Dynamic Arithmetic Optimization Algorithm for Truss Optimization Under Natural Frequency Constraints

Metaheuristic algorithms have successfully been used to solve any type of optimization problem in the field of structural engineering. The newly proposed Arithmetic Optimization Algorithm (AOA) has recently been presented for mathematical problems. The AOA is a metaheuristic that uses the main arithmetic operators’ distribution behavior, such as multiplication, division, subtraction, and addition in mathematics. In this paper, a dynamic version of the arithmetic optimization algorithm (DAOA) is presented. During an optimization process, a new candidate solution change to regulate exploration and exploitation in a dynamic version in each iteration. The most remarkable attribute of DAOA is that it does not need to make any effort to preliminary fine-tuning parameters relative to the most present metaheuristic. Also, the new accelerator functions are added for a better search phase. To evaluate the performance of both the AOA and its dynamic version, minimizing the weight of several truss structures under frequency bound is tested. These algorithms ’ efficiency is obtained by five classical engineering problems and optimizing different truss structures under various loading conditions and limitations.


I. INTRODUCTION
Various metaheuristic optimization techniques for almost any engineering problem have been created in the past few decades. These algorithms discover the search area in a pseudo-random method complying with some motivating principles and without demanding gradient. Metaheuristic algorithms have lately been popular in a variety of fields because they are more efficient, need less computing capacity, and take less time to implement than deterministic algorithms. To get the best outcomes, simple principles are needed, and transplants are carried out in a multitude of areas. Local optimality can be avoided by using random elements in meta-heuristic algorithms, which allow the algorithm to search for the best solution inside the search area, The associate editor coordinating the review of this manuscript and approving it for publication was Gustavo Olague . thus preventing it from becoming optimal locally. Specific gradient descent algorithms are more useful in using gradient information than stochastic algorithms in direct and straightforward problems. Indeed, the convergence rate of metaheuristic algorithms will be far below the gradient descent algorithms and may be considered a disadvantage [1].
Meta-heuristic algorithms, which are used to find better answers for optimization problems, are typically based on human, natural, physical, and art phenomena. Under actual circumstances, the solution space of many issues is endless or usually unlimited. By traversing the solution space in the current situation, it might be impossible to discover optimal solutions. Metaheuristic algorithms detect the almost optimum solution of the problem by randomly detecting the significant solution area in one method to identify or create much better solutions for the problem of optimization under minimal circumstances or computational capacity [2].
Natural frequency is a critical criterion provided based on knowledge of structural dynamics. The natural frequencies of a structure have a significant impact on its performance. The optimal design of trusses based on dynamic behavior is a demanding research area. In other words, natural frequencies give vital information on the dynamic behavior of structures. In addition, optimization of trusses based on frequency constraints has seen many factors to consider in the past ten years. An important practical concern is to increase the truss's dynamic behavior by considering its natural frequencies. This criterion must be controlled to prevent the resonance phenomenon and improve the structural performance. Lightweight structures are very important in engineering. When it comes to optimizing trusses, mass minimization conflicts with frequency constraints and also increases the complexity of the problem. As a result, an effective optimization technique is required for the design of trusses based on primary frequency constraints, and academics are taking proactive steps to improve their understanding of this element.
Bellagamba and Yang [32] investigated the truss optimization with frequency constraints for the first time, and then many researchers examined this research area. A bi-factor algorithm was developed for these structures by Lin et al. [33]. Wei et al. [34] presented a parallel genetic algorithm. Kaveh and Zolghadr suggested charged system search and enhanced CSS [35], democratic particle swarm optimization (DPSO) [36], and tug of war optimization (TWO) [37]. Pholdee and Bureerat [38] tested various metaheuristic algorithms. Tejani et al. [28] improved symbiotic organisms search (ISOS) for truss structures with frequency bound. Multi-class teaching learning-based algorithm [39] was applied for truss structures subjected to frequency constraints.
All these researches confirmed stochastic optimization algorithms' efficiency in managing many problems when solving structure design troubles. In the optimization field, there is no technique to solve all optimization problems, according to the no free lunch (NFL) theorem [40]. As a result, a new algorithm that has been modified will be able to handle a particular set of problems better than the existing algorithms. At the same time, they still carry out equal, taking into consideration all optimization problems. This motivated our attempts to boost the efficiency of the recently suggested arithmetic optimization algorithm (AOA) [41] and adjust it much better for structure design problems.
Laith Abualigah et al. [41] recently developed an arithmetic optimization algorithm for constraint and unconstrained optimization problems based on the mathematical model. Arithmetic is the mathematics branch that deals with numerical study with various operations. Adding, subtraction, multiplication, and division are the basic mathematical operations.
The Dynamic Arithmetic Optimization Algorithm (DAOA), a recently developed population-based meta-heuristic, is applied to structural design problems in this study. The motivation for this research is to use the AOA and DAOA for the optimal weight design of truss structures with frequency limitations for the first time in the literature. Two dynamic features have been successfully introduced in the basic version of AOA in order to increase its performance. Since no prior fine-tuning of parameters in connection to the most recent meta-heuristic is required, DAOA offers an advantage over other optimization algorithms.
This new algorithm provides a proper equilibrium between exploration and exploitation strategies that generate excellent accuracy along with swift convergence. All the results of optimizing distinct architectures are thoroughly analyzed and evaluated in detail. The structural weight with frequency constraints is used as an objective function to solve these challenges, and distinct and continuous areas are considered design variables.
The paper is arranged as follows: Section II presents the formulation of truss structures optimization. Section III and IV provide an extensive explanation of the arithmetic optimization algorithm (AOA) and its dynamic version (DAOA), respectively. Section V identifies the problem and discusses numerical findings. Finally, section VI provides the final observations.

II. FORMULATION OF TRUSS STRUCTURES OPTIMIZATION
Several natural frequency constraints are included in this section's formulation of truss structure optimization. Figure 1 depicts the flow chart for solving the truss optimization problem. Optimization of the truss structures suggests achieving the best possible cross-sectional (A i ) values, which reduce the weight (W ) of construction. This minimum design has to satisfy the following requirements [36] additionally: Subjected to where {x} presents the design variables, the number of design variables is defined by ng defines the variety of design variables, the structure weight is introduced by W ({x}) and the variety of structural members is specified by nm. In addition, the material density, member's length, the member's crosssectional area for all components is shown as γ i , L i and x i , respectively. The jth and kth natural frequency of the truss are defined by ω j (ω * j is upper bound) and ω k (ω * k is lower bound). The popular appropriate function for dealing with the restrictions as a result of the fundamental principle and also simplicity of application is revealed as follows: where ν is the total amount of the constraints violated and constants ε 1 and ε 2 are selected considering the exploration and the exploitation rate of the search space. In this case, ε 1 is set to 1, ε 2 is chosen to minimize penalties and to reduce cross-sections. ε 2 is initially set to 1.5 and then increased to 3 as the search progresses [42].

III. ARITHMETIC OPTIMIZATION ALGORITHM (AOA)
This algorithm was proposed in 2020 by Abualigah [41] using several mathematical equations and operators. Just like other metaheuristics, the AOA algorithm starts with a population of random solutions. In each iteration, the objective value of each solution gets calculated. There are two controlling parameters in this algorithm called MOA and MOP that should be updated prior to updating the position of solutions as follows: MOA(t) is the value of the function at tth iteration, t is the current iteration, T shows the maximum iteration, and Max/Min is the maximum and minimum values to bound MOA.
where math optimizer probability (MOP) is a coefficient, MOP(t) is the value of the function at tth iteration, T is the maximum number of iterations, t is the current iteration and α shows a controlling parameter. After updating MOA and MOP, a random number is generated called r1 to switch between exploration and exploitation. For exploration, the following equation is used: where t is the current iteration, µ is a controlling parameter, is a small number to avoid division by 0, and r2 is a random number in [0,1].
For exploitation, the following equation is used: where x i (t + 1) indicates the ith solution in the next iteration, x i,j (t) indicates the jth position of the ith solution at the current iteration, and best(x j ) is the jth position in the best-obtained solution so far, t is the current iteration, µ is a controlling parameter, is a small number to avoid division by 0, and r3 is a random number in [0,1]. In addition, the upper bound value and lower bound value of the jth position are described by UB j and LB j , respectively.

IV. DYNAMIC ARITHMETIC OPTIMIZATION ALGORITHM (DAOA)
Two dynamic characteristics with a new accelerator function are implemented in the basic arithmetic optimization algorithm version to improve this performance. The dynamic version, which controls the exploration and exploitation behavior, changes the candidate solutions and search phase during the optimization process. The most remarkable attribute of DAOA is that it does not need to make any effort to preliminary fine-tuning parameters relative to the most present metaheuristic. Algorithm. 1 shows the DAOA pseudo-code. These new dynamic features are discussed in the following section. phase. In the AOA, one needs to adjust the Min and Max initial values of the accelerated function. It is better to have an algorithm without adjustable internal parameters since DAF is replaced with a new downward function. In the optimization algorithm, this modification factor is presented as follow: where Iter describes the current number of iterations, Iter max is the maximum number of iterations, and α has the constant value. This function is decreased during every iteration in the algorithm.

B. DYNAMIC CANDIDATE SOLUTION FOR DAOA
In this section, the following dynamic features for candidate solutions in DAOA are introduced. The two main phases of metaheuristic algorithms are exploration and exploitation, which has a good balance between them is essential for the algorithm. In the proposed dynamic version to emphasize the exploration and exploitation, each solution renews its positions dynamically from the best-obtained solution during the optimization process. Dynamic candidate solution (DCS) function is added to Eq (10) and Eq (11) instead of Eq (7) and Eq (8) in the basic version, respectively: where dynamic candidate solution (DCS) function is introduced due to the effect of the decreasing percentage in candidate solution and during every iteration, its value was decreased as follow: Numerous search agents and iterations showed that using candidate solutions in DAOA considerably increased the speed of AOA convergence. As a result of these enhancements, solution quality is also improved. An algorithm's ability to operate with no parameters is generally seen as an advantage for metaheuristic algorithms. The distinction between DAOA and AOA is that DAOA employs dynamic functions, while the remaining approach is identical to the AOA algorithm described in the previous section. The DAOA algorithm benefits from adaptive parameters, so the number of parameters that should be tuned is at the minimum (population size and maximum iteration). This is opposed to the rival algorithms, which require parameter tunings for different problems. As one of the drawbacks of this algorithm, we can mention the adaptive mechanism based on the iteration counter and not fitness improvement.

V. NUMERICAL EXAMPLES A. NUMERICAL EXAMPLES
The optimization technique is performed using the DAOA and AOA algorithms and assessed with four optimization instances of classical engineering problems and truss structures to satisfy this aim. The maximum number of function evaluations was also employed as the final condition in order to establish a fair comparison. Each problem is solved separately 20 times, and DAOA is used in the same number of analyses and representatives to compete fairly. In addition, the stated references provided the other control parameters for the comparative algorithms. The DAOA and its standard version are used in the same range of evaluations and representatives to compete fairly.

1) TENSION/COMPRESSION SPRING
One of the most common optimization problems is presented in Fig. 2 by Belegundu [43] and Arora [44]. The goal is to make the tension/compression spring as light as possible.
There are other constraints (shear stress, frequency, and minimum deflection.) that must be met in order for this reduction to be successful.   The best result gained by DAOA is 4% lighter than that of AOA, and its solution obtained the 1 st rank in terms of the best solution. In addition, the result and best variable values for different algorithms such as WCA [45], BA [46], DELC [47], GWO [7], HS [48], PSO [49], GA [50], Belegundu [43] and Arora [44] are shown in Table 1.

2) WELDED BEAM
Coello [50] suggested this benchmark design issue, and several researchers discussed it. The vertical force of the beam is shown in Fig. 3. The goal is to achieve a design that will have the minimum objective function. Seven stress, deflection, welding, and geometry constraints are present in the problem.
The formulation of this problem is given below:  Table 2 contains the result of DAOA and AOA in comparison with other algorithms. As seen here, DAOA finds the better variables for this problem than CSS [19], GWO [7], CDE [49], GA [50], PSO [49], AOA, HS [48], APPROX [51], and Random [51]. The results of the DAOA for this problem are compared to several other optimization algorithms published in the literature. The DAOA algorithm provides very competitive results, and its best solution obtained is ranked second to none, the same as WSA [52] and MFO [53]. In comparison to well-known optimization approaches, DAOA is a competitive algorithm, according to this study.

3) THREE BAR-TRUSS
The following example is designing a three-bar truss to reduce weight. As shown in Fig. 4, there are three bar  components of the truss structure with symmetric configuration. The objective function is fundamental, but the problem is extremely limited. There is a wide range of constraints to structural design problems, such as stress, deflection, and buckling constraints. This problem is mathematically  formulated as follows: Ten well-known algorithms are chosen for comparison with DAOA. The comparison results of best values are provided in Table 3. DAOA finds a design, which is the lowest among all other methods. Table 3 shows the best optimum designs. The DAOA algorithm produces excellent results, and its optimal solution is unrivaled.

4) COMPOUND GEAR
In mechanical engineering, this example is a discrete design issue. It is intended to reduce the gear ratio as defined by the ratio of the output shaft's angular speed to the angular velocity of the input shaft. As shown in Fig. 5, The number of gears VOLUME 10, 2022   teeth is known to be a discrete variable. The following is the mathematical formula: The best number of teeth were found by the DAOA, CS [54], WSA [52], MBA [55], GA [50], ALO [56], SCA [57], SSA [58] and GWO [7]. Table 4 displays DAOA's optimal findings, which is clear that DAOA can outperform other approaches, amongst others, by obtaining the lowest total cost. Overall, the results of this research demonstrate the efficiency and effectiveness of DAOA in solving this problem.

5) CANTILEVER BEAM
Chickermane and Gea [62] have taken up the cantilever beam issue. The beam is rigidly supported, and at the free end of the cantilever, the vertical force acts, as shown in Fig. 6. The challenge is reducing the weight of the beam. The beam consists of five hollow square blocks with constant thickness,  whose height decision. The classic principle of the beam develops the problem as follows: Subject to g X = 61 to any other approach has been obtained by DAOA and WSA [52].

B. STRUCTURAL EXAMPLES
In order to demonstrate the effectiveness of DAOA, various common structural optimum design problems are investigated in this section. Material properties, cross-sectional area, and natural frequency constraints applied for a 37-bar planer bridge, a 72-bar space truss, a 120-bar dome truss, and a 200-bar planer truss are summarized in Table 6. In order to provide a point of comparison, the results of a few other optimization algorithms are also presented. In MATLAB 2021b, the algorithm was made. SAP2000 v14.1 solves the trusses with a direct stiffness method, and also the API is used to make changes during the optimization VOLUME 10, 2022  process. The computer's current work is done with the help of these features: 2.3 GHz CPU, 16 GB 2400 MHz DDR4 RAM, and a Macintosh platform (macOS Big Sur).

1) 37-BAR PLANER TRUSS
The first instance is the weight reduction of the planar 37-bar truss structure depicted in Fig 7. Wang et al. [34] initially explored this example, and a large number of scholars later investigated it. For this problem, the design properties are shown in Table 6. The problem consists of fourteen sizes and five design variables. Each lower chord free node has a concentrated mass of 10Kg. The cross-sectional areas of the lower chord bars are 0.4 cm 2 while the remaining bars are supposed to have a cross-section area of 1 cm 2 . All nodes of the upper chord can be moved along the y-way while maintaining the structure's symmetry. This structure had been optimized previously with different metaheuristic algorithms. In this section, 37-bar planer bridge under natural frequency constraints is investigated by AOA and DAOA by considering population size 50 and function number evaluations as 10000. The best and average convergence curves obtained by AOA and DAOA for the 72-bar planer bridge are depicted in Fig 8. As seen in Fig. 8, the best design of AOA and DAOA is 359.5617 Kg and 378.2591 Kg, which have been located at 2300 and 9000 analyses respectively. The results presented above clearly show the high convergence capability of the dynamic version of AOA. The design found by DAOA is 4.94% lighter than that found by AOA. Tables 7 and 8 show optimization results and the first three natural frequencies obtained by DAOA, AOA in comparison with other referenced algorithms using particle swarm optimization (PSO) [36], harmony Search (HS) [37], firefly algorithm (FA) [37], teaching-learning-based optimization (TLBO) [63], vibrating particles system (VPS) [64], schoolbased optimization (SBO) [63], symbiotic organisms search (SOS) [28] and colliding-bodies optimization (CBO) [65].
Obviously, DAOA gained the lightest structure overall and strictly satisfied all constraints, while some algorithms violated these constraints. The standard deviation and average of results for DAOA are better than AOA. It should be noted that DAOA is more reliable than AOA and has better performance. Fig 9. shows the 20 independent runs for both AOA and DAOA. It is clear that the final results of DAOA are close to the value of average weight.

2) 72-BAR SPACE TRUSS
The second instance for weight minimization of the structure is a spatial truss of 72 bar, as shown in Fig 10. This example was divided into 16 groups because of structural symmetry; therefore, this problem has 16 sizing variables. Four non-structural masses of 10 Kg have been added at nodes 1-4. This example demonstrates material properties and constraints in Table 6. Both AOA and DAOA are evaluated for 72-space truss with natural frequencies.
Optimization outcomes for DAOA are compared with other methods by considering population size 50 and function number evaluations as 10000. Table 9 highlights size variables, best weight, average weight, standard deviation (STD) of weight, and a number of function evaluations gained for FIGURE 11. Best and average convergence curve obtained by AOA and DAOA for the 72-bar spatial truss.     [65] algorithms, respectively (see Table 9). According to Table 10, the natural frequency constraints of the presented method are strictly satisfied all bound. Fig 11. demonstrates that DAOA needs 3800 number analyses to obtain a feasible solution and ranked first among all other algorithms in this paper in terms of a number of function evaluations. Moreover, DAOA gives the best average weight among the mentioned algorithms. The twenty independent runs for 72-spatial bar truss for AOA and DAOA are shown in Fig 12. As depicted in Table 4 [35], TLBO [39], SBO [63], SOS [28]and CBO [65] algorithms, respectively. The standard deviation of DAOA is 0.3731, which ranked second among its competitors. These results show that DAOA is more reliable and superior than the other results reported in the literature. Moreover, it is found from the results that DAOA is more efficient than AOA.

3) 120-BAR DOME TRUSS
The 3 rd benchmark is presented in Fig 13. Initially, the 120-bar 3-D dome truss was optimized for size optimization by Kaveh and Zolghadr [68]. Table 6 shows the design considerations. There are non-structural masses added as 3000 Kg at node 1, 500 Kg at nodes 2 to 13 and 100 Kg at the rest of the free nodes. The elements are classified into seven groups by assuming symmetry about the z-axis. The minimum and maximum cross-sectional area are 1 and 129.3cm 2 , respectively. This example is solved with various algorithms such as PSO [36], CSS [35], DPSO [36], and VPS [64] by considering population size 50 and function number evaluations as 10000. Table 11 reveals size variables, best weight, average weight, standard deviation (STD) of   weight, and a number of function evaluations. As shown in Table 11, VPS [64] and DAOA ranked first and second, respectively, regarding the best optimization weight. Furthermore, DAOA finished the search process within 2400 function evaluations, the lightest number of function evaluations (see Fig 14.). AOA results show that this method found infeasible optimized designs with the highest weight of structures and could not escape from the local  trap. Moreover, after 2400 analyses, DAOA has reached satisfactory solutions. The best and average convergence curves of best runs for AOA and DAOA are depicted in Fig 14. The DAOA has the best weight of 8890.044 Kg, demonstrating that the new approach is more effective than the standard version of AOA. This is an optimal design improvement using the current algorithm. As regards Table 12, this approach still satisfies frequency constraints. Fig 15. demonstrates 20 individual runs of the final weights for AOA and DAOA.

4) 200-BAR PLANAR TRUSS
This study solved the fourth test problem concerning reducing weight of a planar structure of 200 bar shown in Fig 16. The design considerations for this problem are shown in Table 6. This example comprises 29 size variables for the cross-sectional areas of the element groups listed in Table 13.  The frequency restrictions are taken as follows: ω 1 ≥ 5 Hz, ω 2 ≥ 10 Hz, ω 3 ≥ 15 Hz. The upper nodes (1 to 5) of the truss are supplemented with 100 Kg non-structural masses. Table 16 demonstrates the lightest weight of structure obtained by DAOA is better than those other algorithms by considering population size 50 and function number evaluations as 20000. The DAOA has the best weight of 2102.458 Kg, demonstrating that the new approach is more effective than the other algorithms. This best of DAOA is 47.27%, 6.96%, 2.5%, 2.5%, 3.57%, 2.71% and 11.86% lighter than those of PSO [36], CSS [35], SBO [63], TLBO [39], SOS [28],CBO [65] and AOA. Fig 17. shows the best and mean convergence curves for the standard and dynamic version of AOA. Table 14 shows that the DAOA algorithm's average is lower than that of other algorithms, demonstrating the DAOA algorithm's superior performance. Compared with some other researchers, minimum weight and associated cross-sections of AOA and DAOA are acquired, and the findings are shown in Table 14. The natural frequencies of the best design obtained by other algorithms structures are shown in Table 15, which are satisfied by AOA and DAOA. In this study, the final weight of the 20 independent runs for AOA and DAOA is seen in Fig 18. This example's outcomes reveal DAOA surpasses the compared algorithms in regards to performance and accuracy.
The robustness of DAOA compared with AOA and other metaheuristic algorithms is proved by statistical results  obtained from 60 independent runs. Due to the introduction of two novel functions, the algorithm is able to break out of local optima and achieve great performance. The most remarkable attribute of DAOA is that there is no need for tuning parameters. The performance of DAOA is tested for four different truss structures. Performance and accuracy of VOLUME 10, 2022 the dynamic version of AOA surpass the standard version of AOA and compared algorithms.

VI. CONCLUSION
In this paper, the Dynamic Arithmetic Optimization Algorithm (DAOA) approach was proposed and tested for optimum weight design of four benchmark truss structures under frequency constraints. The DAOA benefits from two dynamic mechanism to alleviate the drawbacks of AOA. Truss optimization with natural frequency bound is a complicated problem in optimization, which has extraordinarily nonlinear and non-convex search areas with varying local optima. These examples are used to evaluate the proposed method's Efficiency (DAOA) against the standard version of AOA and some well-established metaheuristic algorithms. Four classical truss weight minimization problems (i.e., planar 37-bar, spatial 72-bar truss, 120-bar dome truss, 200-bar trusses), including up to 29 optimization variables, were used to prove the efficiency of the proposed algorithm. This new algorithm provides a proper balance between exploration and exploitation strategies that produce excellent accuracy and rapid convergence. The structural results of the design examples examined point to the algorithm's benefits in optimizing final solutions. The statistical results obtained by is considered as a competent rival for new metaheuristics. Also, the efficiency, accuracy, and performance of DAOA are much better than its standard version and other latest algorithm. The comparisons of convergence speeds also reveal that the algorithm provided is rapidly convergent. Results show that DAOA is an excellent approach for the sizing optimization of planar and spatial trusses and dome structures in the face of natural frequency design constraints.
Another area of research that should be pursued in the future is the combination and tuning of DAOA with other algorithms.
[67] A. Kaveh  NIMA KHODADADI (Member, IEEE) received the bachelor's degree in civil engineering and the master's degree in structural engineering from the University of Tabriz (one of the ten top universities in Iran). He is currently working as a Researcher with the Iran University of Science and Technology (IUST). His main research interests include the field of steel structures, particularly in the experimental and numerical investigation of steel braced frames. In addition, he has been actively involved in the area of engineering optimization, especially in evolutionary algorithms. Using comprehensive finite element analyses, he has also investigated the use of different shaped sections in real steel frames. Recently, he has been engaged in research in the area of engineering optimization, especially in solving large-scale and practical structural design problems.
VACLAV SNASEL (Senior Member, IEEE) is currently a Professor with the Department of Computer Science, VSB-Technical University of Ostrava, Czech Republic. He works as a Researcher and a University Teacher. He is also the Dean of the Faculty of Electrical Engineering and the Computer Science Department. He is also the Head of the Research Program IT4 Knowledge Management, European Center of Excellence IT4 Innovations. His research and development experience includes over 30 years in the industry and academia. He works in a multi-disciplinary environment involving artificial intelligence, social networks, conceptual lattice, information retrieval, semantic web, knowledge management, data compression, machine intelligence, neural networks, web intelligence, nature and bio-inspired computing, data mining, and applied to various real-world problems.
SEYEDALI MIRJALILI (Senior Member, IEEE) is currently a Professor and the Founding Director of the Centre for Artificial Intelligence Research and Optimization, Torrens University Australia. He is internationally recognized for his advances in optimization and swarm intelligence, including the first set of algorithms from a synthetic intelligence standpoint-a radical departure from how natural systems are typically understood-and a systematic design framework to reliably benchmark, evaluate, and propose computationally cheap robust optimization algorithms. He has published over 300 publications with over 40,000 citations and an H-index of 70. As the most cited researcher in robust optimization, he has been on the list of 1% highly-cited researchers and named as one of the most influential researchers in the world by Web of Science for three consecutive years, since 2019. In 2020, he was ranked 21st across all disciplines and 4th in artificial intelligence and image processing in the Stanford University's list of World's Top Scientists. In 2021, The Australian newspaper named him as the top researcher in Australia in three fields of artificial intelligence, evolutionary computation, and fuzzy systems. His research interests include optimization, swarm intelligence, evolutionary algorithms, and machine learning. He is an Associate Editor of several AI journals including Neurocomputing, Applied Soft Computing, Advances in Engineering Software, Computers in Biology and Medicine, Healthcare Analytics, Applied Intelligence, and IEEE ACCESS.