Unmanned aerial vehicle (UAV) swarms utilizing collaborative beamforming (CB) in low-altitude wireless networks (LAWN) demonstrate significant potential for enhanced communication range, energy efficiency, and signal directivity through the formation of virtual antenna arrays (VAA). However, environmental disturbances, particularly wind fields, significantly degrade CB performance by introducing positional errors that disrupt beam patterns, thereby compromising transmission reliability. This paper investigates the critical challenge of maintaining CB performance in UAV-based VAAs operating in LAWN under wind field disturbances. We propose a comprehensive framework that models the impact of three distinct wind conditions (constant, shear, and turbulent) on UAV array performance, and formulate a long-term real-time optimization problem to maximize directivity while minimizing maximum sidelobe levels through adaptive excitation current weight adjustments. To address the inherent complexity of this problem, we propose a novel proximal policy optimization algorithm with long short-term memory (LSTM) structure and adaptive learning rate (PPO-LA), which effectively captures temporal patterns in wind field disturbances and enables real-time adaptation without requiring extensive prior training for specific wind conditions. Our simulation results demonstrate that the proposed PPO-LA algorithm successfully recovers degraded CB performance across various wind scenarios, and thus significantly outperforming benchmark algorithms.

The rapid development of the low-altitude economy (LAE) has significantly increased the utilization of autonomous aerial vehicles (AAVs) in various applications, necessitating efficient and secure communication methods among AAV swarms. In this work, we aim to introduce distributed collaborative beamforming (DCB) into AAV swarms and handle the eavesdropper collusion by controlling the corresponding signal distributions. Specifically, we consider a two-way DCB-enabled aerial communication between two AAV swarms and construct these swarms as two AAV virtual antenna arrays. Then, we minimize the two-way known secrecy capacity and maximum sidelobe level to avoid information leakage from the known and unknown eavesdroppers, respectively. Simultaneously, we also minimize the energy consumption of AAVs when constructing virtual antenna arrays. Due to the conflicting relationships between secure performance and energy efficiency, we consider these objectives by formulating a multi-objective optimization problem, which is NP-hard and with a large number of decision variables. Accordingly, we design a novel generative swarm intelligence (GenSI) framework to solve the problem with less overhead, which contains a conditional variational autoencoder (CVAE)-based generative method and a proposed powerful swarm intelligence algorithm. In this framework, CVAE can collect expert solutions obtained by the swarm intelligence algorithm in other environment states to explore characteristics and patterns, thereby directly generating high-quality initial solutions in new environment factors for the swarm intelligence algorithm to search solution space efficiently. Simulation results show that the proposed swarm intelligence algorithm outperforms other state-of-the-art baseline algorithms, and the GenSI can achieve similar optimization results by using far fewer iterations than the ordinary swarm intelligence algorithm. Experimental tests demonstrate that introducing the CVAE mechanism achieves a 58.7% reduction in execution time, which enables the deployment of GenSI even on AAV platforms with limited computing power.

The integration of simultaneous wireless information and power transfer (SWIPT) technology in 6G Internet of Things (IoT) networks faces significant challenges in remote areas and disaster scenarios where ground infrastructure is unavailable. This paper proposes a novel unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) system enhanced by directional antennas to provide both computational resources and energy support for ground IoT terminals. However, such systems require multiple trade-off policies to balance UAV energy consumption, terminal battery levels, and computational resource allocation under various constraints, including limited UAV battery capacity, non-linear energy harvesting characteristics, and dynamic task arrivals. To address these challenges comprehensively, we formulate a bi-objective optimization problem that simultaneously considers system energy efficiency and terminal battery sustainability. We then reformulate this non-convex problem with a hybrid solution space as a Markov decision process (MDP) and propose an improved soft actor-critic (SAC) algorithm with an action simplification mechanism to enhance its convergence and generalization capabilities. Simulation results have demonstrated that our proposed approach outperforms various baselines in different scenarios, achieving efficient energy management while maintaining high computational performance. Furthermore, our method shows strong generalization ability across different scenarios, particularly in complex environments, validating the effectiveness of our designed boundary penalty and charging reward mechanisms.

Unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) is emerging as a promising paradigm to provide aerial-terrestrial computing services in close proximity to mobile devices (MDs). However, meeting the demands of computation-intensive and delay-sensitive tasks for MDs poses several challenges, including the demand-supply contradiction between MDs and MEC servers, the demand-supply heterogeneity between MDs and MEC servers, the trajectory control requirements on energy efficiency and timeliness, and the different time-scale dynamics of the network. To address these issues, we first present a hierarchical architecture by incorporating terrestrial-aerial computing capabilities and leveraging UAV flexibility. Furthermore, we formulate a joint computing resource allocation, computation offloading, and trajectory control problem to maximize the system utility. Since the problem is a non-convex and NP-hard mixed integer nonlinear programming (MINLP), we propose a two-timescale joint computing resource allocation, computation offloading, and trajectory control (TJCCT) approach for solving the problem. In the short timescale, we propose a price-incentive model for on-demand computing resource allocation and a matching mechanism-based method for computation offloading. In the long timescale, we propose a convex optimization-based method for UAV trajectory control. Besides, we theoretically prove the stability, optimality, and polynomial complexity of TJCCT. Extended simulation results demonstrate that the proposed TJCCT outperforms the comparative algorithms in terms of the system utility, average processing rate, average completion delay, and average completion ratio.

The rise of the low-altitude economy (LAE) is propelling urban development and emerging industries by integrating advanced technologies to enhance efficiency, safety, and sustainability in low-altitude operations. The widespread adoption of unmanned aerial vehicles (UAVs) and electric vertical takeoff and landing (eVTOL) aircraft plays a crucial role in enabling key applications within LAE, such as urban logistics, emergency rescue, and aerial mobility. However, unlike traditional UAV networks, LAE networks encounter increased airspace management demands due to dense flying nodes and potential interference with ground communication systems. In addition, there are heightened and extended security risks in real-time operations, particularly the vulnerability of low-altitude aircraft to cyberattacks from ground-based threats. To address these, this paper first explores related standards and core architecture that support the development of LAE networks. Subsequently, we highlight the integration of technologies such as communication, sensing, computing, positioning, navigation, surveillance, flight control, and airspace management. This synergy of multi-technology drives the advancement of real-world LAE applications, particularly in improving operational efficiency, optimizing airspace usage, and ensuring safety. Finally, we outline future research directions for LAE networks, such as intelligent and adaptive optimization, security and privacy protection, sustainable energy and power management, quantum-driven coordination, generative governance, and three-dimensional (3D) airspace coverage, which collectively underscore the potential of collaborative technologies to advance LAE networks.

Beam tracking is crucial for maintaining stable data transmission in uncrewed aerial vehicle (UAV) communications. However, a communication link can be disrupted by frequent switching of narrow beams between a base station and a UAV at certain moments. In this study, we propose a position prediction-based beam tracking algorithm with adaptive beam reconstruction (PPBT-AR) for high-speed UAV. Specifically, long short-term memory (LSTM) recurrent neural networks are utilized to predict the nonlinear flight trajectory during high-speed flight. Moreover, we employ the generative diffusion model (GDM) to jointly optimize the beam width and signal strength, thereby reducing the number of beam switches. In addition, we design an adaptive beam reconstruction (ABR) mechanism to mitigate communication interruptions caused by prediction errors. Simulation results demonstrate that the proposed PPBT-AR reduces the number of beam switches by 66.6% and 76.9% in low-speed and high-speed scenarios compared to the traditional phased array beam tracking algorithm, respectively.

In this paper, we investigate an unmanned aerial vehicle (UAV)-assistant air-to-ground communication system, where multiple UAVs form a UAV-enabled virtual antenna array (UVAA) to communicate with remote base stations by utilizing collaborative beamforming. To improve the work efficiency of the UVAA, we formulate a UAV-enabled collaborative beamforming multi-objective optimization problem (UCBMOP) to simultaneously maximize the transmission rate of the UVAA and minimize the energy consumption of all UAVs by optimizing the positions and excitation current weights of all UAVs. This problem is challenging because these two optimization objectives conflict with each other, and they are non-concave to the optimization variables. Moreover, the system is dynamic, and the cooperation among UAVs is complex, making traditional methods take much time to compute the optimization solution for a single task. In addition, as the task changes, the previously obtained solution will become obsolete and invalid. To handle these issues, we leverage the multi-agent deep reinforcement learning (MADRL) to address the UCBMOP. Specifically, we use the heterogeneous-agent trust region policy optimization (HATRPO) as the basic framework, and then propose an improved HATRPO algorithm, namely HATRPO-UCB, where three techniques are introduced to enhance the performance. Simulation results demonstrate that the proposed algorithm can learn a better strategy compared with other methods. Moreover, extensive experiments also demonstrate the effectiveness of the proposed techniques.

In this paper， the standard krill algorithm （KH） has the disadvantages of slow convergence speed， insufficient calculation accuracy and easy to fall into local optimal solution for complex problems， an improved krill algorithm （SDEKH） which combines improved differential evolution operator and S-type adaptive inertia weight is proposed in this paper. Through a variety of standard test functions to compare and test a variety of intelligent algorithms such as SDEKH and KH， the excellent performance of SDEKH is verified， and SDEKH is used to optimize the truss structure， and the optimization results of SDEKH are compared with other methods to verify that the optimization efficiency and accuracy are improved， which provides a more efficient and accurate method for engineering structure optimization design.

Unmanned aerial vehicles (UAVs) as aerial relays are practically appealing for assisting Internet of Things (IoT) network. In this work, we aim to utilize the UAV swarm to assist the secure communication between the micro base station (MBS) equipped with the planar array antenna (PAA) and the IoT terminal devices by collaborative beamforming (CB), so as to counteract the effects of collusive eavesdropping attacks in time-domain. Specifically, we formulate a UAV swarm-enabled secure relay multi-objective optimization problem (US2RMOP) for simultaneously maximizing the achievable sum rate of associated IoT terminal devices, minimizing the achievable sum rate of the eavesdropper and minimizing the energy consumption of UAV swarm, by jointly optimizing the excitation current weights of both MBS and UAV swarm, the selection of the UAV receiver, the position of UAVs and user association order of IoT terminal devices. Furthermore, the formulated US2RMOP is proved to be a non-convex, NP-hard and large-scale optimization problem. Therefore, we propose an improved multi-objective grasshopper algorithm (IMOGOA) with some specific designs to address the problem. Simulation results exhibit the effectiveness of the proposed UAV swarm-enabled collaborative secure relay strategy and demonstrate the superiority of IMOGOA.

Unmanned aerial vehicles (UAVs) are playing an increasingly important role in assisting fast-response post-disaster rescue due to their fast deployment, flexible mobility, and low cost. However, UAVs face the challenges of limited battery capacity and computing resources, which could shorten the expected flight endurance of UAVs and increase the rescue response delay during performing mission-critical tasks. To address these challenges, we first present a three-layer post-disaster rescue computing architecture by leveraging the aerial-terrestrial edge capabilities of mobile edge computing (MEC) and vehicle fog computing (VFC), which consists of a vehicle fog layer, a UAV client layer, and a UAV edge layer. Moreover, we formulate a joint task offloading and resource allocation optimization problem (JTRAOP) with the aim of maximizing the time-average system utility. Since the formulated JTRAOP is proved to be NP-hard, we propose an MEC-VFC-aided task offloading and resource allocation (MVTORA) approach, which consists of a game theoretic algorithm for task offloading decision, a convex optimization-based algorithm for MEC resource allocation, and an evolutionary computation-based hybrid algorithm for VFC resource allocation. Simulation results validate that the proposed approach can achieve superior system performance compared to alternative approaches, especially under heavy system workloads.

Communications and networks of unmanned aerial vehicles (UAVs) are of paramount importance, owing to their flexible mobility and fast deployment. However, how to enhance the communication efficiency under the restricted on-board energy and transmit power is still one of the most critical problems. In this paper, we consider a UAV-assisted communication scenario, in which a virtual antenna array (VAA) performed by a swarm of UAVs utilize collaborative beamforming (CB) to communicate with several faraway base stations (BSs). For achieving a superior transmission performance, we formulate a hovering and motion energy consumption multi-objective optimization problem (HMECMOP) of UAV-assisted CB to simultaneously minimize the total hovering and motion energy consumptions of UAVs by jointly optimizing the positions, excitation current weights of UAVs and the order of communicating with different BSs. Moreover, the formulated HMECMOP is analyzed and proven as an NP-hard and classical hybrid multi-objective optimization problem with a complex solution vector that contains continuous and discrete variables. Thus, we propose an improved multi-objective multi-verse optimizer (IMOMVO), which uses the vertical and horizontal renewal strategy and nearest neighbor procedure to solve the complex HMECMOP. Extensive simulations are carried out to demonstrate that the proposed algorithm can effectively reduce the energy consumption of UAVs communicating with multiple remote BSs so that improving the communication performance.

Unmanned aerial vehicles (UAVs)-enabled aerial communication provides a flexible, reliable, and cost-effective solution for a range of wireless applications. However, due to the high line-of-sight (LoS) probability, aerial communications between UAVs are vulnerable to eavesdropping attacks, particularly when multiple eavesdroppers collude. In this work, we aim to introduce distributed collaborative beamforming (DCB) into UAV swarms and handle the eavesdropper collusion by controlling the corresponding signal distributions. Specifically, we consider a two-way DCB-enabled aerial communication between two UAV swarms and construct these swarms as two UAV virtual antenna arrays. Then, we minimize the two-way known secrecy capacity and the maximum sidelobe level to avoid information leakage from the known and unknown eavesdroppers, respectively. Simultaneously, we also minimize the energy consumption of UAVs for constructing virtual antenna arrays. Due to the conflicting relationships between secure performance and energy efficiency, we consider these objectives as a multi-objective optimization problem. Following this, we propose an enhanced multi-objective swarm intelligence algorithm via the characterized properties of the problem. Simulation results show that our proposed algorithm can obtain a set of informative solutions and outperform other state-of-the-art baseline algorithms. Experimental tests demonstrate that our method can be deployed in limited computing power platforms of UAVs and is beneficial for saving computational resources.

Unmanned aerial vehicles (UAVs) have been demonstrated to be a prominent component for wireless communications. In this work, we consider an emergency communication scenario wherein a UAV-based relay system collects data from ground users, and then uses different UAV-enabled virtual antenna arrays (UVAAs) to transmit the collected data to several remote base stations (BSs) via collaborative beamforming (CB). However, several adjacent aerial users (AUs) are carrying out other missions at the same time, which may be interfered by the signal transmitted by the UVAAs. Thus, we formulate a reliable and energy-efficient communication multi-objective optimization problem (RECMOP) to jointly maximize the minimum receiving signal-to-noise ratio (SNR) of the BSs, minimize the maximum average receiving SNR of the AUs, and minimize the propulsion power consumption of the UAVs, so that diminishing the energy cost while enhancing the system performance. The formulated RECMOP is intricate since it is proven to be NP-hard and non-convex. Therefore, an improved multi-objective gravitational search algorithm (IMOGSA) with several specific designs is proposed to handle the formulated problem. Simulation results manifest that the proposed IMOGSA can effectively solve the formulated RECMOP, and it outperforms other benchmarks in both smaller and larger scale UAV networks. Moreover, extended simulation demonstrates the robustness of the proposed CB-based approach under several unexpected circumstances.

Unmanned aerial vehicles (UAV)-assisted mobile edge computing (MEC) is emerging as a promising paradigm to provide aerial-terrestrial computing services close to mobile devices (MDs). However, meeting the demands of computation-intensive and delay-sensitive tasks for MDs poses several challenges, including the demand-supply contradiction between MDs and MEC servers, the demand-supply heterogeneity between MDs and MEC servers, the trajectory control requirements on energy efficiency and timeliness, and the different time-scale dynamics of the network. To address these issues, we first present a hierarchical architecture by incorporating terrestrial-aerial computing capabilities and leveraging UAV flexibility. Furthermore, we formulate a joint computing resource allocation, computation offloading, and trajectory control problem to maximize the system utility. Since the problem is a non-convex mixed integer nonlinear programming (MINLP), we propose a two time-scale joint computing resource allocation, computation offloading, and trajectory control (TJCCT) approach. In the short time scale, we propose a price-incentive method for on-demand computing resource allocation and a matching mechanism-based method for computation offloading. In the long time scale, we propose a convex optimization-based method for UAV trajectory control. Besides, we prove the stability, optimality, and polynomial complexity of TJCCT. Simulation results demonstrate that TJCCT outperforms the comparative algorithms in terms of the utility of the system, the QoE of MDs, and the revenue of MEC servers.

Emerging 6G technologies, such as terahertz communication and ultra-massive multiple-input multiple-output, offer exciting prospects but face challenges like limited range and multipath interference. In this paper, we seek to use an unmanned aerial vehicle (UAV)-carried intelligent reflecting surface (IRS) to assist the terrestrial mmWave networks. Specifically, we consider a typical urban scenario where a UAV-carried IRS rebuilds the line of sight (LoS) channel between a mobile user and a base station under the existence of obstacles. Then, we formulate an optimization problem to maximize the transmission rates and minimize the UAV energy consumption, by jointly optimizing the UAV trajectory and the phase shifts of IRS. The problem is non-convex and with high dynamic, and thus we propose a deep reinforcement learning (DRL)-based algorithm with neural episodic control, long short-term memory (LSTM), and a phase control method to solve the problem, thereby enhancing the stability and accelerate convergence speed. Simulation results demonstrate that the proposed algorithm effectively addresses the problem and outperforms other benchmark algorithms.

With the development of science and technology, high-dimensional global optimization problems have become increasingly prevalent for scientific research and engineering, such as gene recognition, vehicle routing, job scheduling, and network topology. These problems are typically characterized by enormous and complex search spaces and numerous local minima, making it challenging to find the global optimal solution with limited computing resources. This paper introduces an enhanced sparrow search swarm optimizer (ESSSO) based on a bio-mimetic method. The ESSSO employs an adaptive sinusoidal walk strategy based on the von Mises distribution, a learning strategy utilizing roulette wheel selection, a two-stage evolution strategy, and a selection mutation strategy to address these issues. The proposed sinusoidal walk strategy, grounded in the von Mises distribution, supports a balanced evolutionary search. This mechanism disperses the individuals in a swarm in various directions based on a circular normal distribution. It then leads the search and adaptively adjusts their step sizes according to the size of the search domain during each generation of evolution. The learning strategy, based on roulette wheel selection, enhances the diversity of the population and improves the global search capability of the algorithm during the initial iterations. The two-stage evolution strategy involves a sine-learning mechanism based on the von Mises distribution and an adaptive mutation mechanism. The former is designed to boost the convergence speed of ESSSO, while the latter prevents ESSSO from getting trapped in a local optimum. Additionally, the selection mutation strategy further enhances convergence speed while maintaining population diversity. These strategies promote exploration in the early stages of evolution and exploitation in the later stages, enabling a well-balanced search for optimal solutions. We conducted comprehensive experiments two standard benchmark sets (i.e., CEC2010 and CEC2013), antenna array optimization, feature selection, and four engineering design problems. The results indicate that ESSSO outperforms ten comparison algorithms, especially in scenarios with smaller population sizes. This confirms its effectiveness in high-dimensional global optimization tasks and demonstrates that it can achieve better results with less computational resource consumption.

Given flexible mobility, rapid deployment, and low cost, unmanned aerial vehicle (UAV)-enabled mobile edge computing (MEC) shows great potential to compensate for the lack of terrestrial edge computing coverage. However, limited battery capacity, computing and spectrum resources also pose serious challenges for UAV-enabled MEC, which shorten the service time of UAVs and degrade the quality of experience (QoE) of user devices (UDs) without effective control approach. In this work, we consider a UAV-enabled MEC scenario where a UAV serves as an aerial edge server to provide computing services for multiple ground UDs. Then, a joint task offloading, resource allocation, and UAV trajectory planning optimization problem (JTRTOP) is formulated to maximize the QoE of UDs under the UAV energy consumption constraint. To solve the JTRTOP that is proved to be a future-dependent and NP-hard problem, an online joint optimization approach (OJOA) is proposed. Specifically, the JTRTOP is first transformed into a per-slot real-time optimization problem (PROP) by using the Lyapunov optimization framework. Then, a two-stage optimization method based on game theory and convex optimization is proposed to solve the PROP. Simulation results validate that the proposed approach can achieve superior system performance compared to the other benchmark schemes.

Feature selection plays an essential role in data preprocessing, which can extract valuable information from extensive data, thereby enhancing the performance of machine learning classification. However, existing feature selection methods primarily focus on selecting feature subsets without considering the impact of classifier parameters on the optimal subset. Different from these works, this paper considers jointly optimizing the feature subset and classifier parameters to minimize the number of features and achieve a low classification error rate. Since feature selection is an optimization problem with binary solution space while classifier parameters involve both continuous and discrete variables, our formulated problem becomes a complex multi-objective mixed-variable problem. To address this challenge, we consider a single-objective optimization method and a multi-objective optimization approach. Specifically, in the single-objective optimization method, we adopt the linear weight method to convert our multiple objectives into a fitness function and then propose a mixed-variable grey wolf optimizer (MGWO) to optimize the function. The proposed MGWO introduces Chaos-Faure initialization, Log convergence factor adjustment, and optimal solution adaptive update operators to enhance its adaptability and balance the global and local search of the algorithm. Subsequently, an improved multi-objective grey wolf optimizer (IMOGWO) is introduced to directly address the problem. The proposed IMOGWO introduces improved initialization, local search, and binary variable mutation operators to balance its exploration and exploitation abilities, making it more suitable for our mixed-variable problem. Extensive simulation results show that our MGWO and IMOGWO outperform recent and classic baselines. Moreover, we also find that jointly optimizing classifier parameters can significantly improve classification accuracy.

The advantages of autonomy, stability, and high load capability make automated guided vehicles (AGVs) appealing for applications like intelligent transportation networks. Nevertheless, AGVs may face limitations in terms of flexibility and transmission efficiency. In this paper, we consider the scenario where unmanned aerial vehicles (UAVs) serve dual roles in enhancing the communications of AGVs. Specifically, one group of UAVs is employed to support AGVs in data transmission, while another group of UAVs equipped with computational resources, functions as aerial base stations (ABSs) for receiving and processing the collected data. Following this, we explore the collaborative deployment between AGVs and UAVs, and propose a highly efficient, low-interference, and energy-efficient uplink data transmission framework based on distributed collaborative beamforming. Correspondingly, we formulate a high-performance and low-interference transmission multi-objective optimization problem (HLTMOP) to reduce the transmission time and operation energy consumption of the AGVs and UAVs, while minimizing the total sidelobe levels toward the directions of all non-current receiving ABSs. Due to the NP-hardness of the HLTMOP, we propose a swarm intelligence algorithm, namely, improved multi-objective ant lion optimization (IMOALO), with three improved operators. Simulation results show that the proposed IMOALO algorithm performs better and can generate more excellent solutions than other benchmark algorithms.

Sparse synthesis can reduce the maximum sidelobe level (SLL) and overhead of the concentric circular antenna array (CCAA) by switching off partial array elements. However, previous works have not considered finding a balance between the number of switched-on elements of CCAA and reducing the maximum SLL, or jointly optimizing the excitation current weights of array elements to further suppress the maximum SLL. In this work, we address these challenges by formulating a hybrid multi-objective optimization problem (MOP) with discrete and continuous solutions. To solve this hybrid NP-hard problem, we consider two approaches: the two-step and one-step methods. In the two-step method, we convert the original MOP into two subproblems and propose an enhanced non-dominated sorting genetic algorithm-II (ENSGA-II) and an improved genetic algorithm with new mutation and attraction (IGAnMA) to solve these two subproblems. ENSGA-II and IGAnMA involve the hierarchy mechanism and attraction operator to enhance the solving abilities, respectively. In the one-step method, we propose an improved hybrid non-dominated sorting genetic algorithm-II (IHNSGA-II) with global search and hybrid solution update methods to solve the MOP in one step. Numerical simulation results show that the proposed methods are effective and stable for the sparse synthesis of CCAA. Additionally, electromagnetic simulation results demonstrate the validity of the proposed approaches in a more practical environment.