Least Squares Fitting of Chacón-Gielis Curves by the Particle Swarm Method of Optimization

Ricardo Chacón generalized Johan Gielis's superformula by introducing elliptic functions in place of trigonometric functions. In this paper an attempt has been made to fit the Chacón-Gielis curves (modified by various functions) to simulated data by the least squares principle. Estimation has been done by the Particle Swarm (PS) methods of global optimization. The Repulsive Particle Swarm optimization algorithm has been used. It has been found that although the curve-fitting exercise may be satisfactory, a lack of uniqueness of Chacón-Gielis parameters to data (from which they are estimated) poses an insurmountable difficulty to interpretation of findings.Least squares multimodal nonlinear curve-fitting; Ricardo Chacón; Jacobian Elliptic functions; Weierstrass ; Gielis super-formula; supershapes; Particle Swarm method; Repulsive Particle Swarm method of Global optimization; nonlinear programming; multiple sub-optima; global; local optima; fit; empirical; estimation; cellular automata; fractals

Generalised additive multiscale wavelet models constructed using particle swarm optimisation and mutual information for spatio-temporal evolutionary system representation

A new class of generalised additive multiscale wavelet models (GAMWMs) is introduced for high dimensional spatio-temporal evolutionary (STE) system identification. A novel two-stage hybrid learning scheme is developed for constructing such an additive wavelet model. In the first stage, a new orthogonal projection pursuit (OPP) method, implemented using a particle swarm optimisation(PSO) algorithm, is proposed for successively augmenting an initial coarse wavelet model, where relevant parameters of the associated wavelets are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be a redundant model. In the second stage, a forward orthogonal regression (FOR) algorithm, implemented using a mutual information method, is then applied to refine and improve the initially constructed wavelet model. The proposed two-stage hybrid method can generally produce a parsimonious wavelet model, where a ranked list of wavelet functions, according to the capability of each wavelet to represent the total variance in the desired system output signal is produced. The proposed new modelling framework is applied to real observed images, relative to a chemical reaction exhibiting a spatio-temporal evolutionary behaviour, and the associated identification results show that the new modelling framework is applicable and effective for handling high dimensional identification problems of spatio-temporal evolution sytems

Lattice dynamical wavelet neural networks implemented using particle swarm optimization for spatio-temporal system identification

In this brief, by combining an efficient wavelet representation with a coupled map lattice model, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNNs), is introduced for spatio-temporal system identification. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimization (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the OPP algorithm, significant wavelet neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer. The resultant network model, obtained in the first stage, however, may be redundant. In the second stage, an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network. An example for a real spatio-temporal system identification problem is presented to demonstrate the performance of the proposed new modeling framework

Lattice dynamical wavelet neural networks implemented using particle swarm optimisation for spatio-temporal system identification

Starting from the basic concept of coupled map lattices, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNN), is introduced for spatiotemporal system identification, by combining an efficient wavelet representation with a coupled map lattice model. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimisation (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the orthogonal projection pursuit algorithm, significant wavelet-neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated waveletneurons are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be redundant. In the second stage, an orthogonal least squares (OLS) algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet-neurons from the network. The proposed two-stage hybrid training procedure can generally produce a parsimonious network model, where a ranked list of wavelet-neurons, according to the capability of each neuron to represent the total variance in the system output signal is produced. Two spatio-temporal system identification examples are presented to demonstrate the performance of the proposed new modelling framework

The Simulation and Improvement of Particle Swarm Optimization Based on Cellular Automata

AbstractWe observed that PSO algorithm was easily falling into local extreme point by using cellular automata simulation, and developed several improvement strategies which drew inspiration from simulation, such as adding additional particle into updated formula, introducing crossover operator and mutation disturbance when the premature convergence occurs. The experiments validated new algorithm on 10 benchmark functions, and results showed that the improved PSO algorithm has better stability and higher accuracy

Effective Prostate Cancer Detection using Enhanced Particle Swarm Optimization Algorithm with Random Forest on the Microarray Data

Prostate Cancer (PC) is the leading cause of mortality among males, therefore an effective system is required for identifying the sensitive bio-markers for early recognition. The objective of the research is to find the potential bio-markers for characterizing the dissimilar types of PC. In this article, the PC-related genes are acquired from the Gene Expression Omnibus (GEO) database. Then, gene selection is accomplished using enhanced Particle Swarm Optimization (PSO) to select the active genes, which are related to the PC. In the enhanced PSO algorithm, the interval-newton approach is included to keep the search space adaptive by varying the swarm diversity that helps to perform the local search significantly. The selected active genes are fed to the random forest classifier for the classification of PC (high and low-risk). As seen in the experimental investigation, the proposed model achieved an overall classification accuracy of 96.71%, which is better compared to the traditional models like naïve Bayes, support vector machine and neural network

Load balancing in cloud data centers with optimized virtual machines placement

So far, various solutions have been proposed for symmetric distribution of load cloud computing environments. In this article, a new solution to the optimal allocation of virtual machines in the cloud data centers is presented to provide a good load balancing among servers. The proposed method offers a solution uses learning automata as a reinforcement learning model to improve the performance of the optimization algorithm for optimal placement of virtual machines. Also, it helps the search algorithm to converge more quickly to the global optimum. The simulation results show the proposed method has been able to perform good level of load balancing in cloud data centers

Improving Learning Automata based Particle Swarm: An optimization algorithm

Optimization (PSO) algorithms have been recently developed, with the best aim of escaping from local minima. One of these recent variations is PSO-LA model which employs a Learning Automata (LA) that controls the velocity of the particle. Another variation of PSO enables particles to dynamically search through global and local space. This paper presents a Dynamic Global and Local Combined Particle Swarm Optimization based on a 3-action Learning Automata (DPSOLA). The embedded learning automaton accumulates the information from individuals, local best and global best particles then combines them to navigate the particle through the problem space. The proposed algorithm has been tested on eight benchmark functions with different dimensions. The work is unique from its test bed; evaluations contain large population size (150) and high dimension (150). The results show that, fitness and convergence pace is better than traditional PSO, DGLCPSO and previous PSO based LA algorithms. I

Generalised cellular neural networks (GCNNs) constructed using particle swarm optimisation for spatio-temporal evolutionary pattern identification

Particle swarm optimization (PSO) is introduced to implement a new constructive learning algorithm for training generalized cellular neural networks (GCNNs) for the identification of spatio-temporal evolutionary (STE) systems. The basic idea of the new PSO-based learning algorithm is to successively approximate the desired signal by progressively pursuing relevant orthogonal projections. This new algorithm will thus be referred to as the orthogonal projection pursuit (OPP) algorithm, which is in mechanism similar to the conventional projection pursuit approach. A novel two-stage hybrid training scheme is proposed for constructing a parsimonious GCNN model. In the first stage, the orthogonal projection pursuit algorithm is applied to adaptively and successively augment the network, where adjustable parameters of the associated units are optimized using a particle swarm optimizer. The resultant network model produced at the first stage may be redundant. In the second stage, a forward orthogonal regression (FOR) algorithm, aided by mutual information estimation, is applied to re. ne and improve the initially trained network. The effectiveness and performance of the proposed method is validated by applying the new modeling framework to a spatio-temporal evolutionary system identification problem