Constriction Factor Particle Swarm Optimization Research Articles

Modified Opposition-Based Particle Swarm Optimization for Combined Economic and Emission Dispatch Problem

Modification of the particle swarm optimization (PSO) method is proposed with an opposition-based learning strategy to find the optimal solution to electrical power dispatch problems. The objective of the proposed algorithm is to address the combined economic and emissions dispatch problem (CEED) of thermal power plants. This problem includes constraints such as the valve point effect, prohibited zones of operation, and ramp rate limits. In order to assess its performance, the proposed algorithm is first evaluated using a set of benchmark functions. Later, three thermal generating systems having 6, 10, and 40 units respectively are regarded as the test systems to validate the proposed method. The proposed method is tested, and a comparison of the results are made with popular optimization techniques reported in the literature such as PDE, MODE, NSGA II, and MOSSA. Promising results have been obtained with opposition-based PSO in comparison with their current equivalents. A comparison was made between the fuel cost, emissions, and CPU time of the proposed method with the two other PSO variants: inertia factor PSO (IFPSO) and constriction factor PSO (CFPSO). The results showed a decline in the overall cost by approximately 3.73% and a decrease in CPU time by as much as 2.6 s. Furthermore, the obtained predictions consistently exhibit a high level of accuracy, typically approaching 100%.

Optimal allocation of shunt capacitors in radial distribution networks using Constriction-Factor Particle Swarm Optimization and its techno-economic analysis

The optimal penetration of a Shunt Capacitor (SC) is one of the most economical means to enhance the efficiency of radial distribution networks (RDNs). This enhancement includes reducing power loss, and operating costs, improving voltage profiles, and enhancing stability. This paper introduces a constriction-factor Particle Swarm Optimization (Cf-PSO) for SC allocation problem. It leverages the equivalent reactive power voltage stability index (EQVSI) to narrow the search space of the initial Cf-PSO population. The proposed approach analyzes the optimal SC allocation for various scenarios: the base case before SC integration, one SC, two SCs, three SCs, and four SCs. The Cf-PSO technique was tested on the standard IEEE 33- and 69-bus RDNs. For these networks, allocating four SCs resulted in the most significant percentage reduction in power loss: 35.15 % for the IEEE 33-bus and 35.85 % for the IEEE 69-bus, compared to their respective base scenarios. The simulation results also demonstrate that as more SCs are optimally installed, the percentage reduction in power loss and the financial cost-benefit improve. However, beyond two SCs, the rate of improvement significantly diminishes, reaching a point where adding more SCs is no longer economically advantageous compared to the previous number. The power loss results obtained using this approach were validated by comparing them to established techniques found in the open literature, confirming their effectiveness in most cases.

Synthesizing Shaped-Beam Cylindrical Conformal Array Considering Mutual Coupling Using Refined Rotation/Phase Optimization

A novel method of synthesizing shaped-beam cylindrical conformal array by rotating the antenna elements and optimizing their excitation phases is presented. Rotation of antennas on curved surface is mathematically described by rotating its vectorial active element pattern (VAEP) in its local coordinate system (LCS). Then the scalar patterns and polarization unit vectors of all the rotated VAEPs are properly transformed and then interpolated at a unified angle sampling grid in a common coordinate system, where they are summed to obtain an approximated array expression. With this expression, element rotations and phases can be optimized using the constriction factor particle swarm optimization (CF-PSO) to synthesize desired shaped-beam pattern with controlled sidelobe level (SLL) and cross-polarization level (XPL). However, since rotations on curved surface introduce considerable variations to the element curvature and mutual coupling (MC), the synthesized array pattern would have considerable errors. A refined strategy is adopted then to improve the synthesis accuracy. The proposed method uses uniform amplitude weighting, thus saving many unequal power dividers. Three typical shaped pattern synthesis examples are provided to show the effectiveness of the proposed method. A cylindrical array prototype with 24 rotated U-slot loaded patch antennas is fabricated and measured for practical validation.

Spectral Richness PSO algorithm for parameter identification of dynamical systems under non-ideal excitation conditions

This work proposes a new Particle Swarm Optimization (PSO) algorithm specifically designed for parameter identification of physical systems. The key feature of the proposed algorithm is that it takes into consideration the Spectral Richness of the signal used for exciting the system during the identification procedure. The Spectral Richness is essentially the number of spectral lines in the Fast Fourier Transform of a signal, and if this number is large, the variability of the parameter estimates produced by well-known PSO algorithms is small. However, low values of Spectral Richness may cause large variability of the parameter estimates. The proposed approach, which is termed as the Spectral Richness Particle Swarm Optimization (SR-PSO) algorithm, reduces the variability of the parameter estimates when using an excitation signal with a low value of Spectral Richness compared with state-of-the-art PSO algorithms, and maintains the same performance if the Spectral Richness is high. In a first case study, a set of real-time experiments applying excitation signals with different levels of Spectral Richness have been performed on a servomechanism in order to obtain several data sets. The acquired data from each excitation signal has been used to perform a parameter identification process using various algorithms including the classic PSO, the Linear Variable Weight Particle Swarm Optimization (LVW-PSO), the Linear Variable Constriction Factor Particle Swarm Optimization (LVCF-PSO), the state-of-the-art Fractional Order Regulated Particle Swarm Optimization (FOR-PSO) and the proposed Spectral Richness Particle Swarm Optimization (SR-PSO). The pertinence of the parameter estimates is also evaluated by designing and experimentally applying a model-based feedback control to the servomechanism.The proposed SR-PSO algorithm is also tested in a thermoelectric cooler model using numerical simulations. It is shown that the values of the identified parameters heavily depends on the kind of excitation signal applied to this system.

Integrated Physical Modeling and Optimal Control Method of Limited-Angle Torque Motor in Fuel Metering Apparatus

Limited-angle torque motor (LATM) is a critical component to precisely drive the valve angle of an engine’s fuel metering apparatus and accurately measure the fuel flow, and research on it is of great significance. Thus, the LATM of a certain kind is regarded as the research object in this paper. Firstly, a Simscape-based LATM integrated physical modeling method is proposed, which can better demonstrate the real operational characteristics of a motor, compared with the current mathematical model. Secondly, a Proportional-Integral-Derivative (PID) parameter self-tuning method based on a constriction factor particle swarm optimization (CPSO) algorithm is broached since it is difficult to tune due to a large number of multi-loop cascade PID control parameters. Simulation and experimental results showed that the control performance increases by 40% in the triple closed-loop PID control system with a stronger disturbance rejection, simpler design, and quickly responds when compared with the previous empirical tuning method. The triple closed-loop PID control system comprises an angle loop + angle velocity loop + current loop and technically supports the engineering application design of motors.

Intelligent fault diagnosis for power distribution system-comparative studies

Short circuit is one of the most popular types of permanent fault in power distribution system. Thus, fast and accuracy diagnosis of short circuit failure is very important so that the power system works more effectively. In this paper, a newly enhanced support vector machine (SVM) classifier has been investigated to identify ten short-circuit fault types, including single line-to-ground faults (XG, YG, ZG), line-to-line faults (XY, XZ, YZ), double line-to-ground faults (XYG, XZG, YZG) and three-line faults (XYZ). The performance of this enhanced SVM model has been improved by using three different versions of particle swarm optimization (PSO), namely: classical PSO (C-PSO), time varying acceleration coefficients PSO (T-PSO) and constriction factor PSO (K-PSO). Further, utilizing pseudo-random binary sequence (PRBS)-based time domain reflectometry (TDR) method allows to obtain a reliable dataset for SVM classifier. The experimental results performed on a two-branch distribution line show the most optimal variant of PSO for short fault diagnosis.

Constriction Factor Particle Swarm Optimization based load balancing and cell association for 5G heterogeneous networks

With the rapidly growing traffic demand, the cellular industry is moving toward heterogeneity to fulfill the heavy traffic requirement. The existing heterogeneous networks are comprised of the Long-Term Evolution (LTE), LTE-Advanced (LTE-A), and other compatible access technologies. It has been identified that due to the shortage of capacity, cell performance can deteriorate. To deal with users’ requirements, the 5G heterogeneous network architectures comprising LTE-advanced access technology with the combination of comparatively low configured small base stations, and macro eNodeBs (MeNB) have been extended as a solution. Therefore, operators have introduced the 5G with the existing LTE Advanced Heterogeneous Network (5GLHN) where small cells such as Home eNodeBs (HeNBs) are deployed overlapping with the conventional macro eNodeB (MeNB). However, in highly dense and closely compacted 5GLHNs, the cell capacity can still be lower than what is on-demand, thus affecting the system throughput. This article proposes a framework to maximize the throughput in 5GLHNs through a Constriction Factor Particle Swarm Optimization (CFPSO) technique of cell association and load-balancing algorithm to enhance the throughput of the 5GLHN. The proposed approach is designed to offload the traffic of MeNB Users (MUEs) to the small cells (HeNBs). The convergence, cumulative distribution function of the UEs rate, average throughput, and allocation time are analyzed to evaluate the performance of the proposed CFPSO approach. Simulation results reveal that the throughput of the proposed approach is improved by up to 44.08% of the existing index-based approach and by 94.20 \\% of the existing Matching with Minimum Quota (MMQ) approach.

Solving Economic Load Dispatch Problem UsingParticle Swarm Optimization Technique

Economic load dispatch (ELD)is one of the important problems ofpower system operation. Conventional methods like Lambda iteration methodare not efficientfor complex ELD problems. Particle swarm optimization is preferred in ELD problem due to its high performance.The Inertia Weight PSO and Constriction Factor PSO algorithms are performed on threeunit and sixunit systems. The analysis of ELD problem is performed by Conventional method and PSO method. In this paper,losses are neglected in the ELD problem. PSO algorithm obtains the best solution forELD problem.

Siting and Sizing of Distributed Generation and Shunt Capacitor Banks in Radial Distribution System Using Constriction Factor Particle Swarm Optimization

This article proffers an advanced solution to allocate the distributed generation (DG) and shunt capacitor (SC) banks optimally in radial distribution system (RDS) to alleviate the power losses, revamp the voltage profile, inflate the voltage stability index, shrink the total voltage deviation, and acquire more energy savings. In the framework of finding the optimal site and size of DGs and SC banks, Particle swarm optimization (PSO) technique is modified with constriction factor and the same is aimed to apply in IEEE 33-bus system and practical Brazil 136-bus RDS. Different case studies are carried out for multiobjective problems while considering equality and inequality constraints. A comparative analysis with PSO and modified PSO is presented to project the precedence of the adopted algorithm. In addition, the obtained results are also compared to the recently surfaced few state-of-the-art algorithms to present the optimizing capability of the implemented algorithm.

A Robust Game-Based Algorithm for Downlink Joint Resource Allocation in Hierarchical OFDMA Femtocell Network System

Femtocell is a promising technology for wireless service networks to facilitate sustainable and efficient services for users. This paper deals with a downlink joint channel assignment and power allocation problem with multiple channels, users, constraints, and uncertainties in the orthogonal frequency division of a multiple-access hierarchical femtocell network system. Specifically, a hierarchical robust Stackelberg game, which aims to achieve robust equilibrium, is first proposed for resource allocation with uncertainties. Then, a low-complexity, low-interference, high-efficiency, and high-performance algorithm is presented to handle the complex robust joint allocation problem. Considering the demand capacity of macro-base stations, an efficient fitness function in conjunction with particle swarm optimization-constriction factor, is utilized to yield the best response in the upper game to satisfy multiple constraints. Meanwhile, an iterative waterfilling algorithm is exploited to achieve the best response of femto-base stations in the lower game. Lastly, a stop protocol is established for two-tier users to accomplish an efficient robust Stackelberg equilibrium. Comparative results demonstrated that the proposed algorithm is superior to the existing game-based algorithms.

A modified optimal PMU placement problem formulation considering channel limits under various contingencies

Phasor measurement units (PMU) are populating the electricity grids throughout the world rapidly due to their wide range of benefits and applications. The traditional optimal PMU placement (OPP) formulations ensure complete network observability with a minimum number of PMU installation. Most of them disregard the PMU channel limitations, the existence of passive measurements/zero injection buses (ZIB), and enhancement of measurement redundancy. This paper presents a modified and effective OPP formulation considering various contingencies and constraints aiming at minimizing the required number of PMU installation and achieving the maximum number of measurement redundancy subjected to complete network observability. The availability of channels per PMU and the presence of ZIB are also taken into account. Besides, the vulnerability of the PMU along with the possibility of line outages is also considered. The formulated OPP problem is tested on five IEEE test networks employing constriction factor particle swarm optimization (CF-PSO). The proposed formulation effectively ensures complete network observability with the installation of a minimal number of PMU. Furthermore, the obtained results prove the efficacy and superiority of the CF-PSO approach over the mixed integer linear programming (MILP) approach and the reported methodologies in literature in terms of achieved measurement redundancies through the installation of less or same number of PMU. Finally, this research applies the proposed OPP formulation on a large-scale electric network of three different scenarios to justify its’ applicability, scalability, and robustness.

Distribution Grids Fault Location employing ST based Optimized Machine Learning Approach

Precise information of fault location plays a vital role in expediting the restoration process, after being subjected to any kind of fault in power distribution grids. This paper proposed the Stockwell transform (ST) based optimized machine learning approach, to locate the faults and to identify the faulty sections in the distribution grids. This research employed the ST to extract useful features from the recorded three-phase current signals and fetches them as inputs to different machine learning tools (MLT), including the multilayer perceptron neural networks (MLP-NN), support vector machines (SVM), and extreme learning machines (ELM). The proposed approach employed the constriction-factor particle swarm optimization (CF-PSO) technique, to optimize the parameters of the SVM and ELM for their better generalization performance. Hence, it compared the obtained results of the test datasets in terms of the selected statistical performance indices, including the root mean squared error (RMSE), mean absolute percentage error (MAPE), percent bias (PBIAS), RMSE-observations to standard deviation ratio (RSR), coefficient of determination (R2), Willmott’s index of agreement (WIA), and Nash–Sutcliffe model efficiency coefficient (NSEC) to confirm the effectiveness of the developed fault location scheme. The satisfactory values of the statistical performance indices, indicated the superiority of the optimized machine learning tools over the non-optimized tools in locating faults. In addition, this research confirmed the efficacy of the faulty section identification scheme based on overall accuracy. Furthermore, the presented results validated the robustness of the developed approach against the measurement noise and uncertainties associated with pre-fault loading condition, fault resistance, and inception angle.

Automatic selection of fittest energy demand predictors based on cyber swarm optimization and reinforcement learning

Effective demand forecasting is essential for regulating power distribution, scheduling production, and initiating new energy projects. Existing forecasting models have contrasting features and manifest various types of errors. This paper proposes a multi-predictor approach which applies reinforcement learning for selecting the fittest predictors to enhance the collaborative performance. A new univariate predictor is developed based on the Gaussian mixture and phase shifting and rescaling techniques, and two multivariate predictors are developed from a landscape analysis with potential econometrics. Each individual predictor is trained by the cyber swarm algorithm (CSA) to find the optimal parameter values. The 10-fold cross validation for regression parameter optimization by using CSA and the constriction factor particle swarm optimization (CFPSO) shows the effectiveness of the former against the latter. Our reinforcement learning forecasting method is able to automatically select the best predictor to perform at various time instances and allow the embedding predictors to complement one another. Our experimental results experimented with Taiwan’s electricity demand time series during 2001–2014 show that the prediction improvement contributed by the proposed approach over the original individual predictors is significant in terms of the mean absolute percentage error (MAPE) and the mean square error (MSE).

Particle Swarm Optimization as Applied to Electromagnetic Design Problems

Particle swarm optimization (PSO) is a swarm intelligence algorithm inspired by the social behavior of birds flocking and fish schooling. Numerous PSO variants have been proposed in the literature for addressing different problem types. In this article, the authors apply different PSO variants to common design problems in electromagnetics. They apply the Inertia Weight PSO (IWPSO), the Constriction Factor PSO (CFPSO), and the Comprehensive Learning Particle Swarm Optimization (CLPSO) algorithms to real-valued optimization problems, i.e. microwave absorber design, and linear array synthesis. Moreover, the authors use discrete PSO optimizers such as the binary PSO (binPSO) and the Boolean PSO with a velocity mutation (BPSO-vm) in order to solve discrete-valued optimization problems, i.e. patch antenna design. Additionally, the authors apply and compare binPSO with different transfer functions to thinning array design problems. In the case of a multi-objective optimization problem, they apply two multi-objective PSO variants to dual-band base station antenna optimization for mobile communications. Namely, these are the Multi-Objective PSO (MOPSO) and the Multi-Objective PSO with Fitness Sharing (MOPSO-fs) algorithms. Finally, the authors conclude the paper by providing a discussion on future trends and the conclusion.

Analysis method of competitive advantage of new industrial innovation alliance based on contraction factor particle swarm optimization (PSO)

To improve effectiveness of competitive advantage analysis algorithm of emerging industry innovation union, a kind of competitive advantage analysis method of emerging industry innovation union based on constriction factor particle swarm optimization (PSO) is proposed. Firstly, competitive advantage evaluation model of emerging industry innovation union is constructed aimed at uncertain influence factor existing in evaluation to strategic emerging industry; secondly, particle swarm optimization is introduced, and to avoid premature convergence problem existing in particle swarm optimization and realize rapid convergence of particle to global optimal solution, constriction factor and two operators, i.e. “attraction” and “diffusion”, are introduced in this paper so that diversity of particle swarm is kept and better convergence rate is possessed. Finally, through empirical analysis to strategic emerging industry evaluation of an area, feasibility and rationality of the method are verified.

Particle Swarm Optimization of Non Uniform Rational B-Splines for Robot Manipulators Path Planning

The path-planning problem is commonly formulated to handle the obstacle avoidance constraints. This problem becomes more complicated when further restrictions are added. It often requires efficient algorithms to be solved. In this paper, a new approach is proposed where the path is described by means of Non Uniform Rational B-Splines (NURBS for short) with more additional constraints. An evolutionary technique called Particle Swarm Optimization (PSO) with three options of particles velocity updating offering three alternatives namely the PSO with inertia weight (PSO-W), the constriction factor PSO (PSO-C) and the combination of the two(PSO-WC); are used to optimize the weights of the control points that serve as parameters of the algorithm describing the path. Simulation results show how the mixture of the first two options produces a powerful algorithm, specifically (PSO-WC), in producing a compromise between fast convergence and large number of potential solution. In addition, the whole approach seems to be flexible, powerful and useful for the generation of successful smooth trajectories for robot manipulator which are independent from environment conditions.

Novel hybrid approach with elite group optimal computing budget allocation for the stochastic multimodal problem

The stochastic multimodal problem commonly arises in the search for efficiency and solution quality in practice. In this study, a hybrid approach is developed for the stochastic multimodal problem. The proposed approach comprises particle swarm optimization (PSO), constriction factor PSO (CPSO), and elite group optimal computing budget allocation (EGOCBA). CPSO or PSO is applied to determine the correct direction in the design space, and EGOCBA is adopted to allocate the appropriate number of samples to each alternative and provide reliable evaluations and identifications to rank particles in the CPSO or PSO procedure. This work improves the searching efficiency of optimal computing budget allocation (OCBA) in the stochastic multimodal problem. Several alternatives referred to as the “elite group,” the performance of which is close to that of the current best solution in each swarm, absorb most of the computing budget of OCBA. However, distinguishing the best solution from the elite group is time consuming because of the various local and global optima in the stochastic multimodal problem. Therefore, this study proposes EGOCBA that avoids extra computing costs for the elite group by implementing a new selection procedure. This EGOCBA reserves all the solutions of the elite group and filters them to form an optimal set that contains all the best solutions having an equal mean performance without a significant difference. These tasks are achieved through a confidence interval test in the end of the algorithm. The optimal set can provide more than one best solution to support multiple decisions depending on different decision variables. Two experiments are conducted on stochastic multimodal optimization problem and stochastic resource allocation problem. Experimental results reveal the efficiency and effectiveness of the proposed approach in deriving multiple optimal solutions in a multimodal class and stochastic environment.

A partially integrated production-inventory model with interval valued inventory costs, variable demand and flexible reliability

This paper formulates a production-inventory model to investigate the effects of partially integrated production and marketing policy of a manufacturing firm. Demand is assumed to be variable and dependent on the selling price and marketing cost. Also, different inventory costs are considered as interval valued. Shortages are permitted and partially backlogged with a rate dependent on the waiting time. Considering that manufacturing process generates defective units four possible cases have been identified and studied. Basically, the optimization problems (maximization problem for Marketing department and minimization problems for Production and Research & Development departments) have been formulated and solved. For solving these optimization problems, an efficient soft computing algorithm based on Particle Swarm Optimization-Constriction factor (PSO-CO) is proposed. In order to illustrate and validate the production-inventory model a numerical example is solved. Finally, a sensitivity analysis is done to study the effect of changes of different system parameters on optimal policies.

Multi-agent decision support system for missile defense based on improved PSO algorithm

Ballistic missile defense system (BMDS) is important for its special role in ensuring national security and maintaining strategic balance. Research on modeling and simulation of the BMDS beforehand is essential as developing a real one requires lots of manpower and resources. BMDS is a typical complex system for its nonlinear, adaptive and uncertainty characteristics. The agent-based modeling method is well suited for the complex system whose overall behaviors are determined by interactions among individual elements. A multi-agent decision support system (DSS), which includes missile agent, radar agent and command center agent, is established based on the studies of structure and function of BMDS. Considering the constraints brought by radar, intercept missile, offensive missile and commander, the objective function of DSS is established. In order to dynamically generate the optimal interception plan, the variable neighborhood negative selection particle swarm optimization (VNNSPSO) algorithm is proposed to support the decision making of DSS. The proposed algorithm is compared with the standard PSO, constriction factor PSO (CFPSO), inertia weight linear decrease PSO (LDPSO), variable neighborhood PSO (VNPSO) algorithm from the aspects of convergence rate, iteration number, average fitness value and standard deviation. The simulation results verify the efficiency of the proposed algorithm. The multi-agent DSS is developed through the Repast simulation platform and the constructed DSS can generate intercept plans automatically and support three-dimensional dynamic display of missile defense process.

AN ADAPTIVE LOCALIZATION SYSTEM USING PARTICLE SWARM OPTIMIZATION IN A CIRCULAR DISTRIBUTION FORM

Tracking the user location in indoor environment becomes substantial issue in recent research High accuracy and fast convergence are very important issues for a good localization system. One of the techniques that are used in localization systems is particle swarm optimization (PSO). This technique is a stochastic optimization based on the movement and velocity of particles. In this paper, we introduce an algorithm using PSO for indoor localization system. The proposed algorithm uses PSO to generate several particles that have circular distribution around one access point (AP). The PSO generates particles where the distance from each particle to the AP is the same distance from the AP to the target. The particle which achieves correct distances (distances from each AP to target) is selected as the target. Four PSO variants, namely standard PSO (SPSO), linearly decreasing inertia weight PSO (LDIW PSO), self-organizing hierarchical PSO with time acceleration coefficients (HPSO-TVAC), and constriction factor PSO (CFPSO) are used to find the minimum distance error. The simulation results show the proposed method using HPSO-TVAC variant achieves very low distance error of 0.19 meter.