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The Newton-Raphson-Based Optimizer (NRBO), a new metaheuristic algorithm, is suggested and developed in this paper. The NRBO is inspired by Newton-Raphson's approach, and it explores the entire search process using two rules: the Newton-Raphson Search Rule (NRSR) and the Trap Avoidance Operator (TAO) and a few groups of matrices to explore the best results further. The NRSR uses a Newton-Raphson method to improve the exploration ability of NRBO and increase the convergence rate to reach improved search space positions. The TAO helps the NRBO to avoid the local optima trap. The performance of NRBO was assessed using 64 benchmark numerical functions, including 23 standard benchmarks, 29 CEC2017 constrained benchmarks, and 12 CEC2022 benchmarks. In addition, the NRBO was employed to optimize 12 CEC2020 real-world constrained engineering optimization problems. The proposed NRBO was compared to seven state-of-the-art optimization algorithms, and the findings showed that the NRBO produced promising results due to its features, such as high exploration and exploitation balance, high convergence rate, and effective avoidance of local optima capabilities. In addition, the NRBO also validated on challenging wireless communication problem called the internet of vehicle problem, and the NRBO was able to find the optimal path for data transmission. Also, the performance of NRBO in training the deep reinforcement learning agents is also studied by considering the mountain car problem. The obtained results also proved the NRBO's excellent performance in handling challenging real-world engineering problems. [ABSTRACT FROM AUTHOR]

In the mid 1990s two landmark metaheuristics have been proposed: Particle Swarm Optimization and Differential Evolution. Their initial versions were very simple, but rapidly attracted wide attention. During the last quarter century hundreds of variants of both optimization algorithms have been proposed and applied in almost any field of science or engineering. However, no broader comparison of performance between both families of methods has been presented so far. In the present paper ten Particle Swarm Optimization and ten Differential Evolution variants, from historical ones from the 1990s up to the most recent ones from 2022, are compared on numerous single-objective numerical benchmarks and 22 real-world problems. On average Differential Evolution algorithms clearly outperform Particle Swarm Optimization ones. Such advantage of Differential Evolution over Particle Swarm Optimization is in contradiction with popularity: In the literature Particle Swarm Optimization algorithms are two–three times more frequently used than Differential Evolution ones. Problems for which Particle Swarm Optimization performs better than Differential Evolution do exist but are relatively few. Although this result may be an effect of the choice of specific variants, experimental settings or problems used for comparison, some re-consideration of algorithmic philosophy may be needed for Particle Swarm Optimization variants to make them more competitive. [ABSTRACT FROM AUTHOR]