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Particle swarm optimization (PSO) is one of the most famous swarm-based optimization techniques inspired by nature. Due to its properties of flexibility and easy implementation, there is an enormous increase in the popularity of this nature-inspired technique. Particle swarm optimization (PSO) has gained prompt attention from every field of researchers. Since its origin in 1995 till now, researchers have improved the original Particle swarm optimization (PSO) in varying ways. They have derived new versions of it, such as the published theoretical studies on various parameters of PSO, proposed many variants of the algorithm and numerous other advances. In the present paper, an overview of the PSO algorithm is presented. On the one hand, the basic concepts and parameters of PSO are explained, on the other hand, various advances in relation to PSO, including its modifications, extensions, hybridization, theoretical analysis, are included.

The goal of the paper is to present a solution to improve the fault detection accuracy of rolling bearings. The method is based on variational mode decomposition (VMD), multiscale permutation entropy (MPE) and the particle swarm optimization-based support vector machine (PSO-SVM). Firstly, the original bearing vibration signal is decomposed into several intrinsic mode functions (IMF) by using the VMD method, and the feature energy ratio (FER) criterion is introduced to reconstruct the bearing vibration signal. Secondly, the multiscale permutation entropy of the reconstructed signal is calculated to construct multidimensional feature vectors. Finally, the constructed multidimensional feature vector is fed into the PSO-SVM classification model for automatic identification of different fault patterns of the rolling bearing. Two experimental cases are adopted to validate the effectiveness of the proposed method. Experimental results show that the proposed method can achieve a higher identification accuracy compared with some similar available methods (e.g., variational mode decomposition-based multiscale sample entropy (VMD-MSE), variational mode decomposition-based multiscale fuzzy entropy (VMD-MFE), empirical mode decomposition-based multiscale permutation entropy (EMD-MPE) and wavelet transform-based multiscale permutation entropy (WT-MPE)).

In this paper, an improved version of the particle swarm optimization algorithm is proposed for the online tuning of power system stabilizers in a standard four-machine two-area power system to mitigate local and inter-area mode oscillations. Moreover, an innovative objective function is proposed for performing the optimization, which is a weight function of two functions. The first part of fitness is the function of the angular velocity deviation of the generators, and the other part is a function based on the percentage of undershoot and maximum overshoot, and also the damping time of the power system oscillations. The performance of the proposed stabilization method is compared with the genetic algorithm and bacteria foraging algorithm results. Simulations are made in three different power system operation conditions by changing the system load. The simulation results indicate the superiority of the proposed method over the genetic algorithm and bacteria foraging algorithm. In all the scenarios, power system oscillations are damped faster and with lower amplitude when the power system stabilizers coordinate with the proposed optimization method.

The ever-increasing electricity demand, its dependency on fossil fuels, and the consequent environmental degradation are major concerns of this era. The worldwide domination of fossil fuels in bulk electricity generation is rapidly increasing the emissions of CO2 and other environmentally dangerous gases that are contributing to climate change. The economic and emission dispatch are two important problems in thermal power generation whose combination produces a complex highly constrained nonlinear optimization problem known as combined economic and emission dispatch. The optimization of combined economic and emission dispatch aims to allocate the generation of committed units to minimize fuel cost and emissions, simultaneously while honoring all equality and inequality constraints. Therefore, in this article, we investigate a solution of the combined economic and emission dispatch problem using quantum particle swarm optimization and its two modified versions, that is, enhanced quantum particle swarm optimization and quantum particle swarm optimization integrated with weighted mean personal best and adaptive local attractor. The enhanced quantum particle swarm optimization algorithm achieves particles’ diversification at early stages and shows good performance in local search at later stages. The quantum particle swarm optimization integrated with weighted mean personal best and adaptive local attractor boosts search performance of quantum particle swarm optimization and attains better global optimality. The suggested methods are employed to achieve solution for the combined economic and emission dispatch in four distinct systems, encompassing two scenarios with 6 units each, one with a 10-unit configuration, and another with an 11-unit setup. A comparative analysis with methodologies documented in existing literature reveals that the proposed approach outperforms others, demonstrating superior computational performance and robust efficiency.

Particle swarm optimization (PSO) is an effective method for solving a wide range of problems. However, the most existing PSO algorithms easily trap into local optima when solving complex multimodal function optimization problems. This paper presents a variation, called adaptive PSO based on clustering (APSO-C), by considering the population topology and individual behavior control together to balance local and global search in an optimization process. APSO-C has two steps. First, via a K-means clustering operation, it divides the swarm dynamically in the whole process to construct variable subpopulation clusters and after that adopts a ring neighborhood topology for information sharing among these clusters. Then, an adaption mechanism is proposed to adjust the inertia weight of all individuals based on the evaluation results of the states of clusters and the swarm, thereby giving the individual suitable search power. The experimental results of fourteen benchmark functions show that APSO-C has better performance in the terms of convergence speed, solution accuracy and algorithm reliability than several other PSO algorithms.

Particle swarm optimization (PSO) is a population-based swarm intelligence algorithm that falls under the category of nature-inspired algorithms and is similar to evolutionary computing in various ways. Rather than the survival of the fittest, the PSO is driven by a representation of a social psychological model inspired by the group behaviors of birds and other social species. The particle's position is modified in PSO based on its position as well as velocity, while in quantum mechanics, the trajectory idea is absurd; however, the uncertainty principle suggests that a particle's position, as well as velocity, cannot be determined simultaneously. As a result, an advanced version of the quantum mechanics-based PSO method is proposed. The study in this paper is focused on an investigation of a new quantum-behaved PSO (QPSO) method called Gaussian quantum-behaved particle swarm optimization (GQPSO), which uses a mutation operator with a Gaussian distribution and is inspired by classical PSO methods and quantum mechanics concepts. In GQPSO, inadequate control parameter tuning results in poor solutions. To better understand the effect of different control parameters and their implications on GQPSO results, this paper used a full parametric sensitivity analysis on five different problems (the Design of a pressure vessel, Tension/Spring Compression, Rastrigin function, Ackley function, and Constrained Box Volume Problem). By adjusting each parameter one at a time, different optimization problems were used to investigate GQPSO. As a result, to allow particles to change their earliest best solution based on viability, a constraint-handling mechanism was developed. The optimal parameter set for GQPSO is provided based on the analysis of the results. With the help of the proposed optimal parameter set (contraction–expansion coefficient values as (1 = 1.6,2 = 1.3), swarm size as ‘350’, and number of Iterations as ‘500’), GQPSO returned an optimized solution for Rastrigin and Ackley functions. It also performed better in the case of the design of a pressure vessel and tension/spring compression problems in comparison to the existing solution available in related literature. As per the findings of the sensitivity analysis, GQPSO is the most sensitive to the contraction-expansion coefficient in comparison to the maximum number of iterations (itermax) and swarm size (‘n’).

In electric power system, the vital topic to be mooted is economic load dispatch (ELD). It is a non-linear problem with some unavoidable constraints such as valve point loading and ramp rate constraint. For solving ELD problem distint methods were devised and tried for different electric supply systems yielding slow convergence rates. To achieve fast convergence, dual objective multi constraint swarm optimization based advanced economic load dispatch (DOMSOBAELD) algorithm is proposed making use of simulated values of real power outages of a thermal power plant as initial estimates for PSO technique embedded in it and used for optimizing economic dispatch problem in this article. DOMSOBAELD method was developed in the form of amalgamating fluids. Presence of power line losses, multiple valves in steam turbines, droop constraints and inhibited zones were utilized to optimize the ELD problem as genuinely approximate as possible. The results obtained from DOSOBAELD are compared with particle swarm optimization (PSO), PSOIW and differential particle swarm optimization (DPSO) techniques. It is quite conspicuous that DOMSOBAELD yielded minimum cost values with most favourable values of real unit outputs. Thus the proposed method proves to be advantageous over other heuristic methods and yields best solution for ELD by selecting incremental fuel cost as the decision variable and cost function as fitness function.

Hybridizing particle swarm optimization (PSO) with differential evolution (DE), this paper proposes an integrated PSO–DE optimizer and examines the performance of this optimizer. Firstly, a new self-adaptive PSO (SAPSO) is established to guide movements of particles in the proposed hybrid PSO. Aiming at well trade-offing the global and local search capabilities, a self-adaptive strategy is proposed to adaptively update the three main control parameters of particles in SAPSO. Since the performance of PSO heavily relies on its convergence, the convergence of SAPSO is analytically investigated and a convergence-guaranteed parameter selection rule is provided for SAPSO in this study. Subsequently, a modified self-adaptive differential evolution is presented to evolve the personal best positions of particles in the proposed hybrid PSO in order to mitigant the potential stagnation issue. Next, the performance of the proposed method is validated via 25 benchmark test functions and two real-world problems. The simulation results confirm that the proposed method performs significantly better than its peers at a confidence level of 95% over the 25 benchmarks in terms of the solution optimality. Besides, the proposed method outperforms its contenders over the majority of the 25 benchmarks with respect to the search reliability and the convergence speed. Moreover, the computational complexity of the proposed method is comparable with those of some other enhanced PSO–DE methods compared. The simulation results over the two real-world issues reveal that the proposed method dominates its competitors as far as the solution optimality is considered.

Portfolio optimization is a multi-objective optimization problem (MOOP) with risk and profit, or some form of the two, as competing objectives. Single-objective portfolio optimization requires a trade-off coefficient to be specified in order to balance the two objectives. Erwin and Engelbrecht proposed a set-based approach to single-objective portfolio optimization, namely, set-based particle swarm optimization (SBPSO). SBPSO selects a sub-set of assets that form a search space for a secondary optimization task to optimize the asset weights. The authors found that SBPSO was able to identify good solutions to portfolio optimization problems and noted the benefits of redefining the portfolio optimization problem as a set-based problem. This paper proposes the first multi-objective optimization (MOO) approach to SBPSO, and its performance is investigated for multi-objective portfolio optimization. Alongside this investigation, the performance of multi-guide particle swarm optimization (MGPSO) for multi-objective portfolio optimization is evaluated and the performance of SBPSO for portfolio optimization is compared against multi-objective algorithms. It is shown that SBPSO is as competitive as multi-objective algorithms, albeit with multiple runs. The proposed multi-objective SBPSO, i.e., multi-guide set-based particle swarm optimization (MGSBPSO), performs similarly to other multi-objective algorithms while obtaining a more diverse set of optimal solutions.

Restructuring Particle Swarm Optimization (RPSO) algorithm has been developed as an intelligent approach based on the linear system theory of particle swarm optimization (PSO). It streamlines the flow of the PSO algorithm, specifically targeting continuous optimization problems. In order to adapt RPSO for solving discrete optimization problems, this paper proposes the binary Restructuring Particle Swarm Optimization (BRPSO) algorithm. Unlike other binary metaheuristic algorithms, BRPSO does not utilize the transfer function. The particle updating process in BRPSO relies solely on comparison results between values derived from the position updating formula and a random number. Additionally, a novel perturbation term is incorporated into the position updating formula of BRPSO. Notably, BRPSO requires fewer parameters and exhibits high exploration capability during the early stages. To evaluate the efficacy of BRPSO, comprehensive experiments are conducted by comparing it against four peer algorithms in the context of feature selection problems. The experimental results highlight the competitive nature of BRPSO in terms of both classification accuracy and the number of selected features.