properties in the time control aspect. In dynamic UAV path planning, the challenge lies in finding a safe and efficient path for the UAV to reach its target while adapting to changing environmental conditions. In multi-UAV concurrent path planning, the challenge is to optimize the paths of multiple UAVs simultaneously and to avoid the potential collisions brought on by path intersections. Also, simultaneously planning the path of multiple UAVs can be extremely time-consuming. EC algorithms have shown to be a successful strategy for overcoming these difficulties and can offer promising paths for UAVs in complex environments.

4.1 Dynamic UAV path planning

In some application scenarios, UAVs are required to find the optimal path in a dynamically changing environment, which is called dynamic UAV path planning. In this problem, the environments and requirements of the path planning problem dynamically change over time. In such a case, the optimal path in the past time series may not be an optimal path in the current time series. Therefore, the challenge lies in finding a safe and efficient path for the UAV to reach its target while adapting to changing environmental conditions, and the algorithms are required to find the optimal path quickly.

As the EC algorithms have achieved relatively preeminent performance in many dynamic optimization problems (Liu et al. 2020b, 2023c; Wu et al. 2022), some studies have been proposed to utilize EC algorithms for solving dynamic UAV path planning problems. As the search environments of the dynamic UAV path planning problems can dynamically change, the EC algorithms are required to quickly give a near-optimal solution. In this consideration, the current studies aim to enhance the convergence speed and reduce the running time of EC algorithms. Based on their strategies for reducing optimization time, the current studies on EC for dynamic UAV path planning can be categorized into two categories.

The first category includes studies aiming at enhancing the convergence speed via refining the existing evolutionary operations or designing novel strategies. For example, to plan the path of UAVs in an environment with dynamic time-variant constraints, Popovic et al. (2017) designed an informative path planning (IPP) framework, where a covariance matrix adaptation evolution strategy and a global viewpoint selection strategy were utilized to optimize the path. The proposed IPP framework can dynamically generate feasible paths for UAVs. The experimental results indicate that the proposed algorithm showcases a competitive performance to the compared planners. However, the method lacks an extensive discussion on the concerned constraints and its application in some larger-scale problems may be limited. Barkaoui et al. (2019) proposed an information-theoretic-based EA (ITEA), which was assisted by an improved hybrid GA and achieved promising performance on dynamic UAV path planning problems. In several simulations, the ITEA shows competitiveness and efficiency, surpassing other algorithms by over 31% in entropy, indicating its efficacy in target search circumstances. Liu et al. (2019a) proposed an EA based on improved t-distribution (EA-ITD) for dynamic track planning of UAVs in complex and unknown environments. In EA-ITD, prior knowledge was used to help the algorithm locate the optimal path quickly to efficiently handle the environmental changes. The simulation results show the proposed EA-ITD can dynamically plan appropriate tracks and only consumes a low computational complexity. Yang et al. (2020a) proposed a hierarchical recursive multi-agent GA (HR-MAGA), where a hierarchical recursive strategy was designed to enhance search efficiency and to better handle changing environments.

The second category includes studies aiming at reducing the running time via some parallel or GPU-based strategies. For example, to effectively find the optimal path in a dynamic and constrained 3D environment where the positions of obstacles and the forbidden areas change over time, Shin and Bang (2020) proposed a multi-swarm PSO (MSPSO), where a Voronoi diagram and a Dijkstra algorithm were adopted to construct the initial population and a GPU-based implementation strategy was designed to enhance the execution speed, to plan the best route for UAVs in dynamic adversarial environments with uncertain threats. Jarray et al. (2022b) proposed a parallel multiobjective multiverse optimizer (PMOMVO). To enhance the convergence speed, PMOMVO designed a parallel-based master–slave mode to manage multiple subpopulations. The experimental results indicate the PMOMVO achieves promising results with respect to both the hypervolume and the maximum spread.

4.2 Multi-UAV concurrent path planning

Some applications require multiple UAVs to cooperatively accomplish the mission. In such a case, the path planning of multiple UAVs should be simultaneously carried out, which refers to the multi-UAV concurrent path planning task (Cheng et al. 2022; Fevgas et al. 2022; Li et al. 2022d). In multi-UAV concurrent path planning, the challenge is to optimize the paths of multiple UAVs simultaneously and to avoid the potential collisions brought on by path intersections. Also, simultaneously planning the path of multiple UAVs can be extremely time-consuming. Therefore, the algorithms for solving the multi-UAV concurrent path planning task should be able to effectively handle the additional constraints caused by the other UAVs and efficiently find the optimal path within a relatively short time.

EC algorithms have recently shown encouraging results in solving multiple tasks concurrently due to their great global search capacity and potential parallel ability (Liu et al. 2018, 2023b; Jiang et al. 2024a). Therefore, novel variants of EC algorithms were proposed to effectively and efficiently solve the multi-UAV concurrent path planning tasks. According to the basic optimizer, these studies can be classified into two into two categories, which are EA-based optimizer and SI-based optimizer.

Firstly, some studies were proposed to adopt the EA-based optimizers to find the optimal path for multi-UAV concurrent path planning problems. For example, Atencia et al. (2019) designed a weighted-random multi-objective EA that adopted NSGA-II as the basic optimizer, named weighted-random NSGA-II (WRNSGA-II), to effectively solve the multi-objective multi-UAV path planning problems. In the application scenario of searching for missing tourists, multiple UAVs should cooperate and multiple paths should be concurrently planned. To solve the multi-UAV path planning task in this scenario, Du et al. (2019) proposed a hybrid EA with a main algorithm and a sub-algorithm (HEA-MS), where the main algorithm evolved the population to explore the optimal path and the sub-algorithm adopted a tabu search strategy to enhance the exploitation. Bai et al. (2022) formulated the multi-UAV path planning problem as a multi-objective optimization and refined the NSGA-III to propose a dynamic segmentation crossover strategy based NSGA-III (DSNSGA-III) to plan paths concurrently for multiple UAVs. According to the experimental results on comparison between several compared algorithms, the DSNSGA-III was verified to have outstanding performance in multi-UAV path planning tasks.

Also, some studies were proposed to adopt SI-based optimizers to find the optimal path for multi-UAV concurrent path planning problems. For instance, Sun et al. (2019) considered the cooperation and competition scenarios and proposed a lost-water-drop-based multiple swarms intelligent water drops (LMIWD) algorithm to effectively plan multiple collision-free paths for multiple UAVs. The proposed LMIWD algorithm is a variant of the EC algorithm, which adopts a co-evolutionary technique to achieve a tradeoff between cooperation and competition and a soil update technique to enhance the exploration ability. Also, in order to deal with the cooperation and competition of multiple UAVs, Luo et al. (2019) designed an effective coevolution pigeon-inspired optimization (CPIO) algorithm. In this study, the path planning of each UAV includes two parts, which are the search stage and the return stage. CPIO is applied to find the optimal path in the search stage, while a search tracking approach is proposed to be applied in the return stage. The experimental results show that the proposed CPIO generally outperforms the pigeon-inspired optimization algorithm, GA, and PSO on both the convergence speed and located targets. Aiming at overcoming the deficiency of existing EC algorithms in multi-UAV path planning, Xing et al. (2023) combined the advantages of the EC algorithms and the Q-learning algorithm to propose a multiple swarm fruit fly optimization with Q-learning (MSFO-QL). In MSFO-QL, the multiple swarm fruit fly optimization algorithm was utilized to generate relatively good paths, and the Q-learning algorithm was utilized to determine whether the optimization mode should be exploration or exploitation.

4.3 Summarization and discussion

The studies of EC for UAV path planning with complex time control are summarized and discussed in this section. Table 2 lists the most recent EC for UAV path planning with complex time control. Based on Table 2, we can draw several conclusions.

Table 2 The summarization of the existing studies of EC for UAV path planning with complex time control
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First, studies focusing on EC for dynamic UAV path planning emphasize enhancing the algorithms’ ability to quickly allocate optimal or near-optimal paths. This emphasis is critical because UAV operating environments can change rapidly. Most existing studies have proposed refining evolutionary operations within EC algorithms or designing additional search strategies. These improvements aim to enable the algorithms to respond swiftly to environmental changes, thereby improving both their effectiveness and efficiency.

Second, cooperation and competition between various UAVs are crucial factors in research on EC for multi-UAV concurrent path planning. Some studies have developed specific approaches to balance these two factors. Since planning multiple paths for multiple UAVs concurrently can take significantly more time than planning a path for a single UAV, some works have introduced efficient and novel operations to improve the search efficiency of EC algorithms.

Despite these advancements, existing studies still exhibit several shortcomings that need to be addressed. For example, some studies lack extensive discussions on the ability of newly proposed strategies to handle dynamic environments effectively and manage a large number of UAVs concurrently. There is a need for more comprehensive evaluations that test the scalability and adaptability of these algorithms in more complex and realistic scenarios. Therefore, further research is needed to overcome these current limitations.

5 EC For UAV path planning in complex optimization objectives

The reviews of studies on EC to UAV path planning with complex optimization objectives are the main topic of this section. Concerning the optimization objectives aspect of UAV path planning, we discuss two sub-problems called EC for UAV path planning with expensive fitness evaluation and EC for multi-objective UAV path planning. The former problem occurs when it is computationally expensive to evaluate the objective function for a candidate path, while the latter problem involves optimizing the UAVs’ path to fulfill multiple and often conflicting objectives simultaneously. Despite the novel challenges these problems present, EC algorithms have so far exhibited impressive performance in solving both of these two complex UAV path planning problems. The literature on EC for UAV path planning with expensive fitness evaluation and EC for multi-objective UAV path planning is reviewed and compared in the following parts of this section.

5.1 UAV path planning with expensive fitness evaluation

In some application scenarios, it is computationally expensive to evaluate the objective function for a candidate path. For example, evaluating the objective value of a path is extremely time-consuming or can cost many resources (Cabreira et al. 2019; Kusnur et al. 2021; Hebisch et al. 2021). The UAV path planning in such a condition is called UAV path planning with expensive fitness evaluation. To effectively and efficiently solve this kind of problem, two main open issues should be taken into consideration. The first open issue is how to reduce the computational cost of the objective function evaluation while maintaining the accuracy of the objective function evaluation. The second open issue is how to increase the algorithm’s effectiveness and efficiency in finding the optimal path using the fewest number of possible objective function evaluations.

In recent years, the EC algorithms have been successfully and effectively applied in the research field of UAV path planning with expensive fitness evaluation. For example, Wei and Wei (2009) utilized the ant colony system (ACS) to solve the computationally expensive UAV path planning problems for multiple UAVs, which indicated the encouraging performance of ACO and ACS in solving these problems. To achieve a balance between reducing the runtime and enhancing the quality of the found path in the expensive UAV path planning problems, Fareh et al. (2022) proposed a Sobel potential field (SPF) path planning strategy. In the SPF technique, a PSO algorithm is utilized to find the optimal constraint-free path, and a Sobel edge detection mechanism is designed to find out the edges of the constrained regions to enhance effectiveness and efficiency. In experiments, the proposed SPF technique is shown to get better performance than several state-of-the-art path planning algorithms.

5.2 Multi-objective UAV path planning

The multi-objective UAV path planning problem is when the users of an application require the UAV to plan several feasible paths while satisfying multiple different and usually conflicting objectives (Besada-Portas et al. 2013; Liu et al. 2020a; Dasdemir et al. 2020). In multi-objective optimization, the common purpose is to find a set of optimal solutions that trade-off multiple conflicting objectives rather than a single optimal solution. This kind of UAV path planning problem is frequently used in real-world application scenarios where it is necessary to simultaneously optimize multiple objectives. For example, the algorithm for UAV path planning needs to simultaneously minimize the length of the path, minimize the searching time, and avoid the trap in the constrained regions.

Recently, studies on utilizing EC algorithms for solving multi-objective UAV path planning problems have been proposed and got promising results. For instance, Liu et al. (2021) applied the EC algorithm to plan the optimal path satisfying two objectives in the scenario of road segment surveillance, where the two objectives were to reduce the distance of all the UAVs and to reduce the number of used UAVs in the process of target searching. This work proposed a decomposition-based multi-objective EA (DMEA), where the multi-objective UAV path planning problem was decomposed into several single-objective subproblems to effectively find the optimal paths. The experiments conducted between DMEA and several state-of-the-art multi-objective EC algorithms indicate that DMEA is promising in multi-objective UAV path planning problems. Peng et al. (2022) proposed a multi-objective EA with a dynamic infeasibility allocation mechanism (MOEA-DIAM) for multi-objective UAV path planning, where the objectives were to reduce the cost of energy of UAVs and enhance the safety of the path. As the application scenario is a multi-objective constrained UAV path planning problem, MOEA-DIAM designed an achievement scalarizing function to evaluate the paths based on the multiple objectives and a dynamic infeasibility allocation mechanism to select the relatively good path without violating the constraints. Ramirez-Atencia and Camacho (2019) designed a multi-objective EA based on NSGA-II, called NSGA-II for the constraint satisfaction problem (NSGA-II-CSP), to solve the multi-objective UAV mission planning problem. In this work, multiple objectives, such as time cost in sum, cost of the mission, risk, fuel consumption, and the number of used UAVs, are considered. Wang and Deng (2022) designed a multi-objective quantum-inspired seagull optimization algorithm based on decomposition (MOQSOA/D). MOQSOA/D designed a quantum-inspired strategy and a leadership archive to help get the non-dominated solutions for multi-objective optimization problems. Peng and Qiu (2022) formulated the UAV path planning problem into a multi-objective constrained optimization problem via both reducing the path length and avoiding the collisions and designed an M2M-DW algorithm with a local infeasibility utilization method (M2M-DW-LIUM) to solve the formulated multi-objective constrained optimization problem. M2M-DW-LIUM designed a local infeasibility utilization strategy to handle the constraints and an improved mutation scheme to improve the search for the non-dominated paths that achieve a good trade-off between the objectives.

5.3 Summarization and discussion

The studies of EC for UAV path planning with complex optimization objectives are summarized in Table 3. Based on the information presented in Table 3, we can draw several conclusions.

Table 3 The summarization of the existing studies of EC for UAV path planning with complex optimization objectives
Full size table

First, in studies on EC algorithms for UAV path planning with expensive fitness evaluations, designing specific strategies to reduce computational complexity and the cost of fitness evaluations is key to enhancing effectiveness and efficiency.

Second, there are relatively few studies addressing UAV path planning problems with expensive fitness evaluations. This is mainly because most existing studies rely on approximated models of UAV path planning problems, where evaluating the path is straightforward and inexpensive. To reduce the computing load, these models frequently simplify the dynamics of the environment and the characteristics of UAVs. However, as UAV applications become more complex, the evaluation of paths may become more computationally intensive. There, future research is likely to focus more on UAV path planning problems with expensive fitness evaluations, addressing the challenges of high computational cost and the necessity for accurate modeling.

Third, multi-objective optimization in UAV path planning typically involves balancing conflicting criteria such as minimizing travel time, avoiding obstacles, and reducing energy consumption. In the studies on EC algorithms for multi-objective UAV path planning, novel strategies were proposed to enhance the search capacity of non-dominated solutions caused by the requirement of satisfying multiple objectives. However, these strategies should be carefully designed for specific types of environments. A general strategy may not adequately handle the trade-offs between these objectives in different environments.

6 Potential research directions

In the above sections of this survey, the literature on EC algorithms for UAV path planning is reviewed. In future research, the EC algorithms will still show the potential and achieve encouraging performance. In the following part of this section, some potential research directions for future work on EC algorithms for UAV path planning are discussed and analyzed. The potential search directions are described from three aspects, which are problem modeling (i.e., how to design more accurate problem models that are closer to the applications), EC algorithm designing (i.e., how to design more efficient EC algorithms to better solve complex UAV path planning problems), and application scenario extending (i.e., how to extend the EC algorithm in more application scenarios). We hope the discussed potential search directions can enlighten future studies.

6.1 Problem modeling

In some current studies, the problem models are built to approximate the features of real-world UAV path planning problems. The problem models are usually relatively simple, as the models are designed to estimate the performance of EC algorithms in a relatively easy way. Therefore, these problem models may not be able to reflect some complex and essential features of real-world UAV path planning problems. For example, the shapes of the obstacles in the search space can be different, but some problem models just simply model each obstacle as a circle or a sphere. Furthermore, in some real-world applications, the obstacles are also vehicles and can make random movements in the search space, but the problem models simply treat the obstacles as static obstacles or obstacles in uniform motion. Therefore, to further develop the EC algorithms to solve more UAV path planning problems in real-world applications, accurate problem models that are close to the real-world UAV path planning problems should be built.

6.2 EC algorithm designing

6.2.1 Learning-aided EC

With the development of UAVs, users want to design more efficient EC algorithms to cope with UAV path planning problems in increasingly complex environments, e.g., the search space contains many local optimal solutions and the environments may change dynamically. Most of the existing EC algorithms are designed based on the evaluation of fitness values, which makes it difficult to realize an accurate solution to the UAV path planning problem in complex environments. Learning-aided EC (Zhan et al. 2023; Jiang et al. 2023a) is a novel and smart paradigm of EC algorithms, which aims to mimic the intelligent ability of humans to learn knowledge to achieve an intelligent search for globally optimal solutions by learning the effective knowledge generated during the evolutionary process and utilizing the knowledge to guide the evolution. The idea of learning-aided EC can be an effective and efficient method to enhance the quality of solutions for UAV path planning.

6.2.2 Knowledge transfer-based EC

The UAV path planning tasks require the EC algorithms to find an accurate enough optimal path. However, as the application scenarios of the UAV become more complex, e.g., the search space is enlarged and multiple tasks need to be solved, the existing EC algorithms are hard to find the optimal path and UAVs are usually trapped in local optimal paths. It can be found that relatedness widely exists among the UAV path planning tasks, and the knowledge generated in the optimizing process of one UAV path planning task can also be useful for other related tasks. Recently, incorporating EC algorithms and the idea of transferring knowledge among related optimization tasks was shown to be powerful in solving many real-world optimization problems (Li et al. 2022b; Wu et al. 2023a; Jiang et al. 2022b). Therefore, designing the knowledge transfer-based EC algorithms can be a potential mechanism to help enhance the accuracy of the obtained path.

6.2.3 Distributed and matrix-based EC

In UAV path planning, the users often require the EC algorithms to quickly locate an optimal or near-optimal path. In such a case, the running time of the EC algorithms should be reduced to satisfy the requirements of the users. Recently, distributed computing and cloud computing have achieved promising performance in reducing the running time of algorithms (Zhan et al. 2017; Chen et al. 2020; Ge et al. 2021). Also, the idea of matrix-based EC algorithms proposed recently can considerably alleviate the problem of high computational complexity (Zhan et al. 2022b). Therefore, designing the distributed EC algorithms and matrix-based EC algorithms could be feasible ideas to reduce the running time for solving the UAV path planning problems.

6.3 Application scenario extending

According to the above review of the related literature, many EC algorithms for UAV path planning have been proposed in some application scenarios. However, the studies on EC algorithms for UAV path planning with complex properties are still insufficient to satisfy the requirements of some more complicated applications. For example, some application scenarios of UAV path planning problems have more complex properties, such as many-objective (Liu et al. 2019b, 2022a), many-task (Jiang et al. 2023c, 2024b; Wu et al. 2023b), and multimodal (Zhao et al. 2020; Jiang et al. 2022a; Jie et al. 2023). Therefore, a potential research direction on EC for UAV path planning is to design effective and efficient EC algorithms and extend the scenarios of EC algorithms in novel complex applications.

7 Conclusion

This paper gives a comprehensive survey of the existing studies on EC for UAV path planning. For clarity, a novel taxonomy is proposed to categorize the existing relevant studies from three different classes, which are EC algorithms for UAV path planning with complex search space, EC algorithms for UAV path planning with complex time control, and EC algorithms for UAV path planning with complex optimization objectives. The review and discussion of the related studies show the efficiency and great success achieved by the EC algorithms and also reveal the great potential of the EC algorithms in future UAV path planning problems with more complicated properties. In addition, the future potential research directions of EC for UAV path planning are presented and discussed from three aspects: problem modeling, EC algorithm designing, and application scenario extending. We hope this survey can highlight the research trend, promote discussion, and inspire new research ideas on using EC for UAV path planning.