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This review aims to exploit a study on different benchmark test functions used to evaluate the performance of Meta-Heuristic (MH) optimization techniques. The performance of the MH optimization techniques is evaluated with the different sets of mathematical benchmark test functions and various real-world engineering design problems. These benchmark test functions can help to identify the strengths and weaknesses of newly proposed MH optimization techniques. This review paper presents 215 mathematical test functions, including mathematical equations, characteristics, search space and global minima of the objective function and 57 real-world engineering design problems, including mathematical equations, constraints, and boundary conditions of the objective functions carried out from the literature. The MATLAB code references for mathematical benchmark test functions and real-world design problems, including the Congress of Evolutionary Computation (CEC) and Genetic and Evolutionary Computation Conference (GECCO) test suite, are presented in this paper. Also, the winners of CEC are highlighted with their reference papers. This paper also comprehensively reviews the literature related to benchmark test functions and real-world engineering design challenges using a bibliometric approach. This bibliometric analysis aims to analyze the number of publications, prolific authors, academic institutions, and country contributions to assess the field's growth and development. This paper will inspire researchers to innovate effective approaches for handling inequality and equality constraints. [ABSTRACT FROM AUTHOR]

This paper presents an improved arithmetic optimization algorithm that incorporates hybrid elite pool strategies to address the limitations of the arithmetic optimization algorithm (AOA). In AOA, the linear mathematical optimization acceleration (MOA) function cannot balance global exploitation and local exploration well. Therefore, the accuracy and convergence speed of the algorithm cannot be guaranteed. To improve the performance of AOA, this paper reconstructed a nonlinear MOA function, which is expected to balance the exploitation and the exploration of AOA. Furthermore, four hybrid elite pool strategies are integrated to enhance the ability to escape local optima. The proposed algorithm inherits the fast convergence of AOA and develops the performance of escaping local optima. Numerical experiment results on benchmark functions and engineering problems show that the proposed algorithm outperforms other compared meta-heuristic algorithms in terms of convergence speed and accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a data relay system consisting of multiple unmanned aerial vehicles (UAVs) and acess point (AP) with the aim of maximizing the minimum receiving rate of Internet of things devices (IoTDs) as the optimization objective. To enhance the utilization of communication resources, we employed non-orthogonal multiple access (NOMA) and successive interference cancellation (SIC) techniques at the AP side. In addition, we used the Wireless power transmission (WPT) technique on the UAV side to charge the IoTDs and prolong their operational lifetime. We formulated the problem as a mixed integer nonlinear programming (MINLP). To solve the MINLP problem, it was decomposed into four subproblems: connection scheduling between UAVs and IoTDs, time slot allocation, UAV trajectory, and AP's power distribution. Finally, we solved all subproblems by using convex optimization techniques, such as successive convex approximations (SCA), and proposed an iterative algorithm. In the simulation, we compared our proposed algorithm with different optimization schemes. The results indicated that our scheme outperforms the others. [ABSTRACT FROM AUTHOR]

This paper developed a new and efficient approach, the metaheuristic optimisation approach based on the Kalman filter (KF), to accurately identify the infinite impulse response (IIR) system coefficients. A recently developed metaheuristic optimisation technique called the manta-ray foraging optimisation (MRFO) algorithm has been employed to solve the proper parameters tuning exertion of KF. The problem of achieving better unknown state estimations by the conventional KF is closely connected with decent prior information about the noise statistics (measurement and process noise). However, the statistics mentioned above depend on the types of applications and process dynamics. The use of insufficiently known priori filter statistics would reduce the precision of the estimated filter or sometimes lead to a practical divergence of the filter. To alleviate this problem, the proposed technique initially produces optimally tuned KF parameters using the MRFO algorithm, and then the conventional KF method estimates the coefficients of the IIR model using the optimised KF parameters obtained at the beginning. The simulation studies have been carried out on three distinct order benchmark IIR systems (both same and reduced-order), and two prominent IIR applications called direct current (DC) motor and fractional order digital differentiator (FODD) using the proposed method. The overall identification results demonstrate that the proposed MRFO-KF technique significantly improves performance metrics over competing techniques, such as basic KF, other employed metaheuristic-based KF schemes and recently reported state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Particle swarm optimization approach (PSO) has illustrated promising performance on a variety of optimization problems. The critical issues that must be addressed in PSO research are how to balance conflicts around exploration, exploitation, and reasonably distribute computational resources. In this paper, a neighborhood-aware N states Markovian Switching PSO algorithm (NS-MJPSOloc) is proposed, where we have employed a local search based approach. The neighborhood of PSO algorithm is a single particle itself in the early stages of optimization. The neighborhood will eventually expand to include all particles as the amount of generations increases. The search space is segmented into N potential states according to the size of problem. The value of N is dependent on the dimension of problem space. Every iteration serves a transition probability-based Markovian switching technique to estimate the acceleration coefficients in an adaptable way. The transition probability determines the next state and adequate values for acceleration coefficients. Through adopting a local search strategy while interacting with all other particles in the group, every particle possesses a chance of improving itself. Moreover, new features have been incorporated to accomplish accuracy and stability. The primary contributions of the proposed work are to enhance the topological structure of a recently developed PSO variant by using a local search (loc) mechanism rather than a global (gbest) approach. The purpose of this idea is to develop a more adaptable and less sensitive novel version of PSO that can handle multi-modal and highly challenging problems. The proposed algorithm was then tested using a variety of uni-modal, multi-modal and rotated benchmark functions. The experimental findings show that the proposed NS-MJPSOloc outperformed most of the current versions in terms of accuracy and convergence time, notably for multi-modal problems. [ABSTRACT FROM AUTHOR]

Multiple unmanned aerial vehicle (UAV) path planning is the benchmark problem of multiple UAV application, which belongs to the non-deterministic polynomial problem. Its objective is to require multiple UAV to fly safely to the goal position according to their specific start position in three-dimensional space. This issue can be defined as a high-dimensional optimization problem, the solution of which requires optimization techniques with global optimization capabilities. Equilibrium optimizer (EO) is a population-based meta-heuristic algorithm. To improve the optimization ability of EO to solve high-dimensional problems, this paper proposes a modified equilibrium optimizer with generalized opposition-based learning (MGOEO), which improves the population activity by increasing the internal mutation and cross of the population. In addition, the generalized opposition-based learning is used to construct the population, which can effectively ensure that the algorithm has ability to jump out of the limitation of local optimal. First, numerical experiments show that MGOEO has better optimization precision than EO and several other swarm intelligent algorithms. Then, the paths of UAVs are simulated in three different obstacle environments. The simulation results show that MGOEO can obtain safe and smooth paths, which are better than EO and other eight state-of-the-art optimization algorithms. [ABSTRACT FROM AUTHOR]

Teaching–learning-based optimization (TLBO) algorithm is an excellent human-inspired optimization technique. This paper proposes an innovative improved version of TLBO—collectivism teaching–learning-based optimization (CTLBO) algorithm. This algorithm imitates group and individual behaviours in the reality of teaching and learning, applies group-individual multi-mode cooperation strategies to form new search mechanism. The CTLBO contains three phases, i.e. preparation phase, teaching and learning phases. In the preparation phase, there are two operators, i.e. teacher self-learning and teacher-learner interaction operators. In the teaching phase, class teaching and performance-based group teaching operators are implied. In the learning phase, neighbour learning, student self-learning and team-learning strategies are mixed together to form three operators. Two sets of experiments are conducted to test the performance of CTLBO. The first set of experiments validates the improvement effect of CTLBO by comparing it with the original TLBO and other authors' improved versions of TLBO. The second set of experiments illustrates the advantage of CTLBO by comparing it with other 17 meta-heuristic algorithms in solving 30 general benchmark functions and 15 CEC2015 test suit functions. The results of experiments show that CTLBO algorithm has significant improvement effect compared with TLBO. It is the most effective one amongst the improved versions of TLBO selected for comparison, and outperforms all other 17 meta-heuristic algorithms. The algorithm can significantly improve the convergence ability and the accuracy in solving different-scale complex optimization models. [ABSTRACT FROM AUTHOR]