Canonical Particle Swarm Optimization Research Articles

Spectral reflectance reconstruction based on wideband multi-illuminant imaging and a modified particle swarm optimization algorithm.

A method for spectral reflectance factor reconstruction based on wideband multi-illuminant imaging was proposed, using a programmable LED lighting system and modified Bare Bones Particle Swarm Optimization algorithms. From a set of 16 LEDs with different spectral power distributions, nine light sources with correlated color temperatures in the range of 1924 K - 15746 K, most of them daylight simulators, were generated. Samples from three color charts (X-Rite ColorChecker Digital SG, SCOCIE ScoColor paint chart, and SCOCIE ScoColor textile chart), were captured by a color industrial camera under the nine light sources, and used in sequence as training and/or testing colors. The spectral reconstruction models achieved under multi-illuminant imaging were trained and tested using the canonical Bare Bones Particle Swarm Optimization and its proposed modifications, along with six additional and commonly used algorithms. The impacts of different illuminants, illuminant combinations, algorithms, and training colors on reconstruction accuracy were studied comprehensively. The results indicated that training colors covering larger regions of color space give more accurate reconstructions of spectral reflectance factors, and combinations of two illuminants with a large difference of correlated color temperature achieve more than twice the accuracy of that under a single illuminant. Specifically, the average reconstruction error by the method proposed in this paper for patches from two color charts under A + D90 light sources was 0.94 and 1.08 CIEDE2000 color difference units. The results of the experiment also confirmed that some reconstruction algorithms are unsuitable for predicting spectral reflectance factors from multi-illuminant images due to the complexity of optimization problems and insufficient accuracy. The proposed reconstruction method has many advantages, such as being simple in operation, with no requirement of prior knowledge, and easy to implement in non-contact color measurement and color reproduction devices.

Uncovering personal circadian responses to light through particle swarm optimization

Background and objectivesKronauer's oscillator model of the human central pacemaker is one of the most commonly used approaches to study the human circadian response to light. Two sources of error when applying it to a personal light exposure have been identified: (1) as a populational model, it does not consider inter-individual variability, and (2) the initial conditions needed to integrate the model are usually unknown, and thus subjectively estimated. In this work, we evaluate the ability of particle swarm optimization (PSO) algorithms to simultaneously uncover the optimal initial conditions and individual parameters of a pre-defined Kronauer's oscillator model. MethodsA Canonical PSO, a Dynamic Multi-Swarm PSO and a novel modification of the latter, namely Hierarchical Dynamic Multi-Swarm PSO, are evaluated. Two different target models (under a regular and an irregular schedule) are defined, and the same realistic light profile is fed to them. Based on their output, a fitness function is proposed, which is minimized by the algorithms to find the optimum set of parameters and initial conditions of the model. ResultsWe demonstrate that Dynamic Multi-Swarm and Hierarchical Dynamic Multi-Swarm algorithms can accurately uncover personal circadian parameters under both regular and irregular schedules, but as expected, optimization is easier under a regular schedule. Circadian parameters play the most important role in the optimization process and should be prioritized over initial conditions, although assessment of the impact of misestimating the latter is recommended. The log-log linear relationship between mean absolute error and computational cost shows that the number of particles to use is at the discretion of the user. ConclusionsThe robustness and low errors achieved by the algorithms support their further testing, validation and systematic application to empirical data under a regular or irregular schedule. Uncovering personal circadian parameters can improve the assessment of the circadian status of a person and the applicability of personalized light therapies, as well as help to discover other factors that may lie behind the interindividual variability in the circadian response to light.

A Particle Swarm Optimization With Adaptive Learning Weights Tuned by a Multiple-Input Multiple-Output Fuzzy Logic Controller

In a canonical particle swarm optimization (PSO) algorithm, the fitness is a widely accepted criterion when selecting exemplars for a particle, which exhibits promising performance in simple unimodal functions. To improve a PSO's performance on complicated multimodal functions, various selection strategies based on the fitness value are introduced in PSO community. However, the inherent defects of the fitness-based selections still remain. In this paper, a novelty of a particle is treated as an additional criterion when choosing exemplars for a particle. In each generation, a few of elites and mavericks who have better fitness and novelty values are selected, and saved in two archives, respectively. Hence, in each generation, a particle randomly selects its own learning exemplars from the two archives, respectively. To strengthen a particle's adaptive capability, a multipleinput multiple-output fuzzy logic controller is used to adjust two parameters of the particle, i.e., an acceleration coefficient and a selection proportion of elites. The experimental results and comparisons between our new proposed PSO, named as MFCPSO in this paper, and other 6 PSO variants on CEC2017 test suite with 4 different dimension cases suggest that MFCPSO exhibits very promising characteristics on different types of functions, especially on large scale complicated functions. Furthermore, the effectiveness and efficiency of the fuzzy controlled parameters are discussed based on extensive experiments.

Evaluating the risk of uncertainty in smart grids with electric vehicles using an evolutionary swarm-intelligent algorithm

In the last years, distributed clean energy resources such as solar irradiation, wind generation and electric vehicles as dispatchable units have been targeted as alternatives to fossil fuels in supplying the high energy demand of our society. Managing these distributed energy resources is a complex challenge, due to its uncertain behavior. In order to maintain a stable and profitable functioning of electrical systems, the development of strategies and algorithms to deal with the risk associated with this uncertainty deserves proper attention. This work addresses a risk-based energy resource management (ERM) optimization problem that deals with the day-ahead management, considering the occurrence of extreme events in a risk-averse strategy. In a risk-averse strategy, the worst case scenario cost is evaluated through the use of conditional value-at-risk (CVaR) method. To solve this ERM problem, we proposed the use of an improved version of Canonical Differential Evolutionary Particle Swarm Optimization (C-DEEPSO). This modification relies on the use of an adaptive velocity and on local search operators to improve search capability. The results indicated that, compared to two algorithms based on swarm intelligence, the proposed improved C-DEEPSO is able to provide solutions that not only reduce costs (in terms of thousands of monetary units) but also protects the aggregator against extreme scenarios.

Particle swarm optimization with Chebychev functional-link network model for engineering design problems

In recent years, many improved particle swarm optimization (PSO) algorithms have been developed to improve the performance of PSO. These improved algorithms have greatly improved PSO performance, but PSO still has some shortcomings. So, an particle swarm optimization with Chebychev functional-link network model is proposed (APSOCFLN) in this paper. Firstly, in order to make up for the shortcomings of the canonical PSO update search, a novel Chebychev functional-link network (CFLN) elite guidance strategy is proposed. Two different update mechanisms are executed alternately, increasing the diversity of the algorithm population and making the algorithm more capable of jumping out of local optimization. Secondly, in order to better balance the exploration and exploitation of the algorithm, an adaptive probability strategy is proposed. Thirdly, an adaptive weighting strategy is proposed. It will be used for CFLN elite guidance strategy and give different weights to the two alternating update strategies, which can effectively solve the problem of premature convergence of PSO. Fourthly, the APSOCFLN and comparison algorithms are used to solve the practical engineering problems, and the results show that APSOCFLN has high precision, fast convergence , and excellent performance. Finally, the performance of the algorithm is tested with CEC2017 and CEC2022 benchmark functions. The comparative algorithm includes the classical PSO improvement algorithms and the classical other algorithms, and the experimental results show the effectiveness of the proposed strategy and the good performance of the improved algorithm.

Gravity particle swarm optimization algorithm for solving shop visit balancing problem for repairable equipment

The particle swarm optimization (PSO) algorithm has received much attention from engineering and scientific fields since it was proposed. Nevertheless, when solving complex combinatorial optimization tasks such as the proposed shop visit balancing problem for repairable equipment (SVBPRE), the canonical PSO is still prone to fall into the local optimal stagnation. Therefore, a novel intelligent optimization algorithm, namely gravity particle swarm optimization (GPSO) algorithm, is proposed to remedy the above defects. This algorithm improves the velocity updating strategy of particles in the population, which can effectively improve the global search ability of the algorithm without increasing the time complexity, so that it can jump out of the local optimal position and find the feasible solution in the complex solution space. To verify its performance, many experimental verifications were carried out. Firstly, the effectiveness of the proposed GPSO was verified by comparing with the PSO on the 8 benchmark functions. Secondly, the superiority and advancement of GPSO were proved by comparing with 10 state-of-the-art original optimizers and variant algorithms on 23 benchmark tasks. Finally, based on the constructed shop visit balancing problem model, a series of simulation data cases were generated according to the operation and maintenance data in engineering practice for verification. The results obtained by comparing with 4 commonly used algorithms in engineering demonstrate that the proposed GPSO is superior to other competitors in terms of quality of solutions and has important theoretical significance and application value for solving practical tasks with complex search space.

Pyramid particle swarm optimization with novel strategies of competition and cooperation

Particle swarm optimization (PSO) has shown its advantages in various optimization problems. Topology and updating strategies are among its key concepts and have significant impacts on optimization ability. This paper proposes a pyramid PSO (PPSO) with novel competitive and cooperative strategies to update particles’ information. PPSO builds a pyramid and assigns each particle to a specific layer according to its fitness. The particles at the same layer will make a pairwise comparison to determine the winners and the losers. The losers will cooperate with their corresponding winners, while the winners will cooperate with the particles at the upper layer and those at the top layer. Each particle in PPSO has its own learning behavior, having more than one exemplar rather than the only global best to learn from. The diversity of the swarm is enhanced and it positively affects the performance of PSO. Extensive experiments demonstrate that the PPSO has superior performance in terms of accuracy, Wilcoxon signed-rank test and convergence speed, yet achieves comparable running time in most cases, when compared with the canonical PSO and eight state-of-the-art PSO variants. Furthermore, we analyze the influence of parameters for the PPSO. All these illustrate that the PPSO is promising for numerical optimization.

Prediction of exchange rate using improved particle swarm optimised radial basis function networks

In this paper, a radial basis function neural network (RBFN) model has been trained by canonical particle swarm optimisation (PSO) and improved particle swarm optimisation (IMPSO) algorithms to efficiently predict the exchange rate of Indian rupees against the exchange rate of G-7 countries for future days. We have used two variants of PSO such as canonical PSO and IMPSO for optimising the parameters of radial basis function neural network through learning from the past data of exchange rate prediction. Here, we have considered 43 countries' exchange rates to predict the Indian rupees against the G-7 countries. Forty-three exchange rates have been collected and based on their correlation analysis a dataset has been prepared to validate the proposed model. In addition, a fair comparison has been carried out between IMPSO tuned RBFN and canonical PSO tuned RBFN with respect to the results obtained by varying the number of iterations for future days' prediction. From the experimental results, it is observed that the predictive performance of IMPSO tuned RBFN modelling the case of higher number of iterations is promising vis-à-vis canonical PSO tuned RBFNs model.

Adaptive heterogeneous particle swarm optimization with comprehensive learning strategy

This paper proposes an adaptive heterogeneous particle swarm optimization with a comprehensive learning strategy for solving single-objective constrained optimization problems. In this algorithm, particles can use an exploration strategy and an exploitation strategy to update their positions. The historical success rates of the two strategies are used to adaptively control the adoption rates of strategies in the next iteration. The search strategy in the canonical particle swarm optimization algorithm is based on elite solutions. As a result, when no particles can discover better solutions for several generations, this algorithm is likely to fall into stagnation. To respond to this challenge, a new strategy is proposed to explore the neighbors of the elite solutions in this study. Finally, a constraint handling method is equipped to the proposed algorithm to make it be able to solve constrained optimization problems. The proposed algorithm is compared with the canonical particle swarm optimization, differential evolution, and several recently proposed algorithms on the benchmark test suite. The Wilcoxon signed-rank test results show that the proposed algorithm is significantly better on most of the benchmark problems compared with the competitors. The proposed algorithm is also applied to solve two real-world mechanical engineering problems. The experimental results show that the proposed algorithm performs consistently well on these problems.

Performance Comparison of Variants Based on Swarm Intelligence Algorithm of Mathematical and Structural Optimization

In this paper, three different variants of the canonical particle swarm optimization (PSO) algorithm are compared in terms of their optimal solutions to engineering optimization problems. The PSO often face to premature convergence due to its weak capability in local exploitation, which leads to a low optimization precision or even failure. Moreover, the computational burden is also one of the obstacles for the PSO when solving complex problems. To overcome these drawbacks, the original PSO algorithm is integrated with the knowledge sharing and auxiliary mechanisms of comprehensive learning (CL) and Gaussian local search (GLS) strategies to form the so-called GLS-PSO, CLPSO, and GLS-CLPSO algorithms. To demonstrate the accuracy and robustness of the three variants, their performance is tested on a benchmark spatial truss structure with continuous variables. The obtained optimization results are then compared with those by other PSO variants in the literature.

Optimal coordination of directional overcurrent relays using hybrid fractional computing with gravitational search strategy

The protection system has a vital role in subsystems of the power network including the generation, transmission and distribution system. This system combines several types of protection relays including directional over current relay, differential relay, distance relay, earth faults relay, inverse definite minimum time (IDMT) relay for the protection of line, generators bus bars, transformers, line to ground faults and feeder lines of the power system. In this research paper, the overall performance of the protection system is improved by reducing the overall operational time of directional over current relays (DOCRs) through the optimal coordination between the primary and backup over current protective relays while keeping the time multiplier setting (TMS), pickup tap setting (PTS) and coordination time of interval (CTI) within the allowable limits. A new optimization strategy, namely the FPSOGSA, is developed by integrating the concept of fractional calculus inside the mathematical model of canonical particle swarm optimization and combining with traditional gravitational search algorithm to enhance the optimizer characteristics and tested on coordination problem of DOCRs in standard power systems including the IEEE 3, 8 and 15 bus networks. The results, yielded by proposed algorithm and their comparison with other well-known recently established counterparts, reveal that the synergy of FC, PSO and GSA enhance the performance of the optimizer by combining the individual strengths of these tools and finding the best global solution. The consistency, stability and reliability of FPSOGSA is endorsed by comprehensive statistical analysis based on the empirical cumulative distribution function, histograms, boxplot illustrations, quantile–quantile plots, minimum fitness evolution in each independent simulation.

Dynamic Electric Dispatch for Wind Power Plants: A New Automatic Controller System Using Evolutionary Algorithms

In this paper, we use an evolutionary swarm intelligence approach to build an automatic electric dispatch controller for an offshore wind power plant (WPP). The optimal power flow (OPF) problem for this WPP is solved by the Canonical Differential Evolutionary Particle Swarm Optimization algorithm (C-DEEPSO). In this paper, C-DEEPSO works as a control system for reactive sources in energy production. The control operation takes place in a daily energy dispatch, scheduled into 15 min intervals and resulting in 96 operating test scenarios. As the nature of the optimization problem is dynamic, a fine-tuning of the initialization parameters of the optimization algorithm is performed at each dispatch interval. Therefore, a version of the C-DEEPSO algorithm has been built to automatically learn the best set of initialization parameters for each scenario. For this, we have coupled C-DEEPSO with the irace tool (an extension of the iterated F-race (I/F-Race)) by using inferential statistic techniques. The experiments carried out showed that the methodology employed here is robust and able to tackle this OPF-like modeling. Moreover, the methodology works as an automatic control system for a dynamic schedule operation.

Novel Supervisory Management Scheme of Hybrid Sun Empowered Grid-Assisted Microgrid for Rapid Electric Vehicles Charging Area

The spread of electric vehicles (EV) contributes substantial stress to the present overloaded utility grid which creates new chaos for the distribution network. To relieve the grid from congestion, this paper deeply focused on the control and operation of a charging station for a PV/Battery powered workplace charging facility. This control was tested by simulating the fast charging station when connected to specified EVs and under variant solar irradiance conditions, parity states and seasonal weather. The efficacy of the proposed algorithm and experimental results are validated through simulation in Simulink/Matlab. The results showed that the electric station operated smoothly and seamlessly, which confirms the feasibility of using this supervisory strategy. The optimum cost is calculated using heuristic algorithms in compliance with the meta-heuristic barebones Harris hawk algorithm. In order to long run of charging station the sizing components of the EV station is done by meta-heuristic barebones Harris hawk optimization with profit of USD 0.0083/kWh and it is also validated by swarm based memetic grasshopper optimization algorithm (GOA) and canonical particle swarm optimization (PSO).

Bi-objective optimization of a queueing model with two-phase heterogeneous service

This paper presents a novel queueing model describing the operational process of a semi-attended self-checkout counter for retail stores. Specifically, we consider an M/M/(1 + c) queueing system with two-phase heterogeneous service scheme, where the arrival of customers at the check-out system follows a Poisson process. After using the matrix-geometric method to analyze the queueing system in a steady state, important performance measures are developed. We evaluate a single-objective (i.e., cost minimization) problem based on the expected cost function per unit time, and then apply the canonical particle swarm optimization algorithm to solve it. A bi-objective optimization model used to minimize the expected cost and the expected waiting time of customers is also formulated. The proposed analytical approach makes it possible to achieve an appropriate balance between operational costs and service quality.

Particle Swarm Optimization and L´evy Flight integration

Particle Swarm Optimization (PSO) is a well-known and popular stochastic optimization method. The Lévy Flight (LF) properties were used to improve the canonical PSO known as premature convergence. The Lévy Flight was applied to change each particle walk on the fitness landscape. We analyze the literature modifications that concluded that Levy flight improved the PSO providing better search space exploration. Based on this conclusion, we propose new approaches to integrate Lévy Flight with PSO by changing initial points in the search space and learning strategies as inertia and constriction coefficients. We use seven standard test functions for an experimental evaluation and scores based on ranking to compare PSO variants. The ranked benchmarks were average performance, standard deviation, and best and worst found solutions obtained from multiple trials. The main contributions are a systematic overview of LF modifications applied in PSO and three new LF applications in canonical PSO procedure. The new approaches are swarm initialization based on LF, lower dimension LF inertia coefficient, and LF-based constriction factor. Another contribution is numerical evaluations on various benchmark functions with diverse characteristics. Two of the proposed modifications performed better or equal, and the third was only 2% worse than the best canonical PSO from the trial.

Particle Swarm Optimization with Multiple Adaptive Subswarms

Benefiting from its simplicity and efficiency, particle swarm optimization (PSO) algorithm has shown great performance on various problems. However, for different optimization problems or different search areas, it is still difficult to achieve a satisfying trade-off between exploration and exploitation. On the basis of canonical PSO algorithm, a variety of improved algorithms have been proposed, which have different capabilities of exploitation and exploration, and each of them performs effective in some problems. This paper proposes a particle swarm optimization with multiple adaptive sub-swarms (PSOMAS). It uses multiple subswarms strategy, in which each sub-swarm is evolved by different algorithms, and an adaptive strategy is also used to reduce the consumption of computing resources. A comprehensive experimental study is conducted on 30 benchmark functions, to compare with several well-known variants of PSO algorithms. The results show that PSOMAS with RT=100 could obtain a better overall performance than all others. Moreover, PSOMAS could find high-quality solution in different problems by varying the value of RT.

An n-state switching PSO algorithm for scalable optimization

Particle swarm optimization (PSO) is an optimization method that is most widely used to solve a number of problems in various fields such as engineering, economics and computer systems. However, due to its scalability and unsatisfying performance particularly for large-scale optimization problems; numerous PSO variants have been suggested so far, in the literature. This paper also proposes a new variant of the canonical PSO algorithm (‘N-state switching PSO—NS-SPSO’) that uses the evolutionary factor information to update particles velocities and, therefore, further enhance its performance. The evolutionary factor is derived by using the population distribution and the mean distance of each particle from the global best. The population distribution and the mean distance are determined through Euclidean distance. Moreover, algorithmic parameters such as inertia weight, and acceleration coefficients are assigned appropriate values at N stages (derived from exploration, exploitation, convergence and jumping out states) that improves the search efficiency and convergence speed. The proposed algorithm is applied to 12 widely used mathematical benchmark functions that demonstrate its best performance in terms of minimum evaluation error, fast convergence and low computational time. Besides these, seven high-dimensional functions and few other algorithms for large-scale optimization were considered to test the scalability of NS-SPSO algorithm. Our comparative results show that NS-SPSO performs well on low-dimensional problems and is promising for solving large-scale optimization problems. Furthermore, the proposed NS-PSO algorithm almost outperforms its closest rivals for various benchmarks.

Particle swarm optimization with adaptive learning strategy

Population diversity maintenance is a crucial task for preventing a particle swarm optimization (PSO) algorithm from being trapped in local optima. A learning strategy is an effective means of improving population diversity. However, for the canonical PSO algorithm, the learning strategy focuses mainly on the global best particle, which leads to a loss of diversity. To increase the population diversity and strengthen the global search ability in PSO, this paper proposes a PSO algorithm with an adaptive learning strategy (PSO-ALS). To better promote the performance of the learning strategy, the swarm is adaptively grouped into several subswarms. The particles in each subswarm are further classified into ordinary particles and the locally best particle, and two different learning strategies without an explicit velocity are devised for updating the particles to increase the population diversity. Thus, the global optimum is determined by comparing the fitness values of the updated best particles in each subswarm. The proposed algorithm is compared with state-of-the-art PSO variants. The experimental results illustrate that the performance of PSO-ALS is promising and competitive in terms of enhanced population diversity and global search ability.

Modified Particle Swarm Optimization With Effective Guides

Despite of its simplicity, the conventional learning strategy of canonical particle swarm optimization (PSO) is inefficient to handle complex optimization problems due to its tendency of overemphasizing the fitness information of global best position without considering the diversity information of swarm. In this article, a modified particle swarm optimization with effective guides (MPSOEG) is proposed, aiming to improve the algorithm's search performances in handling the optimization problems with different characteristics. Depending on the search performance of algorithm, two types of exemplars can be generated by an optimal guide creation (OGC) module incorporated into MPSOEG by referring to the particles with valuable directional information. Particularly, a global exemplar is generated by OCG module to guide the swarm converging towards the promising solution regions of search space, whereas a unique local exemplar can be customized for each particle to enable it escaping from local or non-optimal solution regions. In contrary to global best particle, the exemplars generated by OGC module are able to guide all MPSOEG particles more effectively by considering both fitness and diversity information of swarm, hence can achieve better balancing of algorithm's exploration and exploitation searches. Another notable contribution of MPSOEG is the simplicity of its learning framework through the elimination of both inertia weight and acceleration coefficients parameters. Comprehensive simulation studies are conducted with 25 benchmark functions and the proposed MPSOEG is reported to outperform its six peer algorithms in terms of search accuracy, search reliability and search efficiency in most tested problems.

Robustness and adaptability analysis for equivalent model of doubly fed induction generator wind farm using measured data

As many large wind farms connected to the power grid, it is necessary to develop a robust and adaptable dynamic equivalent model of the wind farm for system analysis and control. In this paper, the trajectory sensitivity of time-varying parameters of the equivalent model is analyzed. Then the non-time- varying parameters of the equivalent model are fixed as aggregated values, while the time-varying parameters are identified using the genetic learning particle swarm optimization based on phasor measurement unit data at the point of interconnection. The robustness and adaptability of the equivalent model under different scenarios are analyzed. The simulation results using the Western Electricity Coordinating Council benchmark test system show that the global searching capability to find the optimal point of the proposed method is higher than canonical particle swarm optimization and genetic algorithm by 2 orders. Further, the biggest mismatch between the identification results of the proposed method and the true values is within 10% for parameters with high sensitivity which is much better than previous work.