Lagrangian Particle Swarm Optimization Research Articles

A novel microgrid fault detection and classification method using maximal overlap discrete wavelet packet transform and an augmented Lagrangian particle swarm optimization-support vector machine

In this paper, an intelligent method for fault detection and classification for a microgrid (MG) was proposed. The idea was based on the combination of three computational tools: signal processing using the maximal overlap discrete wavelet packet transform (MODWPT), parameter optimization by the augmented Lagrangian particle swarm optimization (ALPSO), and machine learning using the support vector machine (SVM). The MODWPT was applied to preprocess half cycle of the post-fault current samples measured at both ends of feeders. The wavelet coefficients derived from the MODWPT were statistically evaluated using the mean, standard deviation, energy, skewness, kurtosis, logarithmic energy entropy, max, min, and Shannon entropy. These were the input feature datasets and were used to train the SVM classifier. The ALPSO was utilized to reduce the feature subsets and select the sensitive parameters of the SVM (i.e., penalty factor and the slack variable) to further improve the performance of the SVM. The intelligent relaying scheme was executed on a real-time digital simulator (RTDS) which is integrated with Matlab. The performance of SVM-based protection method is compared to several different protection models in terms of signal processing tools, optimization techniques used for selecting datasets and sensitive parameters, and classifiers under different operating conditions. Numerous operating conditions, including islanded or non-islanded operation modes and radial and or loop topologies introducing different characteristics of fault were included as the case studies for the proposed technique. A comprehensive evaluation study of the consortium for electric reliability technology solutions (CERTS) MG system and IEEE 34-bus confirms that the proposed protection scheme is accurate, fast, and robust to noisy measurements. In addition, the obtained results illustrate that the proposed method is superior to the recently published works in the literature.

Integrated supply chain scheduling of procurement, production, and distribution under spillover effects

This paper considers an integrated scheduling problem in an e-commerce supply chain. The supply chain consists of heterogeneous suppliers, consumer-goods manufacturers that offer online channels, and a network of retailers. Suppliers provide raw materials or semi-finished products to manufacturers. Then, manufacturers produce and deliver end items to retailers. The retailers require that the manufacturers maintain a given fill rate, and, otherwise, a penalty will apply. Missing the fill rate can not only result in penalties, but also retailers’ switching, operational issues, and loss of image, and market value. Therefore, the total penalty costs are nonlinear with retailers’ unsatisfied quantities and the fill rate, which exhibits spillover effects. The problem is to select a subset of suppliers, assign retailers’ orders, and identify a production schedule with the manufacturers while minimizing the total costs that includes shipping and penalty. In this paper, we formulate a mixed-integer nonlinear program and develop a hybrid particle swarm optimization algorithm that can find a suitable solution within a reasonable time. The algorithm incorporates augmented Lagrangian relaxation and particle swarm optimization. We then perform computational testing on randomly generated cases and evaluate the performance of the proposed algorithm. Our numerical experiments show that the proposed algorithm is robust and efficient. Moreover, we provide a real case study, which demonstrates that the proposed model can lead to a substantial reduction of both the total and penalty costs.

Post-nonlinear blind source separation with kurtosis constraints using augmented Lagrangian particle swarm optimization and its application to mechanical systems

To accurately estimate source signals from their post-nonlinear mixtures, a post-nonlinear blind source separation (PNLBSS) method with kurtosis constraints is proposed based on augmented Lagrangian particle swarm optimization (PSO). First, an improved contrast function is presented by combining mutual information of the separated signals and kurtosis ranges of source signals. Second, an augmented Lagrangian multiplier method is used to convert PNLBSS into an unconstrained pseudo-objective optimization problem. Then, improved PSO is applied to update the parameters in complex nonlinear spaces. Finally, numerical case studies and experimental case studies are provided to evaluate the performance of the proposed method. By adding the kurtosis ranges constraints, the estimation accuracy of source signals could be improved, which would benefit vibration and acoustic monitoring and control.

Fractional fixed-structure [formula omitted] controller design using Augmented Lagrangian Particle Swarm Optimization with Fractional Order Velocity

The optimization of a fixed-structure controller is in general computationally intractable, posing a challenge to control system engineers. This paper introduces a novel technique for designing such control techniques by formulating it as a nonlinear non-convex constrained problem. A novel PSO algorithm, namely the Augmented Lagrangian Particle Swarm Optimization with Fractional Order Velocity (ALPSOFV), is proposed for improving the convergence rate. The structure of the controller is selectable and, therefore, the Fractional Order Proportional Integral Derivative (FOPID) algorithm is chosen in the scope of the study. The results for three test examples show the good performance of the ALPSOFV.

Variational reconstruction using subdivision surfaces with continuous sharpness control

We present a variational method for subdivision surface reconstruction from a noisy dense mesh. A new set of subdivision rules with continuous sharpness control is introduced into Loop subdivision for better modeling subdivision surface features such as semi-sharp creases, creases, and corners. The key idea is to assign a sharpness value to each edge of the control mesh to continuously control the surface features. Based on the new subdivision rules, a variational model with L1 norm is formulated to find the control mesh and the corresponding sharpness values of the subdivision surface that best fits the input mesh. An iterative solver based on the augmented Lagrangian method and particle swarm optimization is used to solve the resulting non-linear, non-differentiable optimization problem. Our experimental results show that our method can handle meshes well with sharp/semi-sharp features and noise.

Simulation based optimization of torsional vibration dampers in automotive powertrains

In this paper, an approach for the automated design of isolation elements as used in automotive powertrains is presented. The method is based on 1D-MBS models representing various drivetrain configurations and damper concepts. This allows for a dynamical analysis in typical design relevant driving situations like full load acceleration or engine start. The concept design is carried out in a numerical optimization process in order to find a set of geometric parameters with minimal design space requirements and weight. Especially the specifications imposed on the drivetrain’s vibrational behavior lead to a complex optimization problem which requires robust and carefully tuned algorithms. A search method that has been successfully applied to constrained design problems in engineering is the Augmented Lagrangian Particle Swarm Optimization procedure. The dimensioning of a dual mass flywheel with an additional internal damper for an all-wheel drive sports car is used as a test case to evaluate the algorithm’s suitability for this particular application. Several control parameter settings are compared regarding their influence on the optimizer performance.

DESIGN OF PWMSC CONTROLLER USING AUGMENTED LAGRANGIAN PARTICLE SWARM OPTIMIZATION ALGORITHM

This paper presents a systematic process for designing a damping controller for pulse width modulated series compensator (PWMSC) to improve the angular stability of a multi-machine power system. The proposed controller is robust and tuned by satisfying the multiple H∞ performance criteria to stabilize the system at multiple operating conditions. The design problem has been converted into a constrained nonlinear optimization problem with the time domain-based objective function which is solved by an augmented Lagrangian particle swarm optimization (ALPSO) algorithm. The proposed control scheme has been implemented on two nonlinear test systems. The nonlinear simulation results clearly verify that the designed controller with proposed model improves the dynamic stability of the case studies, particularly when the operating loadings changes.

Unit commitment using Lagrangian relaxation and particle swarm optimization

Unit commitment (UC) is a NP-hard nonlinear mixed-integer optimization problem. This paper proposes ELRPSO, an algorithm to solve the UC problem using Lagrangian relaxation (LR) and particle swarm optimization (PSO). ELRPSO employs a state-of-the-art powerful PSO variant called comprehensive learning PSO to find a feasible near-optimal UC schedule. Each particle represents Lagrangian multipliers. The PSO uses a low level LR procedure, a reserve repairing heuristic, a unit decommitment heuristic, and an economic dispatch heuristic to obtain a feasible UC schedule for each particle. The reserve repairing heuristic addresses the spinning reserve and minimum up/down time constraints simultaneously. Moreover, the reserve repairing and unit decommitment heuristics consider committing/decommitting a unit for a consecutive period of hours at a time in order to reduce the total startup cost. Each particle is initialized using the Lagrangian multipliers obtained from a LR that iteratively updates the multipliers through an adaptive subgradient heuristic, because the multipliers obtained from the LR tend to be close to the optimal multipliers and have a high potential to lead to a feasible near-optimal UC schedule. Numerical results on test thermal power systems of 10, 20, 40, 60, 80, and 100 units demonstrate that ELRPSO is able to find a low-cost UC schedule in a short time and is robust in performance.

Robust PWMSC Damping Controller Tuning on the Augmented Lagrangian PSO Algorithm

The paper introduces a new flexible alternating current transmission systems (FACTS) controller based on pulse width modulated series compensator (PWMSC) for damping inter-area oscillations in power systems. The PWMSC can modulate the impedance of a transmission line through the variation of the duty cycle of AC link. The main purpose of this work is to verify the capability of the PWMSC to mitigate low frequency oscillations. For this reason, a novel current injection model of PWMSC is proposed and incorporated in the system model. This study proposes a novel tuning strategy for robust PWMSC damping controller based on the augmented Lagrangian particle swarm optimization (ALPSO) satisfying the multiple H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance criteria. Proposed method does not need any conservative assumption unlike the conventional techniques, and often enables us to find the desired parameters of controller just by solving the constrained optimization problem in a straightforward way. In the paper, a verification of the designed controller by means of digital simulations of single machine and four-machine power systems is presented. The net results show that the proposed controller improves the stability of both test systems significantly in a number of fault cases at different levels of power flow in tie-line.

Constrained structural design optimization via a parallel augmented Lagrangian particle swarm optimization approach

This paper presents an extension to the basic particle swarm optimization approach for the solution of constrained engineering design optimization problems. The approach takes advantage of the PSO ability to find global optimum in problems with complex design spaces while directly enforcing feasibility of constraints using an augmented Lagrange multiplier method. Details in the algorithm implementation and properties are presented and the effectiveness of the approach is illustrated in different benchmark structural optimization test cases. Results show the ability of the proposed methodology to find better solutions for structural optimization tasks as compared to other optimization algorithms.

A PSO-based algorithm designed for a swarm of mobile robots

This paper presents an algorithm called augmented Lagrangian particle swarm optimization with velocity limits (VL-ALPSO). It uses a particle swarm optimization (PSO) based algorithm to optimize the motion planning for swarm mobile robots. Considering problems with engineering constraints and obstacles in the environment, the algorithm combines the method of augmented Lagrangian multipliers and strategies of velocity limits and virtual detectors so as to ensure enforcement of constraints, obstacle avoidance and mutual avoidance. All the strategies together with basic PSO are corresponding to real situations of swarm mobile robots in coordinated movements. This work also builds a swarm motion model based on Euler forward time integration that involves some mechanical properties such as masses, inertias or external forces to the swarm robotic system. Simulations show that the robots moving in the environment display the desired behavior. Each robot has the ability to do target searching, obstacle avoidance, random wonder, acceleration or deceleration and escape entrapment. So, in summary due to the characteristic features of the VL-ALPSO algorithm, after some engineering adaptation, it can work well for the planning of coordinated movements of swarm robotic systems.

Robust PID controller tuning based on the constrained particle swarm optimization

This paper proposes a novel tuning strategy for robust proportional-integral-derivative (PID) controllers based on the augmented Lagrangian particle swarm optimization (ALPSO). First, the problem of PID controller tuning satisfying multiple H∞ performance criteria is considered, which is known to suffer from computational intractability and conservatism when any existing method is adopted. In order to give some remedy to such a design problem without using any complicated manipulations, the ALPSO based robust gain tuning scheme for PID controllers is introduced. It does not need any conservative assumption unlike the conventional methods, and often enables us to find the desired PID gains just by solving the constrained optimization problem in a straightforward way. However, it is difficult to guarantee its effectiveness in a theoretical way, because PSO is essentially a stochastic approach. Therefore, it is evaluated by several simulation examples, which demonstrate that the proposed approach works well to obtain PID controller parameters satisfying the multiple H∞ performance criteria.

LAGRANGIAN RELAXATION-BASED PARTICLE SWARM OPTIMIZATION FOR UNIT COMMITMENT PROBLEM

This paper presents an application of combined Lagrangian relaxation (LR) method and particle swarm optimization (PSO) technique for the Unit Commitment (UC) problem. This hybrid technique uses LR as the main algorithm. The LR method provides a fast solution, but it may suffer from numerical convergence and solution quality problem. The proposed algorithm uses PSO to update the Lagrangian multipliers and improve the performance of LR method. In this paper, ramp rate limit is also considered besides taking minimum up time and minimum down time of thermal units. The proposed method is implemented for solving two examples of UC test problems. The study results have shown that the approach developed is feasible and efficient.

Augmented Lagrangian Particle Swarm Optimization in Mechanism Design

The problem of optimizing nonlinear multibody systems is in general nonlinear and nonconvex. This is especially true for the dimensional synthesis process of rigid body mechanisms, where often only local solutions might be found with gradient-based optimization methods. An attractive alternative for solving such multimodal optimization problems is the Particle Swarm Optimization (PSO) algorithm. This stochastic solution technique allows a derivative-free search for a global solution without the need for any initial design. In this work, we present an extension to the basic PSO algorithm in order to solve the problem of dimensional synthesis with nonlinear equality and inequality constraints. It utilizes the Augmented Lagrange Multiplier Method in combination with an advanced non-stationary penalty function approach that does not rely on excessively large penalty factors for sufficiently accurate solutions. Although the PSO method is even able to solve nonsmooth and discrete problems, this augmented algorithm can additionally calculate accurate Lagrange multiplier estimates for differentiable formulations, which are helpful in the analysis process of the optimization results. We demonstrate this method and show its very promising applicability to the constrained dimensional synthesis process of rigid body mechanisms.

Using augmented Lagrangian particle swarm optimization for constrained problems in engineering"&gt;Using augmented Lagrangian particle swarm optimization for constrained problems in engineering

The comparatively new stochastic method of particle swarm optimization (PSO) has been applied to engineering problems especially of nonlinear, non-differentiable, or non-convex type. Its robustness and its simple applicability without the need for cumbersome derivative calculations make PSO an attractive optimization method. However, engineering optimization tasks often consist of problem immanent equality and inequality constraints which are usually included by inadequate penalty functions when using stochastic algorithms. The simple structure of basic particle swarm optimization characterized by only a few lines of computer code allows an efficient implementation of a more sophisticated treatment of such constraints. In this paper, we present an approach which utilizes the simple structure of the basic PSO technique and combines it with an extended non-stationary penalty function approach, called augmented Lagrange multiplier method, for constraint handling where ill conditioning is a far less harmful problem and the correct solution can be obtained even for finite penalty factors. We describe the basic PSO algorithm and the resulting method for constrained problems as well as the results from benchmark tests. An example of a stiffness optimization of an industrial hexapod robot with parallel kinematics concludes this paper and shows the applicability of the proposed augmented Lagrange particle swarm optimization to engineering problems.