Nature-Inspired Algorithms from Oceans to Space: A Comprehensive Review of Heuristic and Meta-Heuristic Optimization Algorithms and Their Potential Applications in Drones

Round 1

Reviewer 1 Report

This paper performs a comprehensive survey of nature inspired algorithms and their potential applications in drones. A comparison of 27 popular algorithms using benchmark functions was conducted.  This paper will be a valuable asset for researchers who plan to use nature inspired algorithms for drone applications.

One suggestion to improve the paper is that the authors should include a discussion section to point out research challenges and future research directions in this area.

 

 

Author Response

Reviewer #1

The authors thank the reviewers and editor for their comments and feedback on the paper. We have addressed each of the comments individually in this document and written our responses in red. In addition, we have incorporated the comments and made changes to the paper.

Minor Recommendations:

• 1: ” One suggestion to improve the paper is that the authors should include a discussion section to point out research challenges and future research directions in this area.”

Response: Thank you for your suggestions. We have provided a discussion on the future research directions in the paper. The following paragraphs were added to the paper: “This study revealed the massive amount of research on nature-inspired algorithms which are mimicking different aspects of nature. From oceans to space, there can be found an algorithm focusing on a specific phenomenon or creature. Neglecting the open question of the novelty of these algorithms and their similarities to most famous algorithms, the high number of publications in this area is considerable. Most of the publications in this field do not provide any or enough information on the performance of the algorithms, their exact differences, and their contributions. The majority of papers just provide a simple comparison with just one or a few well-known algorithms like GA (which is shown to have one of the lowest performances among nature-inspired algorithms) by only solving a single problem. This cannot of course provide us with a good understanding of the real values of the algorithms. Performance analysis of nature-inspired algorithms is what is felt necessary right now. The main focus of research in this field should be put on the applications of these algorithms and their performance evaluation and improvements. It seems that there are more than enough algorithms available with different perspectives. Studying the current literature reveals that there is a focus on developing hybrid algorithms to increase the performance of the algorithms which can broaden their field of applications. The performance of hybrid algorithms is reported to be significantly better than the basic algorithms which makes it reasonable to expect more research on this topic in the future.

Current research illustrated the latest developments in the field of nature-inspired optimization, the popularity of these algorithms, and some related challenges like constraint handling and their performance in solving different problems. A compact review of the applications of nature-inspired algorithms in aerospace systems has been provided. Based on this review, the most used algorithms in aerospace systems are GA, PSO, and ABC. The field where nature-inspired algorithms have been used widely in is control systems. Based on evaluations in this paper, it is recommended to apply high-performance algorithms like the Sine-Cosine Algorithm, Harris Hawk Optimization, Firefly Algorithm, Fireworks Algorithm, Grey Wolf Optimization, and Cat Swarm Optimization in a wider range of applications from conceptual design, MDO, aerodynamics, and shape design to navigation and identification. Considering the progress of hybrid algorithms, and their considerably improved performance, their application in aerospace systems is recommended. All results of the paper, including data, and codes in Python and MATLAB, are also published in public GitHub repositories.”

Author Response File: Author Response.pdf

Reviewer 2 Report

Please refer to the attached pdf file.

Comments for author File: Comments.pdf

In general, I think the quality of adopted English is good.

Author Response

Reviewer #2

The authors thank the reviewers and editor for their comments and feedback on the paper. We have addressed each of the comments individually in this document and written our responses in red. In addition, we have incorporated the comments and made changes to the paper.

Major Recommendations:

• Comment 1: ” As sketched in my recommendation, I think the discussion about general nature-inspired algorithm is too long and detailed and is not suitable for a journal like Drones. I recommend to the Authors to shorten the description of each algorithm, trying to primarily focus on the nature metaphor that has inspired the algorithm and to essentially describe the major phases of the algorithm, addressing the reader to a major reference for further algorithmic details (I think that including pseudocodes is not necessary, unless this is done for every single algorithm).

Let me remark that, when suggesting to shorten the general discussion, I am also taking into account the existence of high quality surveys about nature-inspired algorithms that should be taken into account and added to the bibliography, namely:

(a) Molina, D., Poyatos, J., Ser, J.D. et al. Comprehensive Taxonomies of Nature- and Bio-inspired Optimization: Inspiration Versus Algorithmic Behavior, Critical Analysis Recommendations. Cogn Comput 12, 897-939 (2020). DOI: 10.1007/s12559-02009730-8

(b) Sörensen, K. (2015), Metaheuristics - the metaphor exposed. Intl. Trans. in Op.Res., 22: 3-18. https://doi.org/10.1111/itor.12001”

Response:

• The authors thank the reviewer for his/her comments and feedback on the paper. We have tried to shorten the first section of the paper by removing extra formulations and referencing the reader to the main publications. We also tried to replace the pseudo-codes with flowcharts (where it is needed) to keep a similar style and make understanding the processes easier. We have also added the suggested survey papers to the introduction. But we insist on keeping the algorithm section comprehensive enough to make the paper useful not only for researchers with aerospace backgrounds but also for those who are working on optimization algorithms and mathematical fields. Keeping this section also broadens the view of readers with aerospace background with the principles and basics of the optimization algorithms which usually is ignored. One of this paper’s goals is to provide readers with potential algorithms which are not being paid enough attention to solve drones’ problems and to bring new ideas. This can only be done by providing a comprehensive review.
• We have highlighted the sections which are now shorter in red color.
• Two proposed references were added to the paper.
• We have added the following paragraphs to the introduction: “Some similar research can be found in the literature on the latest progress of nature-inspired optimization algorithms. Molina et al. have proposed comprehensive taxonomies of nature-inspired optimization algorithms. They have focused on the source of inspiration in these algorithms and have shown the similarity of a big group of algorithms with classic approaches regarding their core computation process. However, their research lacks a performance analysis for these algorithms [4]. Discussions on the novelty and importance of nature-inspired optimization algorithms are still going on, some researchers consider no value for these algorithms while others believe the production of new methods should be stopped and the majority of efforts should be dedicated to more promising research directions in the metaheuristic’s literature. While they confirm the power of nature-inspired optimization, they believe only a few algorithms can really be used for solving problems with high accuracy in a short time[5]. Evaluating the performance of these algorithms in solving different problems seems to be necessary research that is not studied too much. The next section will review similar review papers on nature-inspired optimization and their efforts to manage and classify these algorithms for better understanding and study.

In this paper, we try to study the latest developments in nature-inspired optimization and challenges in this field. First of all, we classified all of these algorithms based on their source of inspiration and provided a comprehensive classification. Considering other classifications in similar papers, we have tried to provide a more comprehensive classification with detailed sub-categories. In each category, the most popular algorithms are studied in detail to provide a good view of their challenges and benefits. Next, in section 3, the performance of a group of selected algorithms is evaluated in solving ten different problems. Critical parameters like mean iterations, average computation time, and mean error are calculated by solving each problem 500 times. A database of sample codes for nature-inspired algorithms is also provided. In addition to this, all of the project’s codes are provided in the GitHub repositories. Most algorithms in this paper have been extracted from a recent work by Tzanetos et al. in addition to classical algorithms and newly developed ones [6]. In the last section, we have studied the different applications of nature-inspired algorithms in drones and aerospace systems. After providing a classification of different applications, we have studied the papers published in this area to find out which algorithms are being used most. This study reveals 1) the areas in drones in which nature-inspired algorithms are more applicable, 2) the algorithms which are widely being used 3) the algorithms with high potential that are neglected in the literature. Finally, we have provided a brief view on the future of nature-inspired algorithms specifically in drones and aerospace systems.”

• Comment 2: ”When covering general metaheuristics, it would be important to enlarge the section about hybrid approaches, in particular those that have attempted to combine exact mathematical optimization approaches (i.e., guaranteeing convergence to an optimal solution with heuristics). Such hybrid approaches have indeed proved their advantage over "pure" algorithms in a wide range of general problems and applications and have attracted a lot of attention in recent years. To this end, the Authors could consider also the following works and the references therein:

(a) Blum, C., Puchinger, J., Raidl, G. R., & Roli, A. (2011). Hybrid metaheuristics in combinatorial optimization: A survey. Applied Soft Computing. DOI: 10.1016/j.asoc.2011.02.032

(b) Dalila B.M.M. Fontes, S. Mahdi Homayouni, Jose F. Goncalves, A hybrid particle swarm optimization and simulated annealing algorithm for the job shop scheduling problem with transport resources, European Journal of Operational Research, 2023, DOI: 10.1016/j.ejor.2022.09.006.

(c) F. D’Andreagiovanni, J. Krolikowski, J. Pulaj, A fast hybrid primal heuristic for multiband robust capacitated network design with multiple time periods, Applied Soft Computing, 2015, DOI: 10.1016/j.asoc.2014.10.016.

(d) S. Hanafi, Y. Wang, F. Glover, W. Yang, R. Hennig, Tabu search exploiting local optimality in binary optimization, European Journal of Operational Research, 2023, DOI: 10.1016/j.ejor.2023.01.001.

(e) Kottath, R., Singh, P. & Bhowmick, A. Swarm-based hybrid optimization algorithms: an exhaustive analysis and its applications to electricity load and price forecasting. Soft Comput (2023). https://doi.org/10.1007/s00500-023-07928-0

(f) S. Perez-Pelo, J. Sanchez-Oro, A. Gonzalez-Pardo, A. Duarte, A fast variable neighborhood search approach for multi-objective community detection, Applied Soft Computing, 2021, DOI: 10.1016/j.asoc.2021.107838.”

 

• The authors thank the reviewer for his/her comments. We agree with the reviewer, the performance of hybrid algorithms is considerable compared to pure algorithms, we just wanted to keep the first section short enough. But as the mentioned algorithms are notable ones, we have expanded the hybrid section to include those hybrid algorithms. The changes are highlighted in red font in the section.
• We have cited the proposed references.
• The following sections and paragraphs were added to the paper.

“Hybrid algorithms are combinations of algorithms. Research on hybrid metaheuristics is considered to still be in its early stages, but it is expected that hybrid algorithms take the majority of publications on metaheuristic optimization in the near future. Hybridization of algorithms can be the key to achieving higher performance but requires a careful analysis and deep understanding of each algorithm’s process and pros and cons. Nature-inspired algorithms can be hybridized by themselves, tree search techniques, constraint programming, dynamic programming, and problem relaxation [397].”

“Applying an exact large neighborhood search along with ACO provided D’Andreagiovanni et al. with a high performance and accuracy in solving an NP-Hard problem considerably better than software solutions like CPLEX[400].”

“Fontes et al. have also combined PSO and SA for solving the optimal scheduling problem in shop environments that have transport tasks and vehicles. Using this technique they were able to reduce computation time and increase the robustness compared to other algorithms [401].”

“Kottah et al. have also evaluated the hybridization of different algorithms like CSA, GWO, HHO, and WOA by solving multiple benchmark functions. Based on their research, a combination of these algorithms provides better solutions compared to the base algorithms. Among all hybrid forms they studied CSA-GWO and HHO-WOA have provided superior results for a majority of the benchmark functions[407].”

 

• Comment 3: ” In my opinion, Section 4 is what really adds value to this work: focusing on heuristics and metaheuristics for specifically tackling problems arising in drones and aerospace engineering. This section should be enlarged, providing a larger overview, survey and analysis of the works that have been alreadly included. In particular, it would be interesting to better discuss the merits and limits of works that have been considered in the bibliography. Furthermore, I think that the review of literature available on heuristics and metaheuristics for UAVs should be strengthened and, to this end, the Authors could consider additional major references such as the following and the references therein:

(a) Bithas, P.S.; Michailidis, E.T.; Nomikos, N.; Vouyioukas, D.; Kanatas, A.G. A Survey on Machine-Learning Techniques for UAV-Based Communications. Sensors 2019, 19, 5170. https://doi.org/10.3390/s19235170

(b) T. R. Beegum, M. Y. I. Idris, M. N. B. Ayub and H. A. Shehadeh, "Optimized Routing of UAVs Using Bio-Inspired Algorithm in FANET: A Systematic Review," in IEEE Access, vol. 11, pp. 15588-15622, 2023, doi: 10.1109/ACCESS.2023.3244067.2

(c) L. Chiaraviglio et al., "Multi-Area Throughput and Energy Optimization of UAVAided Cellular Networks Powered by Solar Panels and Grid," in IEEE Transactions on Mobile Computing, vol. 20, no. 7, pp. 2427-2444, 1 July 2021, doi:10.1109/TMC.2020.2980834.

(d) Chu, H.; Yi, J.; Yang, F. Chaos Particle Swarm Optimization Enhancement Algorithm for UAV Safe Path Planning. Appl. Sci. 2022, 12, 8977. https://doi.org/10.3390/app12188977

(e) Torky, M.; El-Dosuky, M.; Goda, E.; Snášel, V.; Hassanien, A.E. Scheduling and Securing Drone Charging System Using Particle Swarm Optimization and Blockchain Technology. Drones 2022, 6, 237. https://doi.org/10.3390/drones6090237

(f) M. Erdelj, E. Natalizio, K. R. Chowdhury and I. F. Akyildiz, "Help from the Sky:Leveraging UAVs for Disaster Management," in IEEE Pervasive Computing, vol. 16, no. 1, pp. 24-32, Jan.-Mar. 2017, doi: 10.1109/MPRV.2017.11.

(g) M. Mozaffari, W. Saad, M. Bennis and M. Debbah, "Efficient Deployment of Multiple Unmanned Aerial Vehicles for Optimal Wireless Coverage," in IEEE Communications Letters, vol. 20, no. 8, pp. 1647-1650, Aug. 2016, doi: 10.1109/LCOMM.2016.2578312.

(h) A. Trotta et al., "When UAVs Ride A Bus: Towards Energy-efficient City-scale Video Surveillance," IEEE INFOCOM 2018 - IEEE Conference on Computer Communications, Honolulu, HI, USA, 2018, pp. 1043-1051, doi: 10.1109/INFOCOM.2018.8485863.”

 

• The authors thank the reviewer for his/her comments. We have tried our best to expand section 4 by reviewing the related works in aerospace engineering and specifically drones including the references that the reviewer has mentioned. Section 4 is now much more comprehensive compared to the previous version. We have highlighted all the changes in red fonts.
• The following paragraphs were added to the paper:

Section: 4.1.1

“The conceptual design of drones is a challenging problem due to the interdependent nature of their sub-systems. Nature-inspired algorithms are suitable candidates for solving such problems due to their ability to handle complex and nonlinear problems without requiring prior knowledge of the system. Recent research has employed GA and other meta-heuristic algorithms for the conceptual design of aerial vehicles, including helicopters and fixed-wing UAVs. In the design of unconventional drone configurations, such as tilt-rotor, tilt-wing, and helicopter, optimization algorithms serve as a key tool to balance performance requirements and ensure safety and stability. Optimization provides optimal solutions that satisfy multiple design objectives and constraints and can be used to solve the optimal conceptual design of aircraft in general. This section provides an overview of the optimization approaches used in drone conceptual design, with a focus on the application of nature-inspired algorithms and their performance in solving these complex problems[426].”

 

Section 4.2: “Gue and Rosen have used GA along with a detailed mathematical model of the electric system and propeller to design an electric mini UAV [441]. However it is believed in propulsion system optimization, despite its benefits like solving highly nonlinear and non-convex design problems, easy implementation, parallelization capability, and global optimal finding, GA can be less effective when using high fidelity models due to the high number of evaluations [442]. A summarization of the studied publications in optimal design and their algorithm(s) can be provided in Table 5.”

 

Table 5 Different applications of NIAs in design optimization.

Reference	Publication year	Application	Algorithm
[427]	1996	Conceptual design	GA
[428]	2022	Conceptual design	MFA, MPA, SMA, SSA
[433]	2002	Conceptual design	PSO
[437]	2004	Multidisciplinary design optimization	GA
[438]	2009	Multidisciplinary design optimization	PSO
[439]	2016	Multidisciplinary design optimization	ABC
[440]	2019	Engine modeling and design	GA, PSO, ACO, ABC, IWO
[441]	2009	Electric motor optimization	GA
[442]	2021	Propulsion system optimization	GA

 

Section 4.3: “[444]. This section provides an overview of the optimization tools used in aircraft design, with a focus on their applications in optimizing structural features and computational analysis.”

 

Section 4.3.1: “The use of optimization methods in aircraft design is crucial for ensuring safety in crash accidents or reducing weight. The optimization goal can be the geometry of the aircraft or specific structural features such as the rib in wings to optimize stress and manufacturability. Nature-inspired algorithms, including GA, have been widely used to optimize these features. Additionally, bio-inspired algorithms can optimize process parameters of welding in aircraft wing structures, aeroelasticity characteristics, and elastic deformation in classic aluminum-based structures or composite materials. Nature-inspired algorithms can also be applied to computational structural analysis, such as optimizing the fiber orientation of a composite wing to maximize flutter speed.

Drones often use lightweight structures made of Carbon Fiber Reinforced Plastics (CFRP), particularly continuous Unidirectional (UD) carbon fibers due to their superior mechanical properties. The layered nature of UD plies offers design flexibility, allowing the mechanical properties of the resulting laminate to be tailored to best suit the applied loading and stiffness requirements. The challenge in optimizing the stacking sequence of large aerospace structures lies in the mixed discrete and continuous nature of the problem. Structural constraints such as strength and maximum displacements are formulated using continuous quantities, while design and manufacturing rules concern discrete plies. Nature-inspired algorithms have numerous iterations which makes the calculations too expensive. This is while gradient-based algorithms have better performance in physical constraints handling. A hybrid approach is suggested to be the best solution. Heuristic algorithms can handle discrete variables, while gradient-based algorithms are responsible for physical constraints. To bridge the gap between these stages, multiple iterations of the two-stage process are needed, resulting in a significant penalization in terms of performance metrics of the aircraft [434].”

“A summarization of the studied publication in structure optimization and their algorithm(s) is provided in Table 6.

 

Table 6 Different applications of NIAs in structure optimization.

Reference	Publication year	Application	Algorithm
[445]	2005	Component (rib, wing, etc.) design	GA
[446]	2009	Pressure bulkhead design	GA, PSO, CO
[447]	2021	Welding process optimization	GA
[448]	2015	Elastic optimization	PSO
[449]	2018	Stiffened panels optimization	HS
[450]	2014	Aeroelastic composite wing design	BCO
[451]	2014	Aeroelastic tailoring and scaling	BFO

 

Section 4.4.1: “Airfoil shape design optimization is one of the important optimization problems in aerodynamic optimization. Airfoil geometry optimization can reduce drag, increase lift, and optimize weight, while considering different parameters such as the angle of attack for maximum lift. Additionally, wing shape optimization, considering structural loads, deformations, and aerodynamics, is also an essential application in this field. Computational optimization tools have been developed to address these design challenges and improve the performance of airfoil and wing designs.”

 

Section 4.4.2: “Nature-inspired algorithms have shown promise in solving complex multidisciplinary design challenges. Researchers have used algorithms like PSO, ACO, BFO, DE, and ABC in hybrid forms or in combination of machine learning to improve aerodynamic performance, and optimize wing size, topology, aeroelastic design, and morphing wing tip design.”

 

Section 4.4.3: “Table 7 summarizes the studied publications in aerodynamic optimization and the algorithms the have used. The most popular algorithms and applications in this section are GA and airfoil shape design.

 

Table 7 Different applications of NIAs in aerodynamic optimization.

Reference	Publication year	Application	Algorithm
[455]	2018	Airfoil design	GA, SA
[456]	2001	Wing and blade airfoil design	ES
[457]	2019	Airfoil design	FFO
[458]	2021	Airfoil design	PSO, GA
[459]	2016	Airfoil design	CS
[460]	2015	Blade design	ABC
[461]	2017	Airfoil design	GSA
[462]	2022	Airfoil design	HS
[463]	2013	Aerodynamic shape optimization	HS
[382]	2016	Aerodynamic shape optimization	SCA
[466]	1999	Wing design	GA
[467]	2004	Wing design	PSO
[468]	2011	Wing design	ACO
[469]	2019	Wing design	DE
[470]	2019	Wing design	FSO
[471]	2017	Wing tip design	ABC
[474]	2016	Equipment placement in body	GA
[475]	2017	Equipment placement in body	BA
[476]	2017	Body shape design	GA
[478]	2017	Body shape design	PSO
[479]	2012	Body sizing	DE

 

Section 4.5.1: “In hypersonic airframes exhibiting elevated ratios of lift/drag, optimization algorithms are beneficial in designing flight paths characterized by soft gradients and curvature. Such algorithmic optimization permits hypersonic gliders to attain favorable trajectories that reduce stress on structures while minimizing aerodynamic losses, resulting in extended range and endurance[422].”

“Path planning in drones has numerous challenges like, difficulties in navigations and guidance, obstacle detection and avoidance, considering the shape and size of drone, and formation control in swarms. However recent developments in  high-performance navigation with data fusion and intelligent navigation can help in overcoming to these problems. Nature-inspired algorithms are shown to play a dominant role in path planning of drones. PSO, ACO, DE, GA, and GWO are examples of bio-inspired algorithms that are applied in drone path planning. Several studies have proposed algorithms for multi-UAV path planning. Collision-free and obstacle-free 4D-space path planning is studied using PSO. Collision avoidance protocols and the inscribed circle method for smoothness based on the metropolis criterion and predicted three trajectory correction schemes is also done applying ACO. A dynamic discrete pigeon-inspired optimization technique is used for search attack missions with both distributed path generation and central tasks mission. Modified versions of PSO is also studied for UAV path planning, which showed faster convergence rate and better solution [481]. Konatowski et al. have used ACO for autonomous optimal route construction of a UAV. The results of the simulations show the dependency of UAV trajectory on the selected weighting factors, determining the priority of avoiding detected hazards or choosing the shortest path [482]. Yu et al. have proposed using drones for disaster situational awareness by optimizing their path planning through an adaptive selection mutation constrained DE algorithm. The algorithm selects individuals based on their fitness values and constraint violations, improving exploitation and maintaining exploration. Experimental results show that the proposed algorithm is competitive with state-of-the-art algorithms, making it suitable for disaster scenarios [483]. Qu et al. have designed a novel reinforcement learning-based GWO (RLGWO) to address the challenge of high-quality path planning for drones in complex 3D flight environments. The proposed algorithm incorporates reinforcement learning to enable adaptive switching of operations based on accumulated performance. Four operations, namely exploration, exploitation, geometric adjustment, and optimal adjustment, are introduced for each individual to serve UAVs path planning. The generated flight route is smoothed using the cubic B-spline curve, making it suitable for UAVs. Simulation results demonstrate the RLGWO algorithm's feasibility and effectiveness in generating a suitable path for UAVs in complex environments [484]. Another research by Shen et al. focuses on a multi-objective optimization approach to path planning in a 3D terrain scenario with constraints, using an evolutionary algorithm based on multi-level constraint processing (ANSGA-III-PPS) to plan the shortest collision-free flight path of a gliding UAV. The proposed algorithm employs an adaptive constraint processing mechanism to improve path constraints in a three-dimensional environment and an improved adaptive non-dominated sorting GA to enhance path planning ability in a complex environment. Experimental results demonstrate that ANSGA-III-PPS outperforms four other algorithms in terms of solution performance, validating the effectiveness of the proposed algorithm and enriching research results in UAV path planning [485].”

 

“Lou et al. have developed an improved butterfly optimization (BOA-TSAR) algorithm for autonomous 3D pathfinding of drones in complex spaces. The algorithm improves the randomness strategy of initial population generation using the Tent chaotic mapping method, adaptive nonlinear inertia weights, a simulated annealing strategy, and stochasticity mutation with global adaptive features. Simulation experiments verify the superior performance of BOA-TSAR, achieving optimal path length and smoothness measures. The algorithm is competitive among swarm intelligence algorithms of the same type [500].”

 

“UAVs are being increasingly used for a variety of civilian applications such as delivery, logistics, surveillance, entertainment, and more. Path and trajectory selection for UAVs can be formalized as a TSP path optimization problem under constraints, which shares similarities with similar problems that have been studied in the context of urban vehicles. A recent study by Khoufi et al. reveals the applications of GA, PSO, ACO, and SA in solving this problem [501]. Drone-truck problem is one of the famous optimization problems studied by numerous researchers. This problem is usually modeled as a Travelling Sales Man (TSP) problem in which a truck and a drone are used for package delivery. The goal is to deliver packages by only passing each city or node for one time. The drone leaves the truck in a city and returns back in another city for package loading and recharging (switching) batteries. Based on a recent research, the majority of efforts in this field focus on applying heuristic algorithms [502]. Cooperation of drones with other vehicles like underwater and ground vehicles is another problem which can be solved by nature-inspired algorithms. Drones can be used to support the operation of other vehicles and drones or may perform independent missions [503]. Weng et. al. proposes a cooperative truck and drone delivery path optimization problem to minimize delivery task completion time. The truck carries cargo along the outer boundary of a restricted traffic zone and sends/receives the drone responsible for delivering the cargo to customers. To solve this problem, a hybrid metaheuristic optimization algorithm based on WWO is applied to optimize the paths of the truck and drone. Experimental results show that the proposed algorithm performs competitively compared to other popular optimization algorithms like basic WWO, GA, PSO, DE, BBO, and EBO [504].”

 

“Coverage path planning is another field in drone guidance and control which relies on optimization algorithms. In this problem, a path should be found in way such that all points of some area are covered at least once. Some topics like range of the drone’s camera and duplicate coverage avoiding make coverage path planning a challenging problem. It may be combined with other objectives like energy reduction or coverage in minimum time. Other challenges like obstacle avoidance during makes the final optimization problem even harder. This problem is a common in agriculture, environment protection, disaster management, and save and rescue applications. Otto et al. have shown that majority of the research in this area apply heuristic and meta-heuristic algorithms [503].”

 

“The complete automation of fixed-wing UAV operations involves autonomous execution of take-off, cruising, and landing. The landing stage is particularly crucial, requiring the UAV to maintain a constant speed and glide slope to ensure stability and a successful touchdown on the runway, while also estimating the landing point accurately in minimal time. Incorporating bio-inspired algorithms into UAV control systems can improve accuracy and speed of landing point estimation. A study by Ilango and R, utilized the Bats Optimization Algorithm, Moth Flame Optimization algorithm, and Artificial Bee Colony algorithm to determine the computed path coordinates and optimal landing point within the operational limits of the UAV. The objective was to identify the optimal landing point in minimal time based on the computed points. The error rate between the actual path and estimated path computed points was used to measure performance. Empirical results indicate that the Moth Flame Optimization Algorithm performs the best, taking the least amount of time to compute the optimal point with minimal error, compared to the other two optimization algorithms examined [505]. A dual swarm optimization algorithm that combines the dragonfly optimization method and the DE method is designed by Liang et al. to address the obstacle avoidance trajectory planning problem in the landing process of micro drones. An orthogonal learning mechanism is implemented to facilitate adaptive switching between the two algorithms. In the landing route planning process, the planning plane is obtained by making the gliding plane tangent to the obstacle. The obstacle projection is transformed into multiple unreachable line segments in the planning plane. An optimization model is designed to transform the 3D landing route planning problem into a 2D obstacle avoidance route optimization problem. The shortest route is chosen as the optimization objective, and a penalty factor is introduced into the cost function to prevent intersection of the landing route and obstacle. During the optimization process, the hybrid algorithm adaptively selects the next iterative algorithm through orthogonal learning of intermediate iterative results, allowing for the full utilization of the respective advantages of the two algorithms. The optimization results demonstrate that the proposed hybrid optimization algorithm is more effective in solving the landing route planning problem for micro-small UAVs compared to a single optimization algorithm [506].”

 

“Chai et al. have reviewed the optimization techniques in the trajectory design of space crafts. According to their research, in complex trajectory design problems where gradient-based approaches are not applicable, stochastic or evolution-based algorithms like GA, PSO, DE, and ACO have been used solely or in combination with other approaches like gradient-based algorithms to solve the optimal trajectory design of spacecraft. However, they indicate when using NIAs the validation of solution optimality becomes difficult, and the computational complexity due to the heuristic optimization process tends to be very high, making it challenging to treat heuristic-based methods as a standard optimization algorithm that can solve general spacecraft trajectory planning problems [513].”

 

“Yuan et. al. have developed a robust close-formation control system for unmanned aerial vehicle (UAV) flights using dynamic estimation and compensation to address wake vortex effects and advance UAV close-formation flights to an engineer-implementation level. The control system is divided into three control subsystems for the longitudinal, altitude, and lateral channels, using linear active-disturbance rejection control (LADRC) with two cascaded first-order LADRC controllers. Sine-powered pigeon-inspired optimization is proposed to optimize the control parameters for each channel. Simulation results show that the designed control system achieves stable and robust dynamic performance within the expected error range, maximizing the aerodynamic benefits for a trailing UAV [543]. Jing et al. have proposed a disturbance-observer-based nonlinear sliding mode surface controller (SMC) for a simulated PX4-conducted quadcopter and optimized its parameters using PSO. The quadcopter's tracking performance is evaluated and compared under various noise and disturbance conditions against PID control strategies. Results show that the PSO-powered SMC controller with disturbance observer enables accurate and rapid adaptation of the quadcopter in uncertain dynamic environments, outperforming the PID control strategies under the same conditions [544].”

 

“Xiong et al. have proposed a method for multi-drone mission assignments and path planning in a 3D disaster rescue environment using adaptive genetic algorithms and sine-cosine particle swarm optimization. The method considers factors such as drone performance, mission points, elevation cost, and threat sources to formulate a cost-revenue function and employs an AGA to assign missions to multiple drones. The SCPSO is used for optimal flight path planning. Simulation experiments have validated the effectiveness of the proposed method [550]. Qiu et al. have designed a UAV flocking distributed optimization control framework to convert the many-objective optimization problem into a multi-objective optimization problem solved by a single UAV. To account for onboard computing resource limitations, a modified multi-objective pigeon-inspired optimization (MPIO) algorithm is proposed based on the hierarchical learning behavior in pigeon flocks. Comparison experiments with basic MPIO and a modified non-dominated sorting genetic algorithm (NSGA-II) demonstrate the feasibility, validity, and superiority of the proposed algorithm [551]. A study by Ali et al. investigates the path planning of multiple unmanned aerial vehicles in a dynamic environment using a hybrid algorithm that combines maximum-minimum ACO and DE. The proposed algorithm addresses the limitations of existing classical ACO and maximum-minimum ACO, which face challenges in balancing excessive information and global optimization. The proposed MMACO is used to identify the best ant of each colony to construct the path, and DE is used to optimize the path that escapes maximum-minimum ACO. This ensures the identification of the best global colony that provides optimal solutions for the entire colony. The proposed approach also enhances robustness while preserving the global convergence speed. The simulation experiments are conducted in common benchmark functions to test the effectiveness of the proposed algorithm [552].”

 

“Xiang et al. have proposed a multi-UAV mission planning model that considers mission execution rates, flight energy consumption costs, and impact costs. A lightning search algorithm based on multi-layer nesting and random walk strategies (MNRW-LSA) is proposed to address 3D UAV kinematic constraints and poor uniformity in traditional optimization algorithms. The algorithm's convergence performance is demonstrated and compared to other algorithms using optimization test functions, Friedman and Nemenyi tests. They have also used a greedy strategy to the RRT algorithm to initialize trajectories for simulation experiments using a 3D city model. The proposed algorithm is shown that improves global convergence, robustness, UAV execution coverage, and reduces energy consumption. The proposed method has greater advantages than other algorithms such as PSO, SA, and LSA in addressing multi-UAV trajectory planning problems [557].”

 

Table 8 Different applications of NIAs in guidance and control optimization

Reference	Publication year	Application	Algorithm
[481]	2022	Path and motion planning	PSO
[482]	2019	Path and motion planning	ACO
[483]	2020	Path and motion planning	DE
[484]	2023	Path and motion planning	GWO
[485]	2021	Path and motion planning	GA
[486]	2019	Path and motion planning	BA
[487]	2020	Target tracking	BA
[488]	2017	Optimal Control	BA
[489]	2013	Optimal Landing	BA
[490]	2017	Route evaluation	CSA
[491]	2019	Trajectory tracking	CS
[492]	2019	Trajectory planning	CS
[493]	2011	Path and motion planning	DE, PSO, GA
[494]	2005	Path and motion planning	DE
[495]	2016	Path and motion planning	FAO, DE, PSO, GA
[496]	2022	Path and motion planning	FAO, DE
[497]	2022	Trajectory planning	FPA
[498]	2012	Path and motion planning	GSA
[499]	2020	Path and motion planning	GWO
[500]	2022	Path and motion planning	BOA
[504]	2023	Drone-Truck path planning	WWO, GA, PSO, DE, BBO, EBO
[505]	2020	Optimal landing	MFO, BOA, ABC
[506]	2021	Optimal landing	DFO, DE
[507]	2020	Optimal landing	FPA
[508]	2018	Optimal landing	FPA
[509]	2021	Optimal landing	GWO
[510]	2017	Optimal landing	HS
[511]	2014	Optimal landing	BA
[512]	2008	Optimal landing	CSA
[513,514]	2019	Optimal space trajectory	GA, PSO, ACO
[516]	2015	Optimal space trajectory	GSA
[517]	2020	Optimal space control	FAO
[518]	2016	Optimal trajectory	FAO
[519]	2016	Air traffic control	GSA
[520]	2019	Trajectory tracking	GWO
[521]	2019	Engine control	GWO
[522]	2015	Robust control	BA
[523]	2015	Control parameter tunning	ABC
[524]	2019	Control parameter tunning	BFA
[525]	2010	Control parameter tunning	BFA
[526]	2016	Control parameter tunning	BA
[527]	2015	Control parameter tunning	BeeA
[528]	2015	Control parameter tunning	CS
[529]	2022	Control parameter tunning	BA, PSO, CS
[530]	2020	Control parameter tunning	CS
[531]	2016	Control parameter tunning	DE
[532]	2016	Control parameter tunning	DE
[533]	2021	Control parameter tunning	FA
[534]	2021	Control parameter tunning	FA
[535]	2015	Control parameter tunning	FA
[536]	2022	Control parameter tunning	FA
[537]	2018	Control parameter tunning	FAO
[538]	2019	Control parameter tunning	FPA
[539]	2020	Control parameter tunning	GSO
[540]	2017	Control parameter tunning	GSO
[541]	2021	Control parameter tunning	HS
[542]	2020	Control parameter tunning	HHO
[543]	2023	Control parameter tunning	PIO
[544]	2022	Control parameter tunning	PSO
[545]	2022	Swarm motion and formation	BeeA
[546]	2019	Swarm motion and formation	DE
[547]	2019	Swarm motion and formation	DE
[548]	2020	Swarm motion and formation	GWO
[549]	2022	Swarm motion and formation	MFO
[550]	2023	Swarm motion and formation	PSO
[551]	2020	Swarm motion and formation	GA
[552]	2023	Swarm motion and formation	ACO, DE
[553]	2017	Swarm motion and formation	HS
[554]	2022	Swarm mission planning and task allocation	FAO
[555]	2022	Swarm mission planning and task allocation	FAO
[556]	2022	Swarm mission planning and task allocation	HS
[557]	2023	Swarm mission planning and task allocation	LSA, PSO, SA
[558]	2017	Vibration reduction	BeeA
[559]	2014	Vibration reduction	BeeA

 

“Table 8 summarizes the studied publications in this section. As it can be seen although this section includes a wide range of algorithms, the majority of papers have focused on a limited number of algorithms like DE, PSO, BA, GWO, and GA. Figure 74 provides the share of different nature-inspired algorithms from the reviewed publications in this section. It can be said the most popular applications of bio-inspired algorithms in this group are controller parameter tunning, path, and trajectory planning, and optimal swarm motion.”

 

“Figure 74 Share of nature-inspired algorithms and applications from guidance and control publications.”

 

Section 4.5.2: “Researchers have also applied various other metaheuristic algorithms such as DE, CS, and HS for parameter identification in chaotic systems and infinite impulse response identification. These algorithms have been used in combination to provide better results and have shown promise for system identification of quadrotors, multi-rotor UAVs, unmanned helicopters, and small fixed-wing drones. The effectiveness of algorithms like HS has also been demonstrated in aircraft and small helicopter parameter estimation.”

“Table 9 summarizes the studied publications in optimal system identification. We can say multirotor in general are the most attractive systems that being studied for NIA-based optimal identification. Among algorithms GA, PSO, DE, ABC, and HS seem to have equal potentials in solving optimal system identification problems.”

Table 9 Different applications of NIAs in system identification optimization.

Reference	Publication year	Application	Algorithm
[560]	2015	Helicopter UAV identification	ABC, GA
[561]	2017	Helicopter UAV identification	ABC, PSO
[563]	2019	Quadrotor identification	PSO, CS
[564]	2014	Quadrotor identification	GA
[565]	2016	Multirotor UAV identification	DE
[566]	2014	Helicopter UAV identification	DE
[567]	2022	Fixed-wing drone identification	AlO, DA, GOA, GWO, SlpSO, WOA, SCA, WCA, ES, MFO
[568]	2014	Aircraft identification	HS
[569]	2014	Helicopter UAV	HS

 

Section 4.5.3: “Nature-inspired algorithms have shown great potential in the navigation of robots, particularly in challenging environments like urban and crowded areas. Optimization algorithms like Bat Algorithm, MFO, PSO, CS, and GWO have been applied to automatic robot navigation, image processing, and localization problems in swarm systems. These algorithms have been used in various applications such as integrated navigation, target recognition, and source localization in UAV-based search and rescue missions. Additionally, researchers have used CS and DE algorithms for automatic guided vehicles' navigation and autonomous UAV swarm coordination, respectively. Furthermore, hybrid versions of GWO and SCA have been applied to energy-efficient localization of UAVs and visual tracking techniques, respectively, resulting in better performance. These algorithms provide safe and collision-free trajectories in present of uncertainty, error and external disturbances.”

 

“Li et al. have developer a 3D localization approach for multiple UAVs using a flipping ambiguity avoidance optimization algorithm. Beacon UAVs collect data and utilize a semidefinite programming-based approach to estimate the global position of GPS-denied UAVs. They have applied an improved GWO algorithm is used to improve positioning accuracy in noisy environments. Simulation results show the superiority of the proposed approach on similar methods [484]. Arafat and Moh have developed a similar energy-efficient localization method for UAVs in swarms based on a hybrid version of GWO [578].”

 

“Hao et al. have proposed a passive location and tracking algorithm for moving targets using a UAV swarm. The algorithm is based on an improved particle swarm optimization (PSO) algorithm. The localization method of cluster cooperative passive localization is employed, and the problem of improving passive location accuracy is transformed into the problem of obtaining more target information. The A criterion is used as the optimization target, and a Recursive Neural Network (RNN) is used to predict the probability distribution of the target’s location in the next moment, making the localization method suitable for moving targets. The particle swarm algorithm is improved using grouping and time period strategies, and the algorithm flow for moving target location is constructed. Simulation verification and algorithm comparison demonstrate the advantages of the proposed algorithm [581].

Li et al. have developed a method to improve the navigation accuracy of inertial navigation systems in drones by identifying errors in horizontal gyroscopes and accelerometers using the improved pigeon-inspired optimization (PIO) method. This approach has the potential to reduce the need for sending the inertial navigation system back to the manufacturer for calibration, saving time and resources [582].

Table 10 summarizes the studied publications in optimal navigation using nature-inspired algorithms and the algorithms which have been used in them. It can be seen that a wide range of algorithms have been applied on a wide range of applications. However, the list of algorithms in this section is limited to a few number algorithms like other categories.”

Table 10 Different applications of NIAs in navigation optimization.

Reference	Publication year	Application	Algorithm
[570]	2022	Automatic drone navigation	BA, MFO, PSO, CS, GWO
[571]	2022	Localization in swarm	PSO
[572]	2022	INS error reduction	ABC
[573]	2014	Target recognition	ABC
[574]	2021	In-door navigation	CSA
[575]	2021	Target recognition	CS
[576]	2018	Localization in swarm	DE
[577]	2016	Rada imaging	DE
[578]	2021	Localization in swarm	GWO
[484]	2023	GPS-denied navigation	GWO
[579]	2016	Obstacle avoidance	GWO
[580]	2022	Target tracking	SCA, PSO, FAO, SMOA
[581]	2023	Target tracking	PSO
[582]	2022	INS error reduction	PIO

 

• Section 4.6.: “6 Communication

“A UAV-based communication system can potentially pair heuristic/meta-heuristic solutions with UAVs to enhance the performance of wireless communication networks, namely in the spectral efficiency and coverage of these networks. A UAV-based communication system can be readily applied in an emergency or offloading scenario. For example, researchers have proposed methods to prejudice, asses, and preserve a response in emergency situations [583]. The combination of heuristics and UAV platforms can potentially mitigate the inherent weaknesses of a pure UAV-based communication system, such as channel modeling, resource management, positioning, and security [584]. UAVs are currently utilized for data delivery and collection from dangerous or inaccessible locations. However, trajectory planning remains a major issue for UAVs. Khoufi et al. have conducted research on determining optimized routes for data pickup and delivery by drones within a time window and intermittent connectivity network, while allowing for battery recharge in route to destinations. The problem is formulated as a multi-objective optimization problem and solved using Non-dominated Sorting GA II (NSGA-II). Various experiments validated the proposed algorithm in different scenarios [585]. Optimizing device-device communication, the deployment process, and limited power supply for the devices and hardware they carry are practical issues to be addressed in applying drones in disaster response scenarios. In this field, the bio-inspired self-organizing network (BISON) achieved promising results using Voronoi tessellations. However, in this approach, the wireless sensor network nodes were using knowledge about their coverage areas center of gravity, which a drone would not automatically know. To address this, Eledlebi et al. have augmented BISON with a GA to further improve network deployment time and overall coverage. Their evaluations show an increase in energy cost [586].

The development of the edge computing paradigm, IoT-based devices, and 5G technology has led to increased data traffic that requires efficient processing. UAVs can replace edge servers used in mobile edge computing (MEC). Subburaj et al. have proposed a self-adaptive trajectory optimization algorithm (STO) for a UAV-assisted MEC system using DE. The STO is a multi-objective optimization algorithm that aims to minimize the energy consumed by MEC and the process emergency indicator. The proposed self-adaptive multi-objective differential evolution-based algorithm improves the population diversity by self-adapting the strategies and crossover rate using fuzzy systems. The algorithm's performance is evaluated on a single UAV-assisted MEC system with hundreds of fixed IoT device instances on the ground level [587].”

 

Section 4.6.1: “Positioning and placement”

“Within a drone-enabled network, the utilization of drones may encompass the allocation of drones to fixed locations, thereby operating as intermediaries to interconnect mobile devices with macrocell base stations. Alternatively, a drone may traverse a cyclical trajectory to facilitate this connection. Furthermore, a drone-to-drone communication paradigm can be implemented, allowing mobile devices connected to one drone to establish connections with those linked to other drones. Importing communication constraints and modeling into the problem makes it a challenging optimization problem. A recent study reveals more than two-third of the papers in this area are based on heuristic and meta-heuristic algorithms [503].”

 

“4.6.2 Network security and routing

UAV networks must be robust against cyber-attacks to maintain the integrity of the network. One effective approach to safeguarding UAV networks is physical layer security (PLS), which protects against jamming and eavesdropping [595,596]. PLS uses information-theoretic methods and encryption solutions to enhance the secrecy of transmission [597]. In a review paper, bio-inspired nature algorithms were examined in their ability to rout multiple UAVs in Flying Ad-hoc networks (FANETS). Based on this research several optimization techniques such as the KH, GWO, BAT, Red Deer Optimization, PSO, FSA, WOA, ACO, BCO, GSO, MFO, FFA, and BFA are used for this aim. In addition to basic algorithms, hybrid forms of NIAs with combination to each other or other methods like fuzzy logic are also studied in this specific application [598]. A recent study by Otto et al. reveals the applications of heuristic and meta-heuristic algorithms in FANET operations [503]. A summarization of the studied publications in this section and their application is provided in Table 11.”

 

Table 11 Different applications of NIAs in communication optimization.

Reference	Publication year	Application	Algorithm
[585]	2021	Optimized routing	GA
[586]	2020	Network deployment and coverage	GA
[587]	2023	Mobile edge computing	DE
[588]	2019	Coverage optimization	BeeA
[589]	2020	Coverage optimization	PSO
[590]	2022	Optimal charging (by path planning and obstacle avoidance)	PSO
[593]	2023	Wireless sensing	ACO
[594]	2022	Coverage optimization	GA

 

• “4.7. Energy management

Battery power supply is a widely used energy source for UAVs, particularly in smaller ones. This is while the energy storage capacity of batteries is limited, which poses a significant challenge to their commercial and industrial application. To increase the endurance of UAVs, batteries must be frequently charged. Several battery charging techniques have been developed, including battery swapping, which involves recharging or replacing UAV batteries either conventionally or via hot swapping. In conventional swapping, the depleted UAV leaves its service location to the charging station and is replaced by an already charged UAV, while in hot swapping, new batteries are quickly inserted into UAVs as soon as they reach the charging station. Automated battery swapping mechanisms have been developed to replace depleted batteries with new ones using robotic actuators. However, effective swapping requires a battery recharging station, multiple UAVs, and a management system to coordinate the battery recharging and replacement cycle of the UAV swarm. Fuel cell-powered UAVs have been shown to be more efficient than battery-powered UAVs, that can increase endurance by up to six times. However, fuel cells have lower energy density and require special fuel tanks. To address this, compressed hydrogen gas, liquid hydrogen, or chemical hydrogen can be used. Renewable energy sources such as wind and solar power can also be used to power drones, but they depend on environmental conditions and have limitations such as reduced efficiency during rainy conditions and nights. Hybrid power supply methods, combining battery, fuel cells, and renewable energy sources, can provide a blend of power supply for UAVs. In all cases an optimal energy management system is a necessary requirement in industrial applications[599].

UAV-based cellular networks face challenges due to the energy consumption of UAVs. The use of UAV-Base Station(UAV-BSs) can hinder the improvement of network EE if energy consumption is not carefully considered. Energy optimization is important because of the limitations of UAV power supply and charging techniques. Four major aspects of energy optimization are identified in UAV-based cellular networks: optimization of propulsion energy and communication energy, joint optimization of communication and propulsion energy, and optimization of energy consumption in UAV-assisted cellular networks. Joint optimization of communication and propulsion energy results in the most energy conservation. Strategies have been developed to reduce the energy consumption of both UAV-BSs and fixed BSs, including using a UAV-assisted BS sleeping strategy. Conventional optimization methods for energy optimization in UAV-based cellular networks can be classified into three categories: exact methods, heuristic methods, and meta-heuristic methods. Meta-heuristic methods are problem-agnostic and can treat functions as black boxes which makes them suitable for this purpose. Algorithms like PSO have been applied to minimize transmission power of UAVs serving as relays in IoT communications while considering the outage probability of IoT devices. Other algorithms like GA were used to design an energy-efficient trajectory for UAV-BSs during backhaul connection to terrestrial BSs in post-disaster scenarios. A UAV-BS path planning framework can be impowered with GA to determine the optimal path with minimal turns and energy consumption [599].”

 

“4.8 Infrastructure and operation:

The concepts advocated to facilitate the incorporation of drone operations within civilian airspace include airspace that is solely accessible to drones or air corridors as well as shared airspace with manned aircraft. Under any of these circumstances, the integration of drones into civilian airspace would necessitate the development of relevant air traffic regulations and management schemes along with collision avoidance and automatic flight path replanning capabilities for individual drones. These approaches could, for instance, delineate a set of conflict resolution rules (e.g. priority rules), types of surveillance (e.g. aircraft locations are determined by centralized radar or on the basis of information broadcasted by the aircraft themselves), and forms of coordination (i.e. Whether aircraft can communicate with each other in case of conflict) [503].

Some studies focus on locating distribution centers and transfer points to supply emergency items via drones after disasters. Centers supply damaged areas where roads are intact by trucks, while drones deliver to areas with damaged infrastructure. Limited drone range poses a challenge. Off-road vehicles proved more beneficial than drones in simulations due to longer drone loading and unloading times. Some research focuses on recharging stations and automatic service centers for drones. Studies aim to minimize costs by considering fixed facility costs and inventory costs, while disaster-related objectives like delivery lead times and travel times also matter[503].

Many important civilian drone applications require a human operator to examine the sensory information sent by the drone in real time. The drone's operations must account for potential idle time of the human operator and give the operator enough time to examine information at each point of interest. A heuristic algorithm is proposed for path planning that takes this factor into consideration, assuming the sequence of point of interest visits for each drone is given. In addition, cognitive underload and overload of human operators should be avoided by alternating demanding and less demanding tasks appropriately and providing enough rest breaks.  Researchers have scheduled as many monitoring tasks to multiple operators as possible within a given time horizon, considering drone routes and speeds, while penalizing situations of cognitive underload and overload[503].

The main trade-off in scheduling drone maintenance operations like refueling, launching and repair is balancing the drone's priority to return to its tasks quickly with not wasting fuel by making it wait too long. The refueling sequence for drones at an automatic refueling tank is optimized to achieve this balance. In addition, experience-based planning rules have been used at aircraft carriers to optimal integer programming solutions for scheduling drone maintenance. Similar planning problems may arise at mobile warehouses servicing drone fleets, like Amazon's floating warehouses or Ford's auto deliveries[503]. In all cases, heuristic and meta-heuristic algorithms play a dominant role due their ability to solve complex, nonlinear, non-convex, and multivariable problems. Direct methods can hardly be applied on such problems which makes nature-inspired algorithms suitable alternatives [503].”

• Comment 4: ” I do not understand the reason for proposing a comparison of performance of 27 general algorithms for 10 general problems. In a manuscript that should be published in Drones, wouldn’t be more interesting to focus on some general drone optimization problem (e.g., some travelling salesman problem that typically appears in drone optimal path planning problems) and then propose a comparison of performance for it?”
• Thanks for the comment. Benchmark functions are standard ways to compare the performance of optimization algorithms. They are usually functions with controllable complexity and an exact and single optimal answer. This is while aerospace problems are usually multi-answer problems which are not suitable and standard problems to measure the performance of different algorithms. Instead, we tried to choose variant benchmark functions to provide the reader with the closest problems to their aerospace related applications. Like by providing single and multi-variable, unimodal and multimodal, etc. problems. One of the critical discussions in nature-inspired optimization is that many researchers believe that majority of these algorithms are in fact the same and there is no considerable difference between them. Which is nor completely true neither false. Evaluating the performance of these algorithms makes us one step closer to the answer. This section reveals the differences between the algorithms and also shows us that some of the algorithms have higher performance compared to most popular and widely used algorithms (like GA, PSO, ABC, etc.) while they are not being paid enough attention. This is the logic behind our suggestion at the end of paper for applying other powerful algorithms. This should be noted that we have reviewed some papers that already have solved some aerospace problems with multiple algorithms and compared their results with our results of the section 3.

 

• Comment 5: ”After Section 4 (i.e., "Nature-inspired algorithms in drones and aerospace engineering"), it would be important to add a section discussing the limits of current literature (e.g., What are open challenges about metaheuristics in this application context? How could they be tackled from an algorithmic point of view? Which applications are particularly relevant?).”

 

• Thank you for pointing this out. As this was mentioned by Reviewer 1 too, we tried to enrich the final section of the paper by addressing your comments.
• The following paragraphs were added to the paper: “This study revealed the massive amount of research on nature-inspired algorithms which are mimicking different aspects of nature. From oceans to space, there can be found an algorithm focusing on a specific phenomenon or creature. Neglecting the open question of the novelty of these algorithms and their similarities to most famous algorithms, the high number of publications in this area is considerable. Most of the publications in this field do not provide any or enough information on the performance of the algorithms, their exact differences, and their contributions. The majority of papers just provide a simple comparison with just one or a few well-known algorithms like GA (which is shown to have one of the lowest performances among nature-inspired algorithms) by only solving a single problem. This cannot of course provide us with a good understanding of the real values of the algorithms. Performance analysis of nature-inspired algorithms is what is felt necessary right now. The main focus of research in this field should be put on the applications of these algorithms and their performance evaluation and improvements. It seems that there are more than enough algorithms available with different perspectives. Studying the current literature reveals that there is a focus on developing hybrid algorithms to increase the performance of the algorithms which can broaden their field of applications. The performance of hybrid algorithms is reported to be significantly better than the basic algorithms which makes it reasonable to expect more research on this topic in the future.

Current research illustrated the latest developments in the field of nature-inspired optimization, the popularity of these algorithms, and some related challenges like constraint handling and their performance in solving different problems. A compact review of the applications of nature-inspired algorithms in aerospace systems has been provided. Based on this review, the most used algorithms in aerospace systems are GA, PSO, and ABC. The field where nature-inspired algorithms have been used widely in is control systems. Based on evaluations in this paper, it is recommended to apply high-performance algorithms like the Sine-Cosine Algorithm, Harris Hawk Optimization, Firefly Algorithm, Fireworks Algorithm, Grey Wolf Optimization, and Cat Swarm Optimization in a wider range of applications from conceptual design, MDO, aerodynamics, and shape design to navigation and identification. Considering the progress of hybrid algorithms, and their considerably improved performance, their application in aerospace systems is recommended. All results of the paper, including data, and codes in Python and MATLAB, are also published in public GitHub repositories.”

• Comment 6: ”In line 2947, the Authors write:

‘ten different algorithms are solved by 27 nature-inspired algorithms’, however, I presume they intended "ten different problems are solved by 27 nature-inspired algorithms".”

• Thank you for pointing this out. It was a typo mistake, and we have fixed it.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The Authors have effectively addressed my comments and remarks and I think the manuscript represents now a valid survey that I suggest to consider for possible acceptance in the journal Drones.

In general, the quality of English adopted throughout the text is fine.