A tunable radial basis function model for nonlinear system identification using particle swarm optimisation

A tunable radial basis function (RBF) network model is proposed for nonlinear system identification using particle swarm optimisation (PSO). At each stage of orthogonal forward regression (OFR) model construction, PSO optimises one RBF unit's centre vector and diagonal covariance matrix by minimising the leave-one-out (LOO) mean square error (MSE). This PSO aided OFR automatically determines how many tunable RBF nodes are sufficient for modelling. Compared with the-state-of-the-art local regularisation assisted orthogonal least squares algorithm based on the LOO MSE criterion for constructing fixed-node RBF network models, the PSO tuned RBF model construction produces more parsimonious RBF models with better generalisation performance and is computationally more efficient.

Nonlinear system identification using particle swarm optimisation tuned radial basis function models

A novel particle swarm optimisation (PSO) tuned radial basis function (RBF) network model is proposed for identification of non-linear systems. At each stage of orthogonal forward regression (OFR) model construction process, PSO is adopted to tune one RBF unit's centre vector and diagonal covariance matrix by minimising the leave-one-out (LOO) mean square error (MSE). This PSO aided OFR automatically determines how many tunable RBF nodes are sufficient for modelling. Compared with the-state-of-the-art local regularisation assisted orthogonal least squares algorithm based on the LOO MSE criterion for constructing fixed-node RBF network models, the PSO tuned RBF model construction produces more parsimonious RBF models with better generalisation performance and is often more efficient in model construction. The effectiveness of the proposed PSO aided OFR algorithm for constructing tunable node RBF models is demonstrated using three real data sets.

Radial basis function classifier construction using particle swarm optimisation aided orthogonal forward regression

We develop a particle swarm optimisation (PSO) aided orthogonal forward regression (OFR) approach for constructing radial basis function (RBF) classifiers with tunable nodes. At each stage of the OFR construction process, the centre vector and diagonal covariance matrix of one RBF node is determined efficiently by minimising the leave-one-out (LOO) misclassification rate (MR) using a PSO algorithm. Compared with the state-of-the-art regularisation assisted orthogonal least square algorithm based on the LOO MR for selecting fixednode RBF classifiers, the proposed PSO aided OFR algorithm for constructing tunable-node RBF classifiers offers significant advantages in terms of better generalisation performance and smaller model size as well as imposes lower computational complexity in classifier construction process. Moreover, the proposed algorithm does not have any hyperparameter that requires costly tuning based on cross validation.

Particle swarm optimisation assisted classification using elastic net prefiltering

A novel two-stage construction algorithm for linear-in-the-parameters classifier is proposed, aiming at noisy two-class classification problems. The purpose of the first stage is to produce a prefiltered signal that is used as the desired output for the second stage to construct a sparse linear-in-the-parameters classifier. For the first stage learning of generating the prefiltered signal, a two-level algorithm is introduced to maximise the model's generalisation capability, in which an elastic net model identification algorithm using singular value decomposition is employed at the lower level while the two regularisation parameters are selected by maximising the Bayesian evidence using a particle swarm optimization algorithm. Analysis is provided to demonstrate how “Occam's razor” is embodied in this approach. The second stage of sparse classifier construction is based on an orthogonal forward regression with the D-optimality algorithm. Extensive experimental results demonstrate that the proposed approach is effective and yields competitive results for noisy data sets.

Optimisation of a fermentation process for butanol production by particle swarm optimisation (PSO)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A taxonomy of heterogeneity and dynamics in particle swarm optimisation

We propose a taxonomy for heterogeneity and dynamics of swarms in PSO, which separates the consideration of homogeneity and heterogeneity from the presence of adaptive and non-adaptive dynamics, both at the particle and swarm level. It thus supports research into the separate and combined contributions of each of these characteristics. An analysis of the literature shows that most recent work has focussed on only parts of the taxonomy. Our results agree with prior work that both heterogeneity and dynamics are useful. However while heterogeneity does typically improve PSO, this is often dominated by the improvement due to dynamics. Adaptive strategies used to generate heterogeneity may end up sacrificing the dynamics which provide the greatest performance increase. We evaluate exemplar strategies for each area of the taxonomy and conclude with recommendations.

A hybrid Particle Swarm Optimization - Simplex algorithm (PSOS) for structural damage identification

This study proposes a new PSOS-model based damage identification procedure using frequency domain data. The formulation of the objective function for the minimization problem is based on the Frequency Response Functions (FRFs) of the system. A novel strategy for the control of the Particle Swarm Optimization (PSO) parameters based on the Nelder-Mead algorithm (Simplex method) is presented; consequently, the convergence of the PSOS becomes independent of the heuristic constants and its stability and confidence are enhanced. The formulated hybrid method performs better in different benchmark functions than the Simulated Annealing (SA) and the basic PSO (PSO(b)). Two damage identification problems, taking into consideration the effects of noisy and incomplete data, were studied: first, a 10-bar truss and second, a cracked free-free beam, both modeled with finite elements. In these cases, the damage location and extent were successfully determined. Finally, a non-linear oscillator (Duffing oscillator) was identified by PSOS providing good results. (C) 2009 Elsevier Ltd. All rights reserved

Multiobjective Particle Swarm Approach for the Design of a Brushless DC Wheel Motor

The roots of swarm intelligence are deeply embedded in the biological study of self-organized behaviors in social insects. Particle swarm optimization (PSO) is one of the modern metaheuristics of swarm intelligence, which can be effectively used to solve nonlinear and non-continuous optimization problems. The basic principle of PSO algorithm is formed on the assumption that potential solutions (particles) will be flown through hyperspace with acceleration towards more optimum solutions. Each particle adjusts its flying according to the flying experiences of both itself and its companions using equations of position and velocity. During the process, the coordinates in hyperspace associated with its previous best fitness solution and the overall best value attained so far by other particles within the group are kept track and recorded in the memory. In recent years, PSO approaches have been successfully implemented to different problem domains with multiple objectives. In this paper, a multiobjective PSO approach, based on concepts of Pareto optimality, dominance, archiving external with elite particles and truncated Cauchy distribution, is proposed and applied in the design with the constraints presence of a brushless DC (Direct Current) wheel motor. Promising results in terms of convergence and spacing performance metrics indicate that the proposed multiobjective PSO scheme is capable of producing good solutions.

Particle swarm optimization based approaches to vehicle-to-grid scheduling

This paper addresses the problem of energy resources management using modern metaheuristics approaches, namely Particle Swarm Optimization (PSO), New Particle Swarm Optimization (NPSO) and Evolutionary Particle Swarm Optimization (EPSO). The addressed problem in this research paper is intended for aggregators’ use operating in a smart grid context, dealing with Distributed Generation (DG), and gridable vehicles intelligently managed on a multi-period basis according to its users’ profiles and requirements. The aggregator can also purchase additional energy from external suppliers. The paper includes a case study considering a 30 kV distribution network with one substation, 180 buses and 90 load points. The distribution network in the case study considers intense penetration of DG, including 116 units from several technologies, and one external supplier. A scenario of 6000 EVs for the given network is simulated during 24 periods, corresponding to one day. The results of the application of the PSO approaches to this case study are discussed deep in the paper.

A decision-support system based on particle swarm optimization for multiperiod hedging in electricity markets

This paper proposes a particle swarm optimization (PSO) approach to support electricity producers for multiperiod optimal contract allocation. The producer risk preference is stated by a utility function (U) expressing the tradeoff between the expectation and variance of the return. Variance estimation and expected return are based on a forecasted scenario interval determined by a price range forecasting model developed by the authors. A certain confidence level is associated to each forecasted scenario interval. The proposed model makes use of contracts with physical (spot and forward) and financial (options) settlement. PSO performance was evaluated by comparing it with a genetic algorithm-based approach. This model can be used by producers in deregulated electricity markets but can easily be adapted to load serving entities and retailers. Moreover, it can easily be adapted to the use of other type of contracts.

Distributed energy resource short-term scheduling using signaled particle swarm optimization

Distributed Energy Resources (DER) scheduling in smart grids presents a new challenge to system operators. The increase of new resources, such as storage systems and demand response programs, results in additional computational efforts for optimization problems. On the other hand, since natural resources, such as wind and sun, can only be precisely forecasted with small anticipation, short-term scheduling is especially relevant requiring a very good performance on large dimension problems. Traditional techniques such as Mixed-Integer Non-Linear Programming (MINLP) do not cope well with large scale problems. This type of problems can be appropriately addressed by metaheuristics approaches. This paper proposes a new methodology called Signaled Particle Swarm Optimization (SiPSO) to address the energy resources management problem in the scope of smart grids, with intensive use of DER. The proposed methodology’s performance is illustrated by a case study with 99 distributed generators, 208 loads, and 27 storage units. The results are compared with those obtained in other methodologies, namely MINLP, Genetic Algorithm, original Particle Swarm Optimization (PSO), Evolutionary PSO, and New PSO. SiPSO performance is superior to the other tested PSO variants, demonstrating its adequacy to solve large dimension problems which require a decision in a short period of time.

A short-term risk management tool applied to OMEL electricity market using particle swarm optimization

Short-term risk management is highly dependent on long-term contractual decisions previously established; risk aversion factor of the agent and short-term price forecast accuracy. Trying to give answers to that problem, this paper provides a different approach for short-term risk management on electricity markets. Based on long-term contractual decisions and making use of a price range forecast method developed by the authors, the short-term risk management tool presented here has as main concern to find the optimal spot market strategies that a producer should have for a specific day in function of his risk aversion factor, with the objective to maximize the profits and simultaneously to practice the hedge against price market volatility. Due to the complexity of the optimization problem, the authors make use of Particle Swarm Optimization (PSO) to find the optimal solution. Results from realistic data, namely from OMEL electricity market, are presented and discussed in detail.

Particle swarm optimization applied to integrated demand response resources scheduling

The concept of demand response has a growing importance in the context of the future power systems. Demand response can be seen as a resource like distributed generation, storage, electric vehicles, etc. All these resources require the existence of an infrastructure able to give players the means to operate and use them in an efficient way. This infrastructure implements in practice the smart grid concept, and should accommodate a large number of diverse types of players in the context of a competitive business environment. In this paper, demand response is optimally scheduled jointly with other resources such as distributed generation units and the energy provided by the electricity market, minimizing the operation costs from the point of view of a virtual power player, who manages these resources and supplies the aggregated consumers. The optimal schedule is obtained using two approaches based on particle swarm optimization (with and without mutation) which are compared with a deterministic approach that is used as a reference methodology. A case study with two scenarios implemented in DemSi, a demand Response simulator developed by the authors, evidences the advantages of the use of the proposed particle swarm approaches.

Entropy diversity in multi-objective particle swarm optimization

Multi-objective particle swarm optimization (MOPSO) is a search algorithm based on social behavior. Most of the existing multi-objective particle swarm optimization schemes are based on Pareto optimality and aim to obtain a representative non-dominated Pareto front for a given problem. Several approaches have been proposed to study the convergence and performance of the algorithm, particularly by accessing the final results. In the present paper, a different approach is proposed, by using Shannon entropy to analyzethe MOPSO dynamics along the algorithm execution. The results indicate that Shannon entropy can be used as an indicator of diversity and convergence for MOPSO problems.

Demand response management in power systems using a particle swarm optimization approach

Competitive electricity markets have arisen as a result of power-sector restructuration and power-system deregulation. The players participating in competitive electricity markets must define strategies and make decisions using all the available information and business opportunities.