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Review

Evolutionary Computation for Air Transportation: A Survey

School of Computer Science, South China Normal University, Guangzhou 510631, China
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Author to whom correspondence should be addressed.
Mathematics 2025, 13(17), 2867; https://doi.org/10.3390/math13172867
Submission received: 8 July 2025 / Revised: 20 August 2025 / Accepted: 30 August 2025 / Published: 5 September 2025
(This article belongs to the Special Issue Advanced Computational Intelligence for Complex Problems)

Abstract

As the demand for air transportation continues to grow, airspace congestion, flight delays, operational costs, and safety have become important and challenging issues. There are various optimization problems in air transportation, which involve large-scale data, complex operational scenes, multiple optimization objectives, and dynamic environments. In addition, besides conventional commercial aviation, the development of urban air mobility brings new features to air transportation. Evolutionary computation (EC) algorithms have emerged as a promising approach for solving optimization problems in air transportation. This article introduces a hierarchical taxonomy to systematically review the application of EC algorithms in air transportation. At the first level, related studies are categorized into commercial aviation and urban air mobility based on their application domains. At the second level, studies are further classified according to different operational scenes. A comprehensive review of relevant studies in the literature is presented according to the above taxonomy. In addition, future research directions and open issues are discussed to support and inspire further advancements in this field.

1. Introduction

Air transportation is an essential mode of transportation. The number of passengers travelling by air is expected to reach 9.9 billion in 2025, with a 4.8% increase over 2024 [1]. The increasing scale and popularity of air transportation have raised significant public concern about its punctuality, safety, operational costs, and environmental impacts.
In the literature, different kinds of mathematical methods (e.g., integer programming [2] and stochastic programming [3]) have been used to deal with optimization problems in air transportation. However, due to the increasingly complex features of the modern air transportation system, conventional mathematical methods become inapplicable or suffer from poor search efficiency. First, the volume of flights continues to grow. Between 2024 and 2043, global air travel demand is forecasted to increase at a compound annual growth rate of 3.4% [1]. The rapid growth of air transportation results in large-scale data and thus increases the computational time required by mathematical methods. Second, due to the complex features in real-world air transportation scenes (e.g., nonlinear and multiple optimization objectives), mathematical methods are not able to deal with the formulated models considering these features. Adding assumptions in the model formulation to satisfy the requirements of mathematical methods may lead to modeling errors, undermining the validity of the obtained solutions. Third, many air transportation optimization problems are characterized by dynamic environments and uncertainty, which further increase the difficulty of finding effective and robust solutions.
To address the challenges posed by the complexity of air transportation optimization problems, evolutionary computation (EC) has emerged as a promising approach. EC refers to a family of nature-inspired metaheuristic algorithms. The distinguishing characteristic of EC algorithms is that they do not rely on precise mathematical formulations, such as linear or convex programming models. This allows EC algorithms to effectively find the optimal or near-optimal solutions in an acceptable time for complex optimization problems, which also gives EC a significant advantage in solving NP-hard problems.
Over the past decades, EC algorithms have also been extensively applied to deal with the complex optimization problems in air transportation. EC algorithms (e.g., Genetic Algorithms (GAs) [4,5], Ant Colony Optimization (ACO) [6,7], and Particle Swarm Optimization (PSO) [8,9]) have also been used in the field of air transportation. Moreover, the granting of patents for EC applications in air transportation systems [10,11,12,13] demonstrates that EC algorithms have been applied to flight routing, departure time planning, and airport ground operations, providing empirical validation of EC’s practical utility in air transportation. Although studies in this field are increasing, to the best of our knowledge, only two reviews [14,15] have some relevance to the application of EC algorithms in air transportation. The review [14] provided a survey on model-driven approaches (e.g., dynamic programming and mixed-integer linear programming (MILP)) for air transportation optimization, which explicitly highlighted the computational intractability of model-driven approaches in large-scale dynamic scenarios (e.g., NP-hard complexity in surface routing). Notably, the review [14] did not explore EC as a viable alternative, despite EC’s proven capability in handling NP-hard problems through parallel stochastic search. The review [15] encompassed maritime, land, and air transportation domains in smart cities. These reviews [14,15] do not focus on the EC-based research in the air transportation field. Moreover, neither Balakrishnan et al. [14] nor Chen et al. [15] reviews the recent development of urban air mobility (UAM) in air transportation. To address this gap, we propose a hierarchical taxonomy to categorize the recent advancements in the application of EC algorithms in air transportation. Our study provides a focused review of EC-based algorithms specifically designed to address challenges in air transportation, employing a novel classification scheme that better captures the distinctive characteristics of air transportation systems. Moreover, our work extends the scope by incorporating an emerging field, UAM, as a new classification dimension.
The hierarchical taxonomy is shown in Figure 1. At the first level, the application of EC algorithms in air transportation is categorized into two groups based on the application domain: “Commercial Aviation” and “UAM”. Nowadays, air transportation has developed into an integral part of the global transportation system, with commercial aviation serving as the cornerstone of the air transportation system. Commercial aviation refers to long-distance, high-altitude air transportation services conducted by airlines using passenger or cargo aircraft operating on predetermined routes and schedules. The commercial aviation industry is characterized by large-scale operations, a stringent regulatory framework, and a highly structured and mature management system, which has fostered extensive research across its related domains [16,17,18]. In addition to commercial aviation, UAM has emerged as a new type of aviation that focuses on safe, efficient, and affordable aviation service within and around urban areas [19]. The air transportation in UAM involves short-distance, low-altitude flights with autonomous or semi-autonomous control, which is typically based on electric vertical takeoff and landing (eVTOL) technology. UAM aims to alleviate ground congestion, enhance urban mobility, enhance urban transportation efficiency, and improve environmental sustainability, particularly during low-altitude operations and critical phases such as takeoff and landing in urban environments. In addition, compared to commercial aviation, UAM has only begun to develop rapidly in recent years. Thus, research on UAM is still in the initial phase, and the number of related works is significantly lower than that of commercial aviation studies.
At the second level of the proposed hierarchical taxonomy, the related studies in commercial aviation are further classified according to different operational scenes: “Flight Process Scene”, “Ground Scene”, and “Personnel Scene”. Similarly, the related studies in UAM are further classified: “Flight Process Scene”, “Ground Scene”, and “Infrastructure Scene”. Commercial aviation and UAM differ fundamentally, with the former focusing on long-distance, high-altitude transportation and the latter focusing on short-distance, low-altitude mobility. This distinction leads to significant differences in aircraft types, ground operations, and required infrastructure. As a result, the scheduling problems in these three scenes vary considerably between commercial aviation and UAM. Therefore, this article discusses the operational scenes of commercial aviation and UAM separately.
All the studies reviewed in this article were retrieved from the databases of the following publishers: the American Institute of Aeronautics and Astronautics (AIAA), Cambridge University Press, De Gruyter, Elsevier, the Institute of Electrical and Electronics Engineers (IEEE), the Multidisciplinary Digital Publishing Institute (MDPI), Nature, Oxford University Press, Public Library of Science (PLOS), Sage, Springer, Taylor & Francis, and Wiley. A complementary search using Google Scholar was conducted to avoid missing relevant studies from the above-mentioned publishers. The studies included in this survey were required to meet the following criteria: (1) the study is directly related to the topic of this survey; (2) the publication date falls within the period 2020–2025; (3) the study was published in English; (4) the study includes methodological, model-based, algorithmic, or experimental contributions; (5) the study is from peer-reviewed journal/conference research article.
To ensure a transparent review process, we employed a Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA)-style flow diagram to summarize the identification, screening, and inclusion of the reviewed studies, as shown in Figure 2. First, potentially relevant publications were retrieved from the databases of publishers. After the preliminary filtering, duplicates were removed. Second, the remaining records were screened by title and abstract to exclude papers clearly unrelated to the scope of this review. Third, for the records that passed the initial screening, the full texts of the papers were retrieved. Fourth, the full texts of papers were assessed against the inclusion and exclusion criteria. Finally, the remaining eligible studies were included.
The main contributions of this article are summarized as follows: (1) a hierarchical taxonomy is proposed to systematically categorize existing research on the application of EC to the air transportation system, including both commercial aviation and UAM; (2) a comprehensive review of the relevant literature is conducted based on the above taxonomy, highlighting key problems, methodologies, and application scenes; (3) promising future research directions and open issues are identified and discussed. This article aims to provide researchers with a structured and in-depth understanding of EC algorithms in dealing with the optimization problems in air transportation, thereby supporting further advancements in this field.
The rest of this article is organized as follows. Section 2 introduces background knowledge about the air transportation system and EC algorithms. Section 3 and Section 4 review related studies on commercial aviation and UAM, respectively. Section 5 discusses future research directions and open issues. Finally, Section 6 presents the conclusions.

2. Background

Air transportation plays a vital role in modern transportation systems, supporting the movement of people and goods over both short and long distances. With the rapid growth of air transportation and the emergence of new aerial platforms, the operational environment of air transportation has become increasingly complex. It now encompasses not only traditional high-altitude, long-distance flights but also a variety of low-altitude and short-range operations, which require more flexible and intelligent management strategies. There are four main objectives in air transportation optimization: minimizing delays, minimizing operational costs, reducing congestion, and maximizing safety. Air transportation optimization problems exhibit characteristics such as large-scale decision spaces, dynamic environments, multiple conflicting objectives, and nonlinearity, which render traditional mathematical programming approaches insufficient or inapplicable. In response to these challenges, EC has emerged as a promising and flexible set of techniques for solving complex optimization problems in the air transportation domain.
EC refers to a class of metaheuristic algorithms inspired by natural phenomena and biological evolution. Commonly used EC algorithms include GA [20,21,22,23,24,25], differential evolution (DE) [26,27,28], ACO [29,30,31], and PSO [32,33,34]. GA and DE are modeled on the principles of genetic variation and natural selection, while ACO and PSO are inspired by collective behaviors observed in social organisms, such as foraging ants and flocking birds. From a methodological standpoint, GA and ACO are often more effective for discrete optimization tasks, such as flight sequencing or gate assignment, whereas PSO and DE are better suited for continuous domains, such as trajectory planning or parameter optimization. In general, an EC algorithm starts with a randomly generated population of individuals, each individual representing a candidate solution. These individuals are evaluated using a problem-specific fitness function, and a selection and variation process is iteratively applied to evolve the population toward optimal or near-optimal solutions. The algorithm continues this process until a stopping criterion is met, such as reaching the maximum number of fitness evaluations. Due to their strong search ability for complex optimization problems, EC algorithms have been increasingly applied to air transportation optimization problems. Therefore, this article studies the related research on EC for air transportation. To present the operation process of the EC algorithm more clearly, we have placed the pseudocode and brief introduction of a classic EC algorithm, GA, in Appendix A.

3. Evolutionary Computation for Commercial Aviation

Commercial aviation serves as the backbone of global transportation, enabling the rapid transport of passengers and goods across long distances. In this article, the application of EC in commercial aviation is categorized into three main areas based on operational scenes: flight process scene, ground scene, and personnel scene.
Table 1 presents a systematic overview of state-of-the-art EC-based studies in commercial aviation, where all research is categorized by problem type, and the layout of the table is inspired by [35]. Table 1 includes the following information: (1) the specific problem addressed by each study, (2) the underlying EC algorithms employed, (3) the optimization objectives, (4) data sources (real-world vs. simulated), and (5) performance metrics. The most frequently used metrics in multiobjective optimization [36] include Hypervolume (HV) [37] and Inverted Generational Distance (IGD) [38]. In detail, HV measures the solution quality by calculating the volume between the obtained solution set and a reference point in objective space, quantifying both convergence and diversity. IGD evaluates solution sets by measuring their proximity to the ideal Pareto front (PF).

3.1. Flight Process Scene

During the flight process, it is crucial to schedule and manage operations across different flight phases to ensure safety, efficiency, and punctuality. Flight process optimization is typically achieved by adjusting flight altitude (flight level), departure time, flight route, and flight speed. In this article, relevant studies are further categorized into two groups: macro-level and micro-level scheduling based on the scale of the problem.

3.1.1. Macro-Level Scheduling

Macro-level studies primarily focus on improving the overall performance of the airspace system or traffic network. This includes operations such as flight level allocation, flow management strategies, or airspace structure adjustments aimed at reducing system-wide conflict risk, airspace congestion, and flight delays. Amara et al. [39] proposed an integrated optimization framework based on GA and a geographic information system to resolve air traffic conflicts and optimize flight plans. Cai et al. [40] proposed a multiobjective evolutionary algorithm-based framework, designing customized operators for the air traffic domain to minimize lateral collision risk by assigning flight levels to flights. Guo et al. [41] introduced a learning-enhanced non-dominated sorting algorithm that dynamically allocates flight delays and incorporates heuristic rules to reduce air traffic system inefficiency and mitigate unfairness across airlines.

3.1.2. Micro-Level Scheduling

Micro-level studies target the operational optimization of individual flights or trajectories, including speed control, trajectory vectoring, and conflict resolution, to enhance operational efficiency and safety. To better optimize at the micro level, trajectory-based operations (TBO) have been proposed [42], focusing on the precise management of each aircraft’s four-dimensional trajectory (3D geographic position and time) to optimize airspace utilization and traffic flow. Xu et al. [43] proposed a cooperative coevolutionary algorithm based on TBO, which combines a new dynamic group method and drives grouping through spatial-temporal correlativity, optimizing flight departure time and level allocation through an improved fast GA, effectively solving the problem of large-scale 4D trajectory strategic conflicts. Oruc et al. [44] employed GA and PSO to optimize a nonlinear model about cruise distance, aiming to enhance the accuracy of traditional formulas and support more efficient fuel consumption and route planning in airline operations.
Table 1. Reviews of recent EC-based research on commercial aviation.
Table 1. Reviews of recent EC-based research on commercial aviation.
ProblemReferencesBasic ECOptimization ObjectivesData SourceMetrics
Macro-level flight process schedulingAmara et al., 2023 [39]GA(1) Minimize flight conflicts
(2) Minimize operational costs
Real-world data from Algerian airspaceConflict resolution rate and operational indicator
Cai et al., 2022 [40]GA and PSO(1) Minimize the incremental risk of lateral collisions
(2) Minimize the number of flights for flight level changing
Real-world data from Singapore airspaceHV
Guo et al., 2022 [41]GAMinimize unfairness among airlinesReal data and simulation dataIGD
Micro-level flight process schedulingXu et al., 2021 [43]GAMinimize number of conflicts Real-world data from Chinese airspaceConflict resolution effectiveness, adjustment costs, and running time
Oruc et al., 2024 [44]GA and PSOMinimize the error in predicted range valuesReal-world data from jet-powered transport aircraftObjective value
Ntakolia et al., 2022 [45]ACO(1) Minimize ground delays
(2) Minimize flight cancellations
(3) Maximize airborne efficiency
Simulation dataWeighted objective value and running time
Guo et al., 2024 [46]GA(1) Minimize total delays
(2) Minimize flight conflict
Real-world data from Chinese airspaceHV and running time
Guo et al., 2024 [47]GA(1) Minimize total delays
(2) Minimize flight conflict
Real-world data from Chinese airspaceHV and running time
Liu et al., 2022 [48]GA and SA(1) Minimize the cost of aircraft deviation
(2) Minimize the cost specific to operations
(3) Minimize the number of conflicts
Real-world data from Chinese airspaceHV, the diversity and convergence of solutions
Xiao et al., 2025 [49]GA(1)Minimize air traffic control workload
(2) Minimize total delays
Real-world data from Chinese airspaceHV, IGD, and spread
Landing schedulingFernando et al., 2024 [50]GAMinimize pollution timeReal-world data from an American airportPollution time, number of constraint violations, and convergence
Xu et al., 2025 [51]ACOMinimize total delay timeSimulation dataTotal delay time, algorithm stability, and running time
Zhang et al., 2020 [52]ICA(1) Minimize total landing delay time
(2) Minimize the aircraft’s airborne stay time in the terminal area
Simulation dataObjective values
Zhang et al., 2024 [53]HSEA(1) Minimize makespan
(2) Minimize the total flight time
Real-world data from Singapore airspaceObjective values and running time
Shirini et al., 2024 [54]GA(1) Minimize operational costs
(2) Minimize fuel consumption
Real-world data from a benchmark datasetHV and IGD
Bhattacharya et al., 2024 [55]PSO(1) Maximize coverage speed
(2) Maximize coverage impact
(3) Minimize cover-break cost
Real-world data from Indian airspaceCoverage efficiency and running time
Ground movementSirigu et al., 2020 [56]PSOMinimize total cost of taxiingReal-world data from an Italian airportObjective values, convergence speed, and running time
Beke et al., 2024 [57]MA (1) Minimize total coasting time
(2) Minimize total fuel consumption
Real data and simulation dataCost saving, the number of non-dominated solutions, and running time
Perea et al., 2023 [58]GA(1) Minimize total coasting time
(2) Minimize total fuel consumption
Real-world data from a UK airportEconomic cost and running time
Gate assignmentDeng et al., 2024 [59] PSO and QEA(1) Minimize the walking distance of passengers
(2) Minimize idle time of gate
(3) Maximize the utilization rate of gates
Real-world data from a Chinese airportConvergence and weighted objective value
Nikolić et al., 2024 [60]BCO(1) Minimize total delay
(2) Minimize the number of jet bridges used
(3) Minimize total walking distance of passengers.
Real-world data from American airportsQuality and convergence of the solution
Xia et al., 2024 [61] GA(1) Maximize utilization rate of gate
(2) Minimize variance of idle time of gate
Real-world data from a Chinese airportPrediction accuracy and objective values
Zhu et al., 2024 [62] GA(1) Maximize utilization rate of gate
(2) Minimize variance of idle time of gate
Real-world data from a Chinese airportPrediction accuracy and gate assignment performance
Gao et al., 2023 [63] GA(1) Minimize fuel consumption during taxiing
(2) Maximize utilization rate of jet bridges
(3) Minimize fuel consumption of tow trucks
(4) Minimize the size of the tow truck fleet
Real-world data from a Chinese airportObjective values and convergence
Hsu et al., 2024 [64] SFLAMinimize total costSimulation dataConvergence and runtime
Crew schedulingAggarwal et al., 2023 [65]GAMinimize total costReal-world data from an American airline Objective value, the number of idle crew, and running time
Zeren et al., 2024 [66]GA(1) Minimize crew pairing cost
(2) Minimize penalty cost
Real-world data from Turkish airlinesCost saving, crew utilization rate, and running time
Zhou et al., 2021 [67]ACO(1) Maximize fairness
(2) Maximize satisfaction
Real-world data from north America airlinesHV, dominance rate, feasible rate,
Zhang et al., 2021 [68]GA(1) Minimize cost
(2) Maximize work time balance
Real-world data from Chinese airlinesObjective values
Chutima 2020 [69]GA(1) Minimize cost
(2) Maximize work time balance
(3) Minimize unsatisfaction
Real-world data from a Thai airlineConvergence and diversity
The above-mentioned micro-level studies focus on single-objective optimization. However, the optimization in flight process scenes typically involves inherently conflicting objectives, such as minimizing delays, reducing fuel consumption, and alleviating congestion. Some studies have optimized related problems from a multiobjective optimization perspective. Ntakolia et al. [45] proposed an ACO algorithm to achieve a balance among minimizing ground delays, which was combined with fuzzy logic, minimizing flight cancellations, and maximizing airborne efficiency. Guo et al. [46] proposed an evolutionary algorithm based on the knee point, which introduces a new solution encoding, a crossover operator, and a mutation operator based on the knee point tailored for air traffic flow management, effectively balancing flight delays and conflict reduction. To solve the large-scale air traffic flow management problem, Guo et al. [47] also proposed a co-evolutionary algorithm that groups flights based on spatiotemporal interactions and uses knee solutions to guide the optimization direction, aiming to minimize delays and maximize safety. Liu et al. [48] proposed a TBO-based planning framework that first clusters aircraft that are spatially and temporally correlated and pose a high risk of conflict, then applied a hybrid simulated annealing (SA) and GA to generate local trajectories and mitigate intra-group conflicts through altitude and speed adjustments to reduce conflicts. Xiao et al. [49] proposed a hybrid cooperative co-evolutionary algorithm that employs a divide-and-conquer-based cooperative co-evolution paradigm to decompose large-scale air traffic network flow optimization problems into multiple subproblems for optimization. Among all micro-level approaches, only Guo et al. [46,47] considered the speed regulation of flights during flight and carried out a more comprehensive scheduling of flights during the flight process. Note that to better clarify the optimization of flight process scheduling, we present a classic model of micro-level flight process scheduling optimization [47] in Appendix B.
The macro-level and micro-level flight process scheduling inherently involves the complex coordination of hundreds to thousands of aircraft and air traffic control units, resulting in an optimization problem with a large-scale solution space. EC methodologies effectively address this dimensionality challenge through their intrinsic population-based parallel search mechanism. EC can perform global search within large-scale solution spaces containing conflicting constraints (e.g., capacity and safety separation), avoiding local optima traps, while generating solutions that balance multiple conflicting objectives. Nevertheless, a significant limitation persists across all existing approaches at both macro-level and micro-level: none adequately address uncertainty disturbances during the scheduling process. This represents a crucial research gap since effectively integrating real-time disturbance such as weather variations and air traffic control instructions continues to pose substantial challenges to EC applications in flight scheduling. As a result, existing approaches show constrained adaptability when responding to dynamic fluctuations in airspace capacity and traffic demand.

3.2. Ground Scene

In this study, relevant studies of the ground scene are classified into three main areas: landing scheduling, ground movement, and gate assignment. Given the combinatorial complexity and multiple objective optimization nature of these problems, EC techniques have been increasingly adopted to develop effective and efficient solutions.

3.2.1. Landing Scheduling

Landing scheduling plays a critical role in ensuring the safe and efficient arrival of aircraft at busy airports, with a focus on optimizing aircraft landing times and sequences to reduce airborne holding, runway occupancy, and arrival delays. Fernando et al. [50] proposed a mixed-integer GA incorporating dual-resource collaborative encoding and dynamic constraint handling to reduce taxiing distances and engine runtime, thereby lowering pollutant emissions. Xu et al. [51] integrated receding horizon control with ACO to simultaneously optimize landing sequences and runway assignments, minimizing total delay time. Zhang et al. [52] proposed a heuristic approach based on the imperialist competitive algorithm (ICA), which significantly reduced flight delays and air traffic control burden. Note that ICA can be regarded as an EC algorithm, because ICA possesses the core characteristics of EC, such as selection, mutation, and population updates. Zhang et al. [53] proposed a metaheuristic harmony search evolutionary algorithm (HSEA) for large-scale free-route planning and scheduling, combining random generation with evolutionary strategies as part of a multi-method decision support framework. Beyond routine scheduling tasks, the emergency landing scene also requires rapid and reliable decision-making under uncertainty and limited resources. Shirini et al. [54] proposed a multiobjective, multi-population GA that utilizes dual independent populations to optimize the two objectives of cost and fuel consumption, while employing a shared archive to store non-dominated solutions, thereby facilitating information exchange between populations and preventing convergence to local optima in single-objective spaces. Bhattacharya et al. [55] proposed a multiobjective approach for emergency flight landing by integrating fuzzy graph covering theory with PSO, achieving efficient demand coverage and resource minimization under emergency conditions.
Aircraft landing scheduling constitutes an intrinsically multiobjective optimization problem. In contrast to conventional operations research methodologies, EC shows superior performance in addressing large-scale landing scheduling challenges. The above studies evaluate multiple potential solutions simultaneously, helping to avoid falling into local optima, and can satisfy various preferences of decision makers (e.g., prioritizing either delay minimization or fuel efficiency). Study [52] offers scalable solutions capable of handling large-scale instances (over 100 aircraft), making them particularly suitable for busy airports. Studies [50,51,52,53,54] fail to account for real-time disturbances such as weather changes or emergency landings, showing limited dynamic adaptability. In contrast, Bhattacharya et al. [55] specifically addressed emergency aircraft landing scenarios, developing algorithms with promising adaptability for dynamic environments.

3.2.2. Ground Movement

With the increase in air transportation, more pressure has been created for ground movement, which focuses on the planning and coordination of taxi routes to minimize taxi time and fuel consumption. However, these two objectives might conflict with each other, as a shorter time usually requires a higher coasting speed and acceleration, which will lead to an increase in fuel consumption. Sirigu et al. [56] proposed a parameter-fixing PSO approach to schedule autonomous electric towing vehicles for managing aircraft taxiing, aiming to minimize energy consumption and delay costs under strict operational constraints. Beke et al. [57] developed an MA for multi-graph path planning and scheduling in airport ground move operations, which enhanced the quality of Pareto solutions for taxi time and fuel consumption, with efficiency and real-time performance in operational scenes. Perea et al. [58] proposed a hybrid optimization framework that integrates an improved multiobjective A* algorithm with the non-dominated solution genetic algorithm II (NSGA-II), aiming to simultaneously minimize flight taxi time and fuel consumption while ensuring compliance with runway safety separation constraints.
In [56], PSO combines with local search to avoid premature convergence. The integration of multigraph modeling and direct-encoded GA proposed by [58] effectively overcomes the solution omission problem caused by non-additive costs that plague conventional A* algorithms. However, these two studies [56,58] employ static preference and constraint settings, whereas real-world operations require dynamic weight adjustments. Their further development must align more closely with the complexity and dynamic nature of actual airport operations. Moreover, the approach proposed in [57] emphasizes the real-time feasibility of their proposed approaches.

3.2.3. Gate Assignment

The airport gate assignment (AGA) problem is a key component of airport resource management, aiming to match flights with suitable gates at a specific time while maximizing operational efficiency and passenger convenience. Limited gate availability, aircraft-gate compatibility, tight transfer times, and frequent schedule disruptions make the gate assignment a complex and critical task. Deng et al. [59] integrated quantum-inspired evolutionary algorithm (QEA) with PSO and adopted niche coevolution to enhance population diversity. Nikolić et al. [60] proposed an improved BCO-based metaheuristic approach that incorporated cooperative mechanisms to flexibly coordinate gate usage among airlines, effectively reducing flight delays and passenger walking distances. Xia et al. [61] proposed a two-stage GA to optimize gate allocation under complex apron configurations, achieving a balance between resource utilization and allocation equity. Zhu et al. [62] proposed a hybrid multiple-strategy GA, effectively solving the multi-constraint AGA problem. The above approaches address static AGA, suitable for airports with stable schedules. In contrast, dynamic approaches are better suited for hub airports with frequent operational changes. Gao et al. [63] proposed an improved NSGA-II within a two-level optimization framework to achieve global energy savings, balancing energy efficiency, passenger experience, and operational costs. Hsu et al. [64] proposed a dynamic optimization approach for airport gate assignment by integrating a shuffled frog-leaping algorithm (SFLA), aiming to minimize the combined costs for passengers, flight route, and airports under flight time uncertainty.
In the above-mentioned gate assignment studies, Nikolić et al. [60] and Xia et al. [61] adopted a relatively simplistic approach to modeling the airport environment, and their proposed approaches still need to be verified in more diverse airport environments. While these studies consider basic scenarios, Deng et al. [59,60,61,62,63] did not account for uncertainties such as flight delays or cancellations. Consequently, their proposed approaches would require integration with dynamic scheduling mechanisms to improve real-world applicability. In contrast, Hsu et al. [64] explicitly accounted for these uncertainties, offering a more robust solution to the dynamic gate assignment problem.

3.3. Personnel Scene

In terms of personnel management, airlines manage extensive daily flight schedules, each requiring an assigned crew, which is an important step in maintaining the normal operation of the airport and flights.

Crew Scheduling

Crew scheduling is used to handle this complex task efficiently, which is typically divided into two stages [70]: crew pairing and crew rostering, which are both NP-hard problems. An illustration of crew scheduling is shown in Figure 3.
First, crew pairing involves generating feasible sequences of flight legs that satisfy regulatory and operational constraints without assigning specific employees, aiming to minimize overall costs. Note that flight leg refers to a single continuous flight segment from takeoff to landing. Aggarwal et al. [65] proposed a domain-knowledge-customized GA that effectively reduced redundant flights, offering advantages in both cost optimization and computational efficiency. Zeren et al. [66] proposed a GA-driven heuristic approach to solve large-scale crew-pairing problems, enabling the generation of low-cost and high-efficiency crew-pairing solutions. The approaches proposed in [65,66] show superior computational capability, accommodating over 100,000 pairings. However, in [66,67], robust optimization for real-time disruptions such as delays or cancellations is missing, limiting their practical applicability in dynamic operational environments.
Second, crew rostering assigns these pairings to specific crew members, forming personalized monthly schedules while respecting additional constraints (e.g., crew qualifications, rest requirements, and individual preferences). The objective of crew rostering is to generate balanced, compliant, and efficient rosters that optimize both operational performance and crew satisfaction. Zhou et al. [67] constructed a multiobjective model and developed a multiobjective and multiple-population ACS algorithm that significantly improved solution performance on large-scale instances to address crew rostering. Zhang et al. [68] proposed an improved multiobjective GA for solving this problem by conducting high-efficiency search under complex constraints. Chutima [69] effectively addressed the complex multiobjective cockpit crew scheduling problem for minimizing the costs of airlines by employing a hybrid multiobjective optimization algorithm that balanced operational costs with crew satisfaction. Zhang et al. [68] focused solely on balancing working hours, neglecting crew members’ individual preferences. In contrast, Zhou et al. [67] and Chutima [69] incorporated these preferences by treating satisfaction as an optimization objective, thereby improving humanized crew scheduling. However, a common limitation in [67,69] is the missing of robust optimization for unexpected disruptions, such as crew absences or flight delays.
In crew scheduling optimization, multiple conflicting objectives need to be satisfied simultaneously. EC approaches can naturally handle multiobjective trade-offs. EC can directly represent pairing and rostering rules (e.g., maximum continuous working hours and rest intervals) through customized chromosome encoding (e.g., binary and integer encoding). The population parallelism in EC [66,68,70] enables rapid exploration of the solution space, making it particularly suitable for large-scale crew-pairing and rostering problems.

4. Evolutionary Computation for Urban Air Mobility

UAM refers to a transformative mode of transportation that leverages low-altitude airspace to alleviate ground traffic congestion and improve urban connectivity. The rapid development of electric vertical take-off and landing (eVTOL) aircraft and unmanned aerial vehicles (UAVs) makes UAM systems increasingly viable. Commercial drone logistics services have achieved stable operational deployment in certain urban and regional markets. Notably, Amazon Prime Air has initiated drone delivery operations in Texas, USA [71], showing the technical feasibility of last-mile aerial logistics. Meanwhile, in China, Meituan’s drone delivery network has expanded to 31 operational routes in several cities (e.g., Shanghai, Shenzhen, and Guangzhou), successfully fulfilling over 300,000 customer orders [72]. With the emergence and growing demand for UAM, ensuring safe, reliable, and sustainable urban air transportation requires the support of efficient operational scheduling. From an operational perspective, scheduling tasks in UAM involve complex, dynamic, and interdependent decisions that require robust optimization techniques. This section categorizes existing EC-based research in UAM operation scenes into three main areas: flight process scene, ground scene, and infrastructure scene. Table 2 presents a systematic overview of relevant state-of-the-art EC-based studies in UAM, where all research is categorized by problem type. Table 2 includes (1) the specific problem addressed by each study, (2) underlying EC algorithms employed, (3) optimization objectives, (4) data sources (real-world vs. simulated), and (5) performance metrics.

4.1. Flight Process Scene

Compared to fuel-powered aircraft used in commercial aviation, eVTOLs in UAM operate at lower altitudes within complex urban environments, face stricter energy and infrastructure constraints, and demand more dynamic and decentralized route scheduling due to their limited range, lower speeds, and higher operational frequency. In the UAM flight process scene, the route scheduling is the focus of this article.

Route Planning

Route planning of UAM involves planning eVTOL aircraft paths, determining passenger or cargo volumes, and allocating operational resources, while accounting for safety, reliability, efficiency, and environmental friendliness. Chan et al. [73] proposed an eVTOL-aircraft path planning approach in complex and dynamic urban wind environments by combining Voronoi-diagram-based environment decomposition and Dijkstra’s algorithm for initial path generation with an efficient PSO-based algorithm to optimize path control points and minimize overall energy consumption. When scheduling eVTOL fleets in real time, uncertain environments often add complexity to path scheduling. To address this challenge, Wang et al. [74] developed an enhanced PSO algorithm combined with cost-scheduling, which hierarchically optimized eVTOL configurations and real-time scheduling, balancing service efficiency and operational costs via PF analysis. Ko et al. [75] formulated a MILP model and integrated GA with receding horizon scheduling to design real-time scheduling for eVTOL fleets under uncertain demand conditions, achieving a balance between operational profitability and service efficiency. Kim et al. [76] proposed a hybrid PSO-GA heuristic embedded in a model predictive control framework to dynamically schedule heterogeneous fleets for UAM mobility-on-demand services under demand variations. Hildemann [77] proposed an integrated approach that combines NSGA-II with geographic information system technologies to optimize eVTOL flight trajectories, aiming to minimize total flight time, energy consumption, and noise pollution under constraints of no-fly zones and regulatory noise limits. Farazi et al. [78] proposed a customized NSGA-II algorithm to address the trade-off between economic efficiency and noise impact in eVTOL parcel delivery, providing an efficient and community-friendly decision-making framework for urban air logistics system planning.
The above studies focus on tactical scheduling, typically emphasizing real-time decisions for managing individual flights, whereas strategic scheduling involves long-term planning and resource allocation to ensure the efficiency and sustainability of the UAM system. From a strategic perspective, Wang et al. [79] developed an innovative two-level optimization framework that integrated SA to generate initial solutions balancing path complexity, followed by the Dafermos algorithm to adjust traffic flow based on marginal costs, thereby achieving system equilibrium and minimizing airspace complexity. Xie et al. [80] developed a novel framework based on hybrid artificial intelligence for low-altitude UAV traffic management in high-density urban airspace, integrating reinforcement learning and GA for data augmentation to dynamically balance airspace resources, reduce overload durations, and enhance operational efficiency.
The aforementioned research shows several advantages of EC in solving path planning for UAM. These approaches proposed by [77,78,79] effectively handle three-dimensional airspace constraints, supporting encoding for building avoidance, no-fly zones, and other spatial restrictions. The above EC-based approaches also show potential for distributed computing, with the origin–destination pair independent optimization feature in [73] enabling parallel path calculation for eVTOL fleets. Furthermore, the approaches proposed by [75] facilitate the integration of heterogeneous traffic by simultaneously handling the mixed scheduling of logistics drones and passenger carrying eVTOLs. The approach in [74] enhances real-time applicability by incorporating a rolling horizon approach to address dynamic demands.
However, there are also some limitations: some approaches suffer from high memory consumption, significant time costs, and strong hardware dependency [79,80]. Disturbances from dynamic obstacles are not considered in any of the cited work [73,74,75,76,77,78,79,80]. Consideration of microscale meteorology is also limited, with only the approach proposed in [73] demonstrating the ability to dynamically adapt to different wind fields.

4.2. Ground Scene

UAM operations differ substantially from those of commercial aviation, as they involve vertical take-off and landing (VTOL) aircraft and utilize vertiports located both on the ground and elevated structures, such as building rooftops. In commercial aviation, landing scheduling typically involves large aircraft operating in highly structured, capacity-constrained airspace and airports, managed by centralized air traffic control systems. By contrast, UAM landing scheduling must coordinate a large number of small, distributed eVTOL vehicles operating at lower altitudes in dense urban environments. These operations often require decentralized and highly dynamic scheduling strategies, while also facing stricter constraints related to noise, energy consumption, vertiport availability, and variable passenger demand. As a result, landing scheduling is a critical component in ensuring both operational efficiency and safety within UAM systems. In the ground operations context of UAM, landing scheduling stands out as a central research topic.

Landing Scheduling

Landing scheduling of UAM aims to maximize vertiport throughput and minimize delays by coordinating VTOL aircraft arrival times, landing sequences, and speeds. Research on landing scheduling for UAM remains in the nascent stages, with the current literatures showing limited exploration of this critical operational challenge. To the best of our knowledge, the existing studies include only one employing the EC approach and two additional investigations utilizing heuristic approaches with moderate relevance to UAM landing scheduling domain. Espejo-Díaz et al. [81] proposed a heuristic algorithm to maximize throughput of the vertiport and minimize delays. Pradeep et al. [82] proposed an optimization approach based on an insertion and local search heuristic algorithm, aiming to maximize throughput. Ge [83] proposed an approach based on ACO and a modular system architecture to minimize the total mission time by optimizing task assignment, landing sequences, and resource scheduling paths for eVTOL aircraft.
The above-mentioned two heuristic algorithms [81,82] primarily rely on local search mechanisms that may converge to local optima, potentially missing globally optimal solutions. In contrast, the ACO-based algorithm [83] shows superior global optimization capabilities through its pheromone-based mechanism, which preserves historical search experience while guiding exploration through heuristic information to effectively prevent premature convergence. Moreover, the two above-mentioned heuristic algorithms [81,82] are limited to small-scale problems involving fewer than 10 eVTOLs, whereas the ACO-based algorithm [83] significantly outperforms these heuristic approaches by efficiently handling complex scheduling scenarios with 50 or more eVTOLs, presenting greater practical potential for real-world urban air mobility operations.

4.3. Infrastructure Scene

In the UAM infrastructure scene, the facility location scheduling is a challenging problem. Facility location scheduling in UAM focuses on determining the optimal placement and allocation of infrastructure, such as vertiports, charging stations, or hubs, to support safe and efficient urban air operations. This problem is complicated by spatial constraints, demand uncertainty, and the need to balance operational efficiency, accessibility, and cost-effectiveness.

Facility Location Scheduling

Zhang et al. [84] proposed an enhanced NSGA-II based on an adaptive operator to address hub location and infrastructure network layout in urban aerial logistics systems. The approach balances operational costs and third-party safety which includes potential harm to pedestrians, vehicles, buildings, and infrastructure. Senthilnathan et al. [85] developed a three-phase hybrid optimization framework combining CLARA clustering, GA, and simulation modeling to determine optimal vertiport locations for UAM infrastructure, which provides a data-driven decision support tool for infrastructure planning. Jiang [86] proposed a comprehensive approach to eVTOL hub site selection by integrating multi-dimensional demand estimation, candidate site selection, a multi-stage optimization model, and an enhanced non-dominated solution genetic algorithm III, effectively balancing demand coverage, traffic relief, and resource efficiency in a Beijing case study.
The above-mentioned EC approaches [84,85,86] achieve the multiobjective optimization in the facility location scheduling. Moreover, the above EC approaches have the adaptive processing ability of complex constraints. However, these approaches still have aspects requiring further refinement and improvement. Zhang et al. [84] do not sufficiently consider the urban 3D terrain characteristics, thereby limiting the practical applicability in real-world scenarios. Furthermore, the passenger acceptance rates for air taxi services in [85,86] rely solely on National Aeronautics and Space Administration’s UAM market research data, which may not accurately reflect regional variations in market receptiveness. This methodological limitation could potentially lead to suboptimal vertiport location selections.

5. Future Research Directions and Open Issues

In this section, the future research directions and open issues of EC for air transportation are discussed, hoping to inspire future research.

5.1. Real-Time Evolutionary Computation for Air Transportation

The air transportation schedule may be interrupted due to unexpected situations, such as temporary air traffic controls and public emergencies, necessitating real-time responsiveness in decision-making. However, the large-scale data in air transportation scenes makes it difficult for ECs to achieve real-time optimization.
With the development of distributed computing technology, running ECs in parallel is a promising approach. In ECs, it is intuitive to conduct the evolution of each individual in parallel. Considering the time-consuming message transfer in distributed computing, how to reduce messages needed to be transferred among individuals while preserving the optimization results is a critical challenging issue and it should be dealt with based on the features of the air transportation optimization problems. In addition, some researchers have combined EC with distributed computing [87,88] and proposed distributed EC frameworks based on multi-population cooperation to address complex optimization problems. These frameworks provide promising insight for real-time decision-making in air transportation.

5.2. Surrogate-Assisted Evolutionary Computation for Air Transportation

Optimization problems in real-world air transportation typically introduce complex features and large-scale data. Thus, the evaluation of candidate solutions requires a large amount of computational effort. When using EC to deal with such problems, performing an exact evaluation on each generated solution is computationally expensive. Unless possessing abundant computational resources, the time efficiency of ECs is weakened.
In recent years, surrogate-assisted ECs have emerged as a promising approach for expensive optimization problems [89,90,91]. The principle of surrogate-assisted ECs is training surrogate models to approximate the costly exact evaluation process. Specifically, during the optimization process, surrogate models provide rapid evaluation of generated solutions, allowing low-cost approximations to partially replace expensive high-fidelity evaluations. Note that the design of surrogate-assisted ECs is highly related to the specific features of the air transportation optimization problems. Guo et al. [92] proposed a surrogate-assisted EC tailored to the optimization of dynamic air transportation problem. Overall, the related research is still in its infancy.

5.3. Evolutionary Computation for Robust Air Transportation Optimization

There are various uncertainties in air transportation. For example, flight data collected from sensors may encounter some errors. In addition, some data in the air environment is time-varying and can only be estimated in a certain range, such as the weather conditions. The uncertainties in air transportation should be sufficiently considered to ensure the effectiveness of the generated solutions.
Robust optimization offers a feasible solution. Unlike conventional optimization, which sets exact model parameters, robust optimization explicitly considers the uncertainty of key parameters during the model formulation phase and aims to find solutions that perform well under a wide range of probable disturbance scenarios. In the design of EC algorithms, robust optimization is typically integrated by introducing perturbations during the solution evaluation phase. Several studies have explored the application of robust optimization in air transportation. For example, Yang et al. [93,94] firstly introduced the concept of total effective resistance into air transportation networks as a robustness metric, formulating the problem as a total effective resistance minimization problem. In [93,94], the sensitivity of effective resistance to network topology changes can be extended to dynamic flight scheduling. Effective resistance combines with EC approaches to generate robust flight schedules, while resistance serves as a resilience metric to mitigate uncertainties such as weather disruptions. In the future, robust optimization based on EC algorithms holds significant potential for addressing a broader range of optimization problems in air transportation.

5.4. Evolutionary Computation for Large-Scale Dynamic Multiobjective Air Transportation Optimization Problems

Large-scale data, dynamic environment, and multiple optimization objectives are three typical complex features in air transportation optimization problems. However, existing EC algorithms for air transportation rarely address all three features simultaneously. Specifically, current research either focuses on EC applications in large-scale multiobjective scenes [47,66,67] (e.g., air traffic flow management and crew scheduling) or concentrates on dynamic multiobjective problem solving [63,75,95] (e.g., air traffic control and dynamic airport gate assignment). A promising direction for future research lies in developing novel EC frameworks that holistically integrate large-scale decision-making, dynamic environment adaptation and multiple optimization objectives of air transportation.

5.5. Evolutionary Computation Combined with Artificial Intelligence for Air Transportation Optimization Problems

The integration of EC with artificial intelligence (AI) is a promising approach to tackling complex air transportation optimization problems.
Existing research has already combined AI and EC to solve engineering problems. Gao et al. [96] integrated the rapid response capability of Reinforcement Learning (RL) with GA’s global optimization strength, establishing a scalable hybrid optimization framework for complex military mission assignment. This GA-RL framework provides a new paradigm of rapid response and global optimization for air transportation challenges, enabling faster real-time decision-making in scenarios such as dynamic route adjustments and sudden weather avoidance. Zhou et al. [97] integrated Graph Neural Networks (GNNs) and NSGA-II, which achieve a balance between safety and efficiency in ride-hailing services. This work offers a roadmap for integrating GNNs with GA to address multiobjective air transportation problems (e.g., flight processing scheduling and crew scheduling). These pioneering integrations of EC and AI lay the foundation for adaptive, real-time decision systems that promise to improve efficiency and real-time performance for increasingly complex air transportation optimization problems.

6. Conclusions

In this article, a comprehensive review of the application of EC in the field of air transportation is presented. A hierarchical taxonomy is proposed to classify the related studies. At the first level, the studies are divided into commercial aviation and UAM based on the application domain. At the second level, the studies are further categorized according to different operational scenes in air transportation, including the flight process scene, the ground scene, personal scene, and the infrastructure scene. Related studies in the literature are discussed in detail according to the hierarchical taxonomy, highlighting the effectiveness of EC in dealing with the complex optimization problems in air transportation. In addition, several future research directions and open issues are discussed, aiming to inspire further advancements in the field of EC for air transportation.

Author Contributions

Methodology, R.H. and Z.-G.C.; conceptualization, Z.-G.C.; writing—original draft, R.H.; writing—review and editing, Z.-G.C. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported in part by the National Natural Science Foundation of China (Grant No. 62206100) and in part by the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2024A1515011708).

Data Availability Statement

The original contributions presented in this study are included in the article.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A

Algorithm A1 presents the pseudocode of genetic algorithm. Algorithm A1 takes four input parameters: population size P, maximum generations Gmax (termination criterion), crossover probability pc, and mutation probability pm. The output is the globally best solution xbest found during the search process.
First, in line 1, t is a variable used to record the current evolution generation, initialized to 0. In lines 2–4, an initial population Pt is randomly constructed containing P individuals, evaluate each individual’s fitness f(xit), and record the best individual x*. Second, in line 5, the evolutionary process starts. The maximum number of iterations Gmax is used as the sole termination condition. In line 6, high-quality parents are selected via a selection operator to form a mating pool Poff. Third, in lines 7–15, the crossover operator is applied to the parent pairs xa and xb with the probability pc to generate offspring y1 and y2, and all offspring y are saved to Poff. Then, in line 16, each individual in Poff mutates with probability pm. Fourth, in line 17–24, all the individuals in Poff are saved into Pt+1 (Pt+1 represents the population at the t + 1th generation). xtbest is used to record the best solution in the population at generation t. Then, the global best individual x* is updated.
Algorithm A1: Genetic Algorithm
  Input: P, Gmax, pc, pm
  Output: xbest
1: t = 0
2: Initialize population Pt = {x1t, …, xpt}
3: Evaluate fitness f(xit) for all xitPt
4: xbest = a r g m a x x i t P t (f(xit))
5: while t < Gmax and stopping criteria not met do
6:     Poff = selection(Pt)
7:     for k = 1 to P/2 do
8:        Randomly select parents xa, xb Poff
9:        if rand() < pc then
10:             y1, y2 = crossover(xa, xb)
11:       else
12:             y1 = xa, y2 = xb
13:       end if
14:        Poff = Poff  {y1, y2}
15:     end for
16:     Each individual in Poff mutates with probability pm
17:     Pt+1 = Poff
18:     Evaluate fitness f(xit) for all xit Pt+1
19:     xtbest = a r g m a x x i t P t + 1 (f(xit+1))
20:     if f(xtbest) is better than f(xbest)
21:       xbest = xtbest
22:     t = t + 1
23: end while
24: return xbest
  end procedure

Appendix B

The micro-level flight process scheduling optimization contains the following decision variables:
  • The departure time of each flight ti ∈ [timin, timax], i = 1, …, N.
  • The route of each flight Ri = (ri1, ri2, …, ri|Ri|) = (aidep, wi1, wi2, …, aiarr) ∈ Πi, where wi1, wi2, …; are waypoints of the route Ri and two waypoints are connected to form a segment. Note that |Ri| represents the number of segments in Ri. aidep and aiarr represent the departure airport and the arrival airport of fi, respectively.
  • The segment speed of selected route for each flight v(rij) ∈ V(rij), i = 1, …, N, j = 1, …, |Ri|.
There are two objective functions in micro-level flight process scheduling optimization, which are the total delay (TD) and the number of flight conflicts (TNCs). Note that all notations in micro-level flight process scheduling optimization formulation are listed in Table A1.
Table A1. Notations in micro-level flight process scheduling formulation.
Table A1. Notations in micro-level flight process scheduling formulation.
NotationDefinition
ASet of airports
FSet of flights
SSet of sectors
ΠiSet of feasible routes of fi
aAn airport in A
fiThe i-th flight in F
tiThe departure time of fi
timinThe minimum departure time of fi
timaxThe maximum departure time of fi
RiThe selected flight route of fi
rijThe j-th segment of Ri
wigThe g-th waypoint of Ri
v(rij)The speed of rij
V(rij)The feasible speed set of rij
aidepThe departure airport of fi
aiarrThe arrival airport of fi
sA sector of S
CaThe maximum capacity of airport a
CsThe maximum capacity of sector s
NThe number of flights in F
TmaxThe latest arrival time among all flights
In the calculation of TD, the arrival time of fi should be obtained. For each flight fi, its arrival time at each waypoint can be calculated as follows:
T w i j = T w i j 1 + | w i j 1 w i j | v r i j
where | w i j 1 w i j | is the geographical distance between wij−1 and wij. Note that T(wi0) = T(aidep) is equal to tidep and tiarr = T(aiarr) is equal to T(ri|Ri|).
The first objective TD is shown in (A2).
TD = φ g + φ f
φ g = i = 1 N t i ϕ i d e p
φ f = i = 1 N T a i a r r ϕ i d e p
where φg is the ground delay and φf is the flight total delay, and ϕ i d e p represents the estimated departure time of fi.
Then, based on the arrival time of each waypoint, the location of fi at each time t can be calculated as (A5):
l o c i t = w i j 1 + v r i j t T i w i j 1
where T(wi,j−1) < t < T(wi,j).
For each time t ∈ [0, Tmax], Tmax = max{T(rij)}, where i ∈ {1,2, …, N} and j ∈ {1, 2, …, |Ri|}, if the geographical distance between fi and another flight fk is less than the safety threshold δ (typically 5 nautical miles), a conflict occurs, i.e.,
i , k , t = 1 , if | loc i t - loc k t | < δ 0 , otherwise
The second objective TNC is shown in (A7):
TNC = t 0 , T max i = 1 , k = i + 1 N i , k , t
Then, the micro-level flight process scheduling optimization can be formulated as follows:
min   TD
min   TNC
s . t . R i = r i 1 , r i 2 , , r i | R i | Π i ,   i = 1 , , N
t i t i m i n , t i m a x ,   i = 1 , , N
v r i j V r i j ,   i = 1 , , N , j = 1 , , | R i |
N a t C a , a A , t 0 , T max
N s t C s , s S , t 0 , T max
Equations (A8) and (A9) represent the objective functions of micro-level flight process scheduling optimization, respectively. Equation (A10) indicates that the route of fi is selected from Πi. Equations (A11) and (A12) restrict the departure time, and each segment speed of fi should be selected within their limited range. Equation (A13) ensures that the number of flights taking off and landing at airport a does not exceed the maximum capacity of the airport at time t. Equation (A14) ensures that the number of flights flying in sector s at time t does not exceed the maximum capacity of sector s.

Appendix C

In Table A2, we summarize all reviewed papers based on the EC algorithms used. Twenty-three papers employed GA to solve their corresponding air transportation optimization problems, validating GA’s promising performance in this field. Since PSO is typically designed for continuous optimization problems, specific encoding strategies are employed in [55,56,75] to use PSO for solving discrete or hybrid optimization problems in air transportation. Bhattacharya et al. [55] utilized a fuzzy graph model to transform the discrete facility location problem into an optimization of continuous membership degrees, where the objective function necessitates calculation via continuous membership degrees. Sirigu et al. [56] mapped discrete variables (e.g., path indices and speed levels) into continuous values through encoding, thereby transforming the discrete combinatorial problem into a continuous space search, while designing a boundary reset mechanism to guarantee solution feasibility. Chan et al. [75] discretized continuous space into a network using Voronoi diagrams, generated initial solutions using Dijkstra’s algorithm, and subsequently refined node positions through local continuous optimization around these initial configurations. Collectively, these approaches establish a continuous-to-discrete transformation paradigm for PSO, offering novel solutions for discrete and hybrid optimization problems. Their effectiveness has been validated in typical air transportation scenarios, including airport ground movement and route planning in UAM. In addition, common EC algorithms such as ACO, SA, and BCO have also been applied to air transportation optimization problems.
Table A2. Reviews of recent EC-based research for air transportation based on the types of EC used.
Table A2. Reviews of recent EC-based research for air transportation based on the types of EC used.
Basic ECReferencesApplication ProblemThe Type of Optimization ProblemBasic ECReferencesApplication ProblemThe Type of Optimization Problem
GAAmara et al., 2023 [39]Macro-level flight process schedulingHybrid continuous and discreteGASenthilnathan et al., 2025 [85] Facility location scheduling in UAMDiscrete
GAGuo et al., 2022 [41]Macro-level flight process schedulingDiscreteGAJiang 2025 [86] Facility location scheduling in UAMDiscrete
GAXu et al., 2021 [43]Micro-level flight process schedulingDiscretePSOBhattacharya et al., 2024 [55]Landing schedulingDiscrete
GAGuo et al., 2024 [46]Macro-level flight process schedulingDiscretePSOSirigu et al., 2020 [56]Ground MovementDiscrete
GAGuo et al., 2024 [47]Micro-level flight process schedulingDiscretePSOChan et al., 2023 [73] Route planning in UAMHybrid continuous and discrete
GAXiao et al., 2025 [49]Micro-level flight process schedulingHybrid continuous and discretePSOWang et al., 2024 [74] Route planning in UAMHybrid continuous and discrete
GAFernando et al., 2024 [50]Landing schedulingHybrid continuous and discreteACONtakolia et al., 2022 [45]Micro-level process flight schedulingHybrid continuous and discrete
GAShirini et al., 2024 [54]Landing schedulingDiscreteACOXu et al., 2025 [51]Landing schedulingHybrid continuous and discrete
GAPerea et al., 2023 [58]Ground MovementDiscreteACOZhou et al., 2021 [67]Crew schedulingDiscrete
GAXia et al., 2024 [61] Gate assignmentDiscreteACOGe 2025 [83] Landing scheduling in UAMDiscrete
GAZhu et al., 2024 [62]Gate assignmentDiscreteBCONikolić et al., 2024 [60] Gate assignmentDiscrete
GAGao et al., 2023 [63] Gate assignmentDiscreteSAFarazi et al., 2024 [78] Route planning in UAMDiscrete
GAAggarwal et al., 2023 [65]Crew schedulingDiscreteICAZhang et al., 2020 [52]Landing schedulingDiscrete
GAZeren et al., 2024 [66]Crew schedulingDiscreteHSEAZhang et al., 2024 [53]Landing schedulingDiscrete
GAZhang et al., 2021 [68]Crew schedulingDiscreteSFLAHsu et al., 2024 [64] Gate assignmentDiscrete
GAChutima 2020 [69]Crew schedulingDiscreteMABeke et al., 2024 [57]Ground MovementDiscrete
GAKo et al., 2025 [75] Route planning in UAMDiscreteGA and PSOCai et al., 2022 [40]Macro-level flight process schedulingDiscrete
GAHildemann 2023 [77] Route planning in UAMDiscreteGA and PSOOruc et al., 2024 [44]Micro-level flight process schedulingContinuous
GAFarazi et al., 2024 [78] Route planning in UAMDiscreteGA and PSOKim et al., 2020 [76] Route planning in UAMDiscrete
GAXie et al., 2021 [80] Route planning in UAMHybrid continuous and discreteGA and SALiu et al., 2022 [48]Micro-level flight process schedulingDiscrete
GA Zhang et al., 2025 [84] Facility location scheduling in UAMDiscretePSO and QEADeng et al., 2024 [59] Gate assignmentDiscrete

Appendix D

The algorithm names (genetic algorithm, particle swarm optimization, differential evolution, ant colony optimization, evolutionary computation, and evolutionary algorithm) are sequentially combined with the following keywords in the search for relevant literature: “air transportation”, “air traffic”, “airport”, “airline”, “commercial aviation”, and “urban air mobility”.
The complete list of search phrases employed in this survey for the literature search is as follows: “genetic algorithm AND air transportation”, “genetic algorithm AND air traffic”, “genetic algorithm AND airport”, “genetic algorithm AND airline”, “genetic algorithm AND commercial aviation”, “genetic algorithm AND urban air mobility”, “particle swarm optimization AND air transportation”, “particle swarm optimization AND air traffic”, “particle swarm optimization AND airport”, “particle swarm optimization AND airline”, “particle swarm optimization AND commercial aviation”, “particle swarm optimization AND urban air mobility”, “differential evolution AND air transportation”, “differential evolution AND air traffic”, “differential evolution AND airport”, “differential evolution AND airline”, “differential evolution AND commercial aviation”, “differential evolution AND urban air mobility”, “ant colony optimization AND air transportation”, “ant colony optimization AND air traffic”, “ant colony optimization AND airport”, “ant colony optimization AND airline”, “ant colony optimization AND commercial aviation”, “ant colony optimization AND urban air mobility”, “evolutionary computation AND air transportation”, “evolutionary computation AND air traffic”, “evolutionary computation AND airport”, “evolutionary computation AND airline”, “evolutionary computation AND commercial aviation”, “evolutionary computation AND urban air mobility”, “evolutionary algorithm AND air transportation”, “evolutionary algorithm AND air traffic”, “evolutionary algorithm AND airport”, “evolutionary algorithm AND airline”, “evolutionary algorithm AND commercial aviation”, and “evolutionary algorithm AND urban air mobility”.

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Figure 1. Hierarchical taxonomy of EC for air transportation.
Figure 1. Hierarchical taxonomy of EC for air transportation.
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Figure 2. PRISMA flow diagram illustrating the study selection process in our survey.
Figure 2. PRISMA flow diagram illustrating the study selection process in our survey.
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Figure 3. Illustration of crew scheduling.
Figure 3. Illustration of crew scheduling.
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Table 2. Reviews of recent EC-based research on UAM.
Table 2. Reviews of recent EC-based research on UAM.
ProblemReferencesBasic ECOptimization ObjectivesData SourceMetrics
Route planningChan et al., 2023 [73] PSO(1) Minimize flight distance
(2) Minimize wind resistance energy consumption
Real-world data from a Chinese cityObjective values
Wang et al., 2024 [74] PSO(1) Maximize the number of passengers served
(2) Minimize costs
Real-world data from six Chinese citiesObjective values
Ko et al., 2025 [75] GA(1) Maximize operational profits
(2) Minimize optimize service quality
Real-world data from Paris, FranceOptimality gap and Average runtime
Kim et al., 2020 [76] GA and PSO(1) Maximize operational profits
(2) Maximize service quality
Simulation dataOptimality gap
Hildemann 2023 [77]GA(1) Minimize flight time
(2) Minimize energy consumption
(3) Minimize noise pollution
Real-world data from New York and simulation dataObjective values
Farazi et al., 2024 [78]GA(1) Minimize operational costs
(2) Minimize noise impact
Real-world data from Chicago, USA Objective values
Wang et al., 2022 [79]SAMinimize the global complexity of the three-dimensional air transport network for UAMReal-world data from SingaporeObjective value
Xie et al., 2021 [80] GA(1) Minimize airspace overload time
(2) Maximize operational efficiency
Simulation dataAirspace overload time, runtime, and convergence iterations
Landing schedulingEspejo-Díaz et al., 2023 [81] Heuristic(1) Maximize throughput
(2) Minimize makespan
Simulation dataComputational efficiency
Pradeep et al., 2024 [82] HeuristicMinimize makespanSimulation dataSolution quality and computational efficiency
Ge 2025 [83] ACO(1) Maximize resource utilization
(2) Minimize makespan
Simulation dataTask completion time reduction rate and gate utilization rate
Facility location schedulingZhang et al., 2025 [84] GA(1) Minimize economic costs
(2) Minimize security risks
Real-world data from AustraliaHV
Senthilnathan et al., 2025 [85] GA(1) Maximize population coverage
(2) Minimize rent and labor costs
(3) Minimize passenger waiting time
(4) Maximize vehicle utilization
Real-world data from New York, USAEconomic efficiency, coverage rate, and resource utilization rate
Jiang et al., 2025 [86] GA(1) Maximize demand coverage
(2) Maximize congestion relief
(3) Minimize redundant coverage
Real-world data from Beijing, ChinaRegular shuttle coverage rate, on-demand mobility coverage rate
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Huang, R.; Chen, Z.-G. Evolutionary Computation for Air Transportation: A Survey. Mathematics 2025, 13, 2867. https://doi.org/10.3390/math13172867

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Huang, R., & Chen, Z.-G. (2025). Evolutionary Computation for Air Transportation: A Survey. Mathematics, 13(17), 2867. https://doi.org/10.3390/math13172867

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