Unmanned Aerial Vehicle Trajectory Planning Research Articles

Iterative Trajectory Planning and Resource Allocation for UAV-Assisted Emergency Communication with User Dynamics

The demand for air-to-ground communication has surged in recent years, underscoring the significance of unmanned aerial vehicles (UAVs) in enhancing mobile communication, particularly in emergency scenarios due to their deployment efficiency and flexibility. In situations such as emergency cases, UAVs can function as efficient temporary aerial base stations and enhance communication quality in instances where terrestrial base stations are incapacitated. Trajectory planning and resource allocation of UAVs continue to be vital techniques, while a relatively limited number of algorithms account for the dynamics of ground users. This paper focuses on emergency communication scenarios such as earthquakes, proposing an innovative path planning and resource allocation algorithm. The algorithm leverages a multi-stage subtask iteration approach, inspired by the block coordinate descent technique, to address the challenges presented in such critical environments. In this study, we establish an air-to-ground communication model, subsequently devising a strategy for user dynamics. This is followed by the introduction of a joint scheduling process for path and resource allocation, named ISATR (iterative scheduling algorithm of trajectory and resource). This process encompasses highly interdependent decision variables, such as location, bandwidth, and power resources. For mobile ground users, we employ the cellular automata (CA) method to forecast the evacuation trajectory. This algorithm successfully maintains data communication in the emergency-stricken area and enhances the communication quality through bandwidth division and power control which varies with time. The effectiveness of our algorithm is validated by evaluating the average throughput with different parameters in various simulation conditions and by using several heuristic methods as a contrast.

UAV Control Method Combining Reptile Meta-Reinforcement Learning and Generative Adversarial Imitation Learning

Reinforcement learning (RL) is pivotal in empowering Unmanned Aerial Vehicles (UAVs) to navigate and make decisions efficiently and intelligently within complex and dynamic surroundings. Despite its significance, RL is hampered by inherent limitations such as low sample efficiency, restricted generalization capabilities, and a heavy reliance on the intricacies of reward function design. These challenges often render single-method RL approaches inadequate, particularly in the context of UAV operations where high costs and safety risks in real-world applications cannot be overlooked. To address these issues, this paper introduces a novel RL framework that synergistically integrates meta-learning and imitation learning. By leveraging the Reptile algorithm from meta-learning and Generative Adversarial Imitation Learning (GAIL), coupled with state normalization techniques for processing state data, this framework significantly enhances the model’s adaptability. It achieves this by identifying and leveraging commonalities across various tasks, allowing for swift adaptation to new challenges without the need for complex reward function designs. To ascertain the efficacy of this integrated approach, we conducted simulation experiments within both two-dimensional environments. The empirical results clearly indicate that our GAIL-enhanced Reptile method surpasses conventional single-method RL algorithms in terms of training efficiency. This evidence underscores the potential of combining meta-learning and imitation learning to surmount the traditional barriers faced by reinforcement learning in UAV trajectory planning and decision-making processes.

Online Joint Optimization of Virtual Network Function Deployment and Trajectory Planning for Virtualized Service Provision in Multiple-Unmanned-Aerial-Vehicle Mobile-Edge Networks

The multiple-unmanned-aerial-vehicle (multi-UAV) mobile edge network is a promising networking paradigm that uses multiple resource-limited and trajectory-planned unmanned aerial vehicles (UAVs) as edge servers, upon which on-demand virtual network functions (VNFs) are deployed to provide low-delay virtualized network services for the requests of ground users (GUs), who often move randomly and have difficulty accessing the Internet. However, VNF deployment and UAV trajectory planning are both typical NP-complete problems, and the two operations have a strong coupling effect: they affect each other. Achieving optimal virtualized service provision (i.e., maximizing the number of accepted GU requests under a given period T while minimizing the energy consumption and the cost of accepting the requests in all UAVs) is a challenging issue. In this paper, we propose an improved online deep reinforcement learning (DRL) scheme to tackle this issue. First, we formulate the joint optimization of the two operations as a nonconvex mixed-integer nonlinear programming problem, which can be viewed as a sequence of one-frame joint VNF deployment and UAV-trajectory-planning optimization subproblems. Second, we propose an online DRL based on jointly optimizing discrete (VNF deployment) and continuous (UAV trajectory planning) actions to solve each subproblem, whose key idea is establishing and achieving the coupled influence of discrete and continuous actions. Finally, we evaluate the proposed scheme through extensive simulations, and the results demonstrate its effectiveness.

Enhancing UAV Path Planning Efficiency through Adam-Optimized Deep Neural Networks for Area Coverage Missions

Efficient Unmanned Aerial Vehicle (UAV) trajectory generation is crucial for successful area coverage missions, aiming to maximize coverage while minimizing resource consumption. In this research, we present a comprehensive study on optimizing UAV trajectory generation using Deep Neural Networks (DNNs) with the Adam optimization algorithm. The DNNs are trained on historical data to produce smooth and continuous trajectories, thereby reducing abrupt changes in direction and enhancing overall efficiency during the mission. To evaluate the performance of the proposed approach, we conducted experiments comparing different activation functions, namely tanh, sigmoid, and ReLU, with the Adam-optimized DNN model. The trajectories generated by each activation function were analyzed using key metrics, including Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and R-squared (R2) scores for both X and Y coordinates. The results of the comparative analysis revealed that the DNN model with the Adam optimizer exhibited superior performance over the other activation functions. It achieved lower MSE, MAE, and RMSE values, indicating better trajectory accuracy and smoother paths. Additionally, the R2 scores demonstrated a higher correlation between the generated trajectories and the actual trajectories, highlighting the model's ability to capture underlying patterns effectively. The findings underscore the significance of leveraging the Adam-optimized DNN approach for UAV trajectory planning, offering promising opportunities for resource optimization, increased mission success, and further advancements in autonomous aerial systems. This research contributes to the ongoing efforts in UAV path planning, optimization, and intelligent control strategies, paving the way for enhanced autonomous systems in various real-world applications.

Trajectory Planning and Control Design for Aerial Autonomous Recovery of a Quadrotor

One of the most essential approaches to expanding the capabilities of autonomous systems is through collaborative operation. A separated lift and thrust vertical takeoff and landing mother unmanned aerial vehicle (UAV) and a quadrotor child UAV are used in this study for an autonomous recovery mission in an aerial child–mother unmanned system. We investigate the model predictive control (MPC) trajectory generator and the nonlinear trajectory tracking controller to solve the landing trajectory planning and high-speed trajectory tracking control problems of the child UAV in autonomous recovery missions. On this basis, the estimation of the mother UAV movement state is introduced and the autonomous recovery control framework is formed. The suggested control system framework in this research is validated using software-in-the-loop simulation. The simulation results show that the framework can not only direct the child UAV to complete the autonomous recovery while the mother UAV is hovering but also keep the child UAV tracking the recovery platform at a speed of at least 11 m/s while also guiding the child UAV to a safe landing.

Multi-UAV Cooperative Trajectory Planning Based on the Modified Cheetah Optimization Algorithm.

The capacity for autonomous functionality serves as the fundamental ability and driving force for the cross-generational upgrading of unmanned aerial vehicles (UAVs). With the disruptive transformation of artificial intelligence technology, autonomous trajectory planning based on intelligent algorithms has emerged as a key technique for enhancing UAVs' capacity for autonomous behavior, thus holding significant research value. To address the challenges of UAV trajectory planning in complex 3D environments, this paper proposes a multi-UAV cooperative trajectory-planning method based on a Modified Cheetah Optimization (MCO) algorithm. Firstly, a spatiotemporal cooperative trajectory planning model is established, incorporating UAV-cooperative constraints and performance constraints. Evaluation criteria, including fuel consumption, altitude, and threat distribution field cost functions, are introduced. Then, based on its parent Cheetah Optimization (CO) algorithm, the MCO algorithm incorporates a logistic chaotic mapping strategy and an adaptive search agent strategy, thereby improving the home-returning mechanism. Finally, extensive simulation experiments are conducted using a considerably large test dataset containing functions with the following four characteristics: unimodal, multimodal, separable, and inseparable. Meanwhile, a strategy for dimensionality reduction searching is employed to solve the problem of autonomous trajectory planning in real-world scenarios. The results of a conducted simulation demonstrate that the MCO algorithm outperforms several other related algorithms, showcasing smaller trajectory costs, a faster convergence speed, and stabler performance. The proposed algorithm exhibits a certain degree of correctness, effectiveness, and advancement in solving the problem of multi-UAV cooperative trajectory planning.

Secure Efficiency Map-Enabled UAV Trajectory Planning

This letter investigates the dynamic changes of security and efficiency in an unmanned aerial vehicle (UAV)-to-ground network with a mobile UAV transmitter, a mobile ground receiver, and a fixed eavesdropper, respectively. To provide communication services with high security, spectrum efficiency, and energy efficiency, a concept of secure efficiency map (SEM) is devised and proposed to plan the UAV trajectory. Specifically, the security-efficiency index of each subarea in a certain area for a certain time slot is firstly calculated. Then, given that the security-efficiency index is time-varying, and CNN-LSTM network can effectively extract data features and accurately reflect time correlation, we take multiple SEMs drawn from the observed security-efficiency indices as the input of the CNN-LSTM network, and output future SEMs. Thirdly, based on predicted future SEMs, an SEM-enabled UAV trajectory planning scheme is further presented to jointly improve security and efficiency of the considered communication network. Finally, simulation results confirm the proposed SEM-enabled UAV trajectory planning scheme achieves a superior joint optimization of security, spectrum efficiency, and energy efficiency to other UAV trajectory planning schemes.

Joint UAV Trajectory Planning, DAG Task Scheduling, and Service Function Deployment Based on DRL in UAV-Empowered Edge Computing

Unmanned Aerial Vehicle (UAV)-empowered edge computing has been widely investigated in obstacle-free scenarios, where a moving UAV is in charge of handling offloaded singleton tasks from mobile devices on the ground. However, little attention has been paid to the scenario, in which the UAV serves a complex area with multiple obstacles and dependent tasks. A dependent task can be formulated as a Directed Acyclic Graph (DAG) that contains a number of sub-tasks; and each sub-task can be executed by a corresponding Service Function (SF) deployed on the UAV. In this backdrop, the joint UAV trajectory planning, DAG task scheduling, and SF deployment is formulated as an optimization problem in this paper. Afterwards, a Deep Reinforcement Learning (DRL)-based algorithm is presented to tackle the NP-hard problem. The state space, action space, and the reward function of the agent, i.e., the UAV, are defined respectively under the DRL framework. To evaluate the effectiveness of the proposal, a series of experiments is conducted with different parameter settings. Results show that the DRL-based algorithm performs much better than three heuristic algorithms in success rate of trajectory planning, the number of executed tasks, and the average task response latency.

Agricultural UAV trajectory planning by incorporating multi-mechanism improved grey wolf optimization algorithm

Unmanned aerial vehicle (UAV) trajectory planning plays an essential role in agricultural production and biological control. To solve the agricultural UAV trajectory planning problem, a multi-mechanism collaborative improved grey wolf optimization algorithm (NAS-GWO) is proposed. In NAS-GWO, the evolutionary boundary constraint processing mechanism is introduced to update the position of the grey wolf individuals that cross the boundary in time to retain the position information of the optimal individuals to the largest degree to enhance the search accuracy of the algorithm. Then, the Gaussian mutation strategy and spiral function are used as perturbation mechanisms to help the algorithm jump out of the local optimum in time to strengthen the exploitation capability of NAS-GWO. Meanwhile, the improved Sigmoid function is used as a nonlinear convergence factor for balancing the exploitation and exploration of the NAS-GWO. By comparing NAS-GWO with ten advanced metaheuristic algorithms on 20 CEC2017 benchmark functions, the experimental results show that the NAS-GWO algorithm has superior merit seeking and robustness. Moreover, the agricultural UAV trajectory planning problem is solved using NAS-GWO. The experimental results show that the NAS-GWO algorithm plans a more viable and stable trajectory path in four different scale missions, while the most important is that it requires less cost. Among them, the algorithm reduces 27.93%, 38.15%, 32.32%, 34.11%, 10.63%, and 13.48% on average in cost function values compared to Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), Aquila Optimizer (AO), Differential Evolution (DE), Dung Beetle Optimizer (DBO), and Grey Wolf Optimization algorithm (GWO), thus proving the effectiveness and significance of NAS-GWO in the agricultural UAV trajectory path planning problem.

Trajectory Planning of UAV-Enabled Data Uploading for Large-Scale Dynamic Networks: A Trend Prediction Based Learning Approach

The unmanned aerial vehicle (UAV) enabled communication technology is regarded as an efficient and effective solution to provide emergency data uploading for some special cases where existing cellular infrastructures cannot provide reliable services to large-scale ground users (GUs). In the face of large-scale dynamic networks where the number and location of GUs change all the time, to maximize the throughput of data upload tasks under the premise of meeting the requirements of fairness, QoS and energy consumption, we propose a UAV trajectory planning approach based on deep reinforcement learning in combination with the prediction of GUs' movement trend in future time slots. Simulation results validate that our proposed approach converges more quickly and achieves better performance in dynamic networks.

3D Smooth Trajectory Planning for UAVs under Navigation Relayed by Multiple Stations Using Bézier Curves

Navigation relayed by multiple stations (NRMS) is a promising technique that can significantly extend the operational range of unmanned aerial vehicles (UAVs) and hence facilitate the execution of long-range tasks. However, NRMS employs multiple external stations in sequence to guide a UAV to its destination, introducing additional variables and constraints for UAV trajectory planning. This paper investigates the trajectory planning problem for a UAV under NRMS from its initial location to a pre-determined destination while maintaining a connection with one of the stations for safety reasons. Instead of line segments used in prior studies, a piecewise Bézier curve is applied to represent a smooth trajectory in three-dimensional (3D) continuous space, which brings both benefits and complexity. This problem is a bi-level optimisation problem consisting of upper-level station routing and lower-level UAV trajectory planning. A station sequence must be obtained first to construct a flight corridor for UAV trajectory planning while the planned trajectory evaluates it. To tackle this challenging bi-level optimisation problem, a novel efficient decoupling framework is proposed. First, the upper-level sub-problem is solved by leveraging techniques from graph theory to obtain an approximate station sequence. Then, an alternative minimisation-based algorithm is presented to address the non-linear and non-convex UAV trajectory planning sub-problem by optimising the spatial and temporal parameters of the piecewise Bézier curve iteratively. Computational experiments demonstrate the efficiency of the proposed decoupling framework and the quality of the obtained approximate station sequence. Additionally, the alternative minimisation-based algorithm is shown to outperform other non-linear optimisation methods in finding a better trajectory for the UAV within the given computational time.

Deep Reinforcement Learning for Joint Trajectory Planning, Transmission Scheduling, and Access Control in UAV-Assisted Wireless Sensor Networks.

Unmanned aerial vehicles (UAVs) can be used to relay sensing information and computational workloads from ground users (GUs) to a remote base station (RBS) for further processing. In this paper, we employ multiple UAVs to assist with the collection of sensing information in a terrestrial wireless sensor network. All of the information collected by the UAVs can be forwarded to the RBS. We aim to improve the energy efficiency for sensing-data collection and transmission by optimizing UAV trajectory, scheduling, and access-control strategies. Considering a time-slotted frame structure, UAV flight, sensing, and information-forwarding sub-slots are confined to each time slot. This motivates the trade-off study between UAV access-control and trajectory planning. More sensing data in one time slot will take up more UAV buffer space and require a longer transmission time for information forwarding. We solve this problem by a multi-agent deep reinforcement learning approach that takes into consideration a dynamic network environment with uncertain information about the GU spatial distribution and traffic demands. We further devise a hierarchical learning framework with reduced action and state spaces to improve the learning efficiency by exploiting the distributed structure of the UAV-assisted wireless sensor network. Simulation results show that UAV trajectory planning with access control can significantly improve UAV energy efficiency. The hierarchical learning method is more stable in learning and can also achieve higher sensing performance.

RIS-Assisted UAV for Timely Data Collection in IoT Networks

Intelligent transportation systems are thriving thanks to a wide range of technological advances, namely 5G communications, the Internet of Things (IoT), artificial intelligence, and edge computing. Meanwhile, in environments where direct communication can be impaired by, for instance, blockages, such as in urban cities, unmanned aerial vehicles (UAVs) can be considered as an alternative for providing and enhancing connectivity. In this article, we consider a time-constrained data gathering problem from a network of sensing devices and with assistance from a UAV. A reconfigurable intelligent surface (RIS) is deployed to further help in improving the connectivity and energy efficiency of the UAV. This integrated problem brings challenges related to the configuration of the phase shift elements of the RIS, the scheduling of IoT devices' transmissions, as well as the trajectory of the UAV. First, the problem is formulated with the objective of maximizing the total number of served devices each during its activation period. Owing to its complexity, we leverage deep reinforcement learning in our solution; the UAV trajectory planning is modeled as a Markov decision process, and proximal policy optimization is invoked to solve it. Next, the RIS configuration is then handled via block coordinate descent. Finally, extensive simulations are conducted to demonstrate the efficiency of our solution approach that, in many cases, outperforms other methods by more than 50%. We also show that integrating an RIS with a UAV in IoT networks can improve the UAV energy efficiency.

UAV Trajectory Planning for AoI-Minimal Data Collection in UAV-Aided IoT Networks by Transformer

Maintaining freshness of data collection in Internet-of-Things (IoT) networks has attracted increasing attention. By taking into account age-of-information (AoI), we investigate the trajectory planning problem of an unmanned aerial vehicle (UAV) that is used to aid a cluster-based IoT network. An optimization problem is formulated to minimize the total AoI of the collected data by the UAV from the ground IoT network. Since the total AoI of the IoT network depends on the flight time of the UAV and the data collection time at hovering points, we jointly optimize the selection of hovering points and the visiting order to these points. We exploit the state-of-the-art transformer and the weighted A*, which is a path search algorithm, to design a machine learning algorithm to solve the formulated problem. The whole UAV-IoT system is fed into the encoder network of the proposed algorithm, and the algorithm’s decoder network outputs the visiting order to ground clusters. Then, the weighted A* is used to find the hovering point for each cluster in the ground IoT network. Simulation results show that the trained model by the proposed algorithm has a good generalization ability to generate solutions for IoT networks with different numbers of ground clusters, without the need to retrain the model. Furthermore, results show that our proposed algorithm can find better UAV trajectories with the minimum total AoI when compared to other algorithms.

UAV Trajectory Planning for Complex Open Storage Environments Based on an Improved RRT Algorithm

Multi-rotor UAVs (Unmanned Aerial Vehicles) have been increasingly used for hazardous inspection tasks in complex open-air warehouse storage environments due to their high maneuverability and aerial perspective. To facilitate rapid response to patrol missions and improve the efficiency of UAV trajectory planning. This paper established a rotary-wing UAV trajectory plan model considering UAV patrol efficiency, trajectory cost, and power consumption cost. Secondly, an improved SSA (salp swarm algorithm) is incorporated for the shortcomings of low algorithmic search efficiency and unsmooth paths when planning paths in the traditional RRT (Rapidly-exploring Random Trees). The predation mechanism of the salps group is incorporated into the random sampling of the RRT algorithm, which reduces the invalid sampling of random points and introduces the adaptive leader structure, and reverses the search strategy to improve the algorithm’s global search for superiority at the later stage of the search. Finally, the designed LASSA-RRT algorithm is subjected to simulation experiments and compared with RRT, RRT*, IRRT, and PF-RRT* in a cross-sectional manner. The results show that the LASSA-RRT algorithm has an average reduction of 55.83% in sampling times, 51.91% in run time, 13.17% in track length, and 0.1491% in flight cost. In summary, this paper’s UAV trajectory planning method can be effectively applied to complex open storage environments. It can provide a helpful reference direction for UAV trajectory planning.

Trajectory optimization of UAV based on Hp-adaptive Radau pseudospectral method

<p style='text-indent:20px;'>Unmanned Aerial Vehicles (UAVs) have been extensively studied to complete the missions in recent years. The UAV trajectory planning is an important area. Different from the commonly used methods based on path search, which are difficult to consider the UAV state and dynamics constraints, so that the planned trajectory cannot be tracked completely. The UAV trajectory planning problem is considered as an optimization problem for research, considering the dynamics constraints of the UAV and the terrain obstacle constraints during flight. An hp-adaptive Radau pseudospectral method based UAV trajectory planning scheme is proposed by taking the UAV dynamics into account. Numerical experiments are carried out to show the effectiveness and superior of the proposed method. Simulation results show that the proposed method outperform the well-known RRT* and A* algorithm in terms of tracking error.</p>

Trajectory planning for OTFS-based UAV communications

Unmanned aerial vehicles (UAVs) have attracted growing research interests in recent years, which can be used as cost-effective aerial platforms to transmit collected data packets to ground access points (APs). Thus, it is crucial to investigate robust air-tos-ground (A2G) wireless links for high-speed UAVs. However, the A2G wireless link is unstable as it suffers from large path-loss and severe Doppler effect due to the high mobility of UAVs. In order to meet these challenges, we propose an orthogonal time frequency space (OTFS)-based UAV communication system to relief the Doppler effect. Besides, considering that the energy of UAV is limited, we optimize the trajectory planning of UAV to minimize the energy consumption under the constraints of bit error rate (BER) and transmission rate, where the Doppler compensation is taken into account. Simulation results show that the performance of OTFS-based UAV system is superior to orthogonal frequency division multiplexing (OFDM)-based UAV systems, which can accomplish transmission tasks over shorter distances with lower energy consumption.

Optimized Views Photogrammetry: Precision Analysis and a Large-Scale Case Study in Qingdao

Unmanned aerial vehicle (UAVs) have become one of the widely used remote sensing platforms and played a critical role in the construction of smart cities. However, due to the complex environment in urban scenes, secure, and accurate data acquisition brings great challenges to 3-D modeling and scene updating. Optimal trajectory planning of UAVs and accurate data collection of onboard cameras are nontrivial issues in urban modeling. This study presents the principle of optimized views photogrammetry and verifies its precision and potential in large-scale 3-D modeling. Different from oblique photogrammetry, optimized views photogrammetry uses rough models to generate and optimize UAV trajectories, which is achieved through the consideration of model point reconstructability and view point redundancy. Based on the principle of optimized views photogrammetry, this study first conducts a precision analysis of 3-D models by using UAV images of optimized views photogrammetry and then executes a large-scale case study in the urban region of Qingdao City, China, to verify its engineering potential. By using GCPs for image orientation precision analysis and terrestrial laser scanning (TLS) point clouds for model quality analysis, experimental results show that optimized views photogrammetry could construct stable image connection networks and could achieve comparable image orientation accuracy. Benefiting from the accurate image acquisition strategy, the quality of mesh models significantly improves, especially for urban areas with serious occlusions, in which 3 to 5 times of higher accuracy has been achieved. Besides, the case study in Qingdao City verifies that optimized views photogrammetry can be a reliable and powerful solution for the large-scale 3-D modeling in complex urban scenes.

Hybrid deterministic non-deterministic data-parallel algorithm for real-time unmanned aerial vehicle trajectory planning in CUDA

The development of autonomous Unmanned Aerial Vehicles (UAVs) is a priority to many civilian and military organizations. Real time optimal trajectory planning is an essential element for the autonomy of UAVs. The use of metaheuristic algorithms for solving such complex optimization problems with non-linearity and multimodality has gained popularity recently. In this paper, we use a non-deterministic Flower Pollination Algorithm (FPA) to deal with the problem's complexity and compute feasible and quasi-optimal trajectories for fixed-wing UAVs in complex 3D environments, taking into account the vehicle's flight properties. The global optimization algorithm is improved with the addition of a deterministic 2-opt local search providing a significant improvement. To achieve real-time performance, the proposed trajectory planner in implemented and parallelized following the data-parallel paradigm on a Graphics Processing Unit (GPU) using the Compute Unified Device Architecture (CUDA) resulting in a 253.4x speedup compared to the sequential implementation on CPU. The parallel implementation is able to compute quasi-optimal trajectories in just 0.369 s.

Computation Bits Maximization in UAV-Assisted MEC Networks With Fairness Constraint

This article investigates an unmanned aerial vehicle (UAV)-assisted wireless-powered mobile-edge computing (MEC) system, where the UAV powers the mobile terminals by wireless power transfer (WPT) and provides computation service for them. We aim to maximize the computation bits of terminals while ensuring fairness among them. Considering the random trajectories of mobile terminals, we propose a soft actor–critic (SAC)-based UAV trajectory planning and resource allocation (SAC-TR) algorithm, which combines off-policy and maximum entropy reinforcement learning to improve the convergence of the algorithm. We design the reward as a heterogeneous function of computation bits, fairness, and destination. Simulation results show that SAC-TR can quickly adapt to varying network environments and outperform representative benchmarks in various situations.