Aritra Chowdhury

An improved differential evolution algorithm with fitness-based adaptation of the control parameters

Differential Evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. DE operates through the similar computational steps as employed by a standard Evolutionary Algorithm (EA). However, unlike the traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used, which makes the scheme self-organizing in this respect. Scale Factor (F) and Crossover Rate (Cr) are two very important control parameters of DE since the former regulates the step-size taken while mutating a population member in DE and the latter controls the number of search variables inherited by an offspring from its parent during recombination. This article describes a very simple yet very much effective adaptation technique for tuning both F and Cr, on the run, without any user intervention. The adaptation strategy is based on the objective function value of individuals in the DE population. Comparison with the best-known and expensive variants of DE over fourteen well-known numerical benchmarks and one real-life engineering problem reflects the superiority of proposed parameter tuning scheme in terms of accuracy, convergence speed, and robustness.

An ecologically inspired direct search method for solving optimal control problems with Bézier parameterization

An optimal control problem can be formulated through a set of differential equations describing the trajectory of the control variables that minimize the cost functional (related to both state and control variables). Direct solution methods for optimal control problems treat them from the perspective of global optimization: i.e. perform a global search for the control function that optimizes the required objective. In this article we use a recently developed ecologically inspired optimization technique called Invasive Weed Optimization (IWO) for solving such optimal control problems. Usually the direct solution method operates on discrete n-dimensional vectors and not on continuous functions. Consequently it can become computationally expensive for large values of n. Thus, a parameterization technique is required to represent the control functions using a small number of real-valued parameters. Typically, direct methods based on evolutionary computing techniques parameterize control functions with a piecewise constant approximation. This has obvious limitations both for accuracy in representing arbitrary functions, and for optimization efficiency. In this paper a new parameterization is introduced using Bezier curves, which can accurately represent continuous control functions with only a few parameters. It is combined with IWO into a new evolutionary direct method for optimal control. The effectiveness of the new method is demonstrated by solving a wide variety of optimal control problems.

Linear antenna array synthesis using fitness-adaptive differential evolution algorithm

Design of non-uniform linear antenna arrays is one of the most important electromagnetic optimization problems of current interest. In this article, an adaptive Differential Evolution (DE) algorithm has been used to optimize the spacing between the elements of the linear array to produce a radiation pattern with minimum side lobe level and null placement control. DE is arguably one of the best real parameter optimizers of current interest takes very few control parameters and is easy to implement in any programming language. In this study two very simple adaptation schemes are used to regulate the control parameters F and Cr, upon which the performance of DE is critically dependent. The adaptation schemes are based on the objective function values of the target vectors and donor vectors. The adaptive DE-variant has been used to solve three difficult instances of the design problem and the optimization goal in each example is easily achieved. The results of the proposed algorithm have been shown to meet or beat the recently published results obtained using other state-of-the-art metaheuristics like the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Memetic Algorithms (MA), and Tabu Search (TS) in a statistically meaningful way.

Automatic shape independent clustering inspired by ant dynamics

Abstract This article describes a simple heuristic algorithm that can automatically detect any number of well-separated clusters, which may be of any shape e.g. convex and/or non-convex. This is in contrast to most of the existing clustering algorithms that assume a value for the number of clusters and/or a particular cluster structure. The algorithm draws inspiration from the dynamics of ants and iteratively partitions the dataset based on its proximity matrix. A runtime complexity analysis shows that the complexity of the algorithm is either quadratic or cubic with respect to the size of the dataset. It can detect outliers from the data and is also able to identify the situation when the data do not have any natural clusters at all. Promising results on both real and artificial datasets have been included to show the effectiveness of the proposed technique.

A Modified Invasive Weed Optimization Algorithm for training of feed- forward Neural Networks

Invasive Weed Optimization Algorithm IWO) is an ecologically inspired metaheuristic that mimics the process of weeds colonization and distribution and is capable of solving multi-dimensional, linear and nonlinear optimization problems with appreciable efficiency. In this article a modified version of IWO has been used for training the feed-forward Artificial Neural Networks (ANNs) by adjusting the weights and biases of the neural network. It has been found that modified IWO performs better than another very competitive real parameter optimizer called Differential Evolution (DE) and a few classical gradient-based optimization algorithms in context to the weight training of feed-forward ANNs in terms of learning rate and solution quality. Moreover, IWO can also be used in validation of reached optima and in the development of regularization terms and non-conventional transfer functions that do not necessarily provide gradient information

Automatic clustering based on invasive weed optimization algorithm

In this article, an evolutionary metaheuristic algorithm known as the Invasive Weed Optimization (IWO) is applied for automatically partitioning a dataset without any prior information about the number of naturally occurring groups in the data. The fitness function used in the genetic algorithm is a cluster validity index. Depending on the results of this index IWO returns the segmented dataset along with the appropriate number of divisions. The proficiency of this algorithm is compared to variable string length genetic algorithm with point symmetry based distance clustering(VGAPS-clustering), variable string length Genetic K-means algorithm(GCUK-clustering) and a weighted sum validity function based hybrid niching genetic algorithm(HNGA-clustering) and is denoted for the nine artificial datasets and four real life datasets.

A hybrid evolutionary direct search technique for solving Optimal Control problems

An Optimal Control is a set of differential equations describing the path of the control variables that minimize the cost functional (function of both state and control variables). Direct solution methods for optimal control problems treat them from the perspective of global optimization: perform a global search for the control function that optimizes the required objective. Invasive Weed Optimization (IWO) technique is used here for optimal control. However, the direct solution method operates on discrete n-dimensional vectors, not on continuous functions, and becomes computationally unmanageable for large values of n. Thus, a parameterization technique is required, which can represent control functions using a small number of real-valued parameters. Typically, direct methods using evolutionary techniques parameterize control functions with a piecewise constant approximation. This has obvious limitations, both for accuracy in representing arbitrary functions, and for optimization efficiency. In this paper a new parameterization is introduced, using Bézier curves, which can accurately represent continuous control functions with only a few parameters. It is combined with Invasive Weed Optimization into a new evolutionary direct method for optimal control. The effectiveness of the new method is demonstrated by solving a wide range of optimal control problems.

Optimization of Antenna Configuration with a Fitness-Adaptive Differential Evolution Algorithm

In this article, a novel numerical technique, called Fitness Adaptive Difierential Evolution (FiADE) for optimizing certain pre-deflned antenna conflguration to attain best possible radiation characteristics is presented. Difierential Evolution (DE), inspired by the natural phenomenon of theory of evolution of life on earth, employs the similar computational steps as by any other Evolutionary Algorithm (EA). Scale Factor and Crossover Probability are two very important control parameter of DE.This article describes a very competitive yet very simple form of adaptation technique for tuning the scale factor, on the run, without any user intervention. The adaptation strategy is based on the fltness function value of individuals in DE population. The feasibility, e-ciency and efiectiveness of the proposed algorithm in the fleld of electromagnetism are examined over a set of well-known antenna conflgurations optimization problems. Comparison with the some very popular and powerful metaheuristics re∞ects the superiority of this simple parameter automation strategy in terms of accuracy, convergence speed, and robustness.

Two-channel quadrature mirror bank filter design using a Fitness- Adaptive Differential Evolution algorithm

In this article, a modification of Differential Evolution (DE), Fitness-Adaptive Differential Evolution (FiADE) is used to design the quadrature mirror filter (QMF) banks with linear phase in frequency domain. The three main attributes used in assessing the performance of filter are reconstruction error, mean square error in pass band and mean square error in stop band. The proposed method produces better result than the result obtained by Particle Swarm Optimization (PSO). As compared to the existing methods this method is very simple to implement for the QMF bank optimization. To implement the proposed DE algorithm, a MATLAB program is developed and three examples have been presented to illustrate the performance of the proposed method.

Joint energy and spinning reserve dispatch in wind-thermal power system using IDE-SAR technique

This paper proposes an informative differential evolution with self adaptive re-clustering (IDE-SAR) technique to solve the optimal energy and spinning reserve scheduling problem of a wind-thermal power system. The goal of the paper is to solve an economic dispatch problem, and to find optimal allocation of energy and spinning reserves among the thermal and wind generators available to serve the demand. The stochastic behavior of wind speed and wind power is represented by Weibull probability density function. The total cost minimization objective includes cost of energy provided by conventional thermal generators and wind generators, cost of reserves provided by conventional thermal generators. It also includes costs due to over-estimation and under-estimation of available wind power. In order to show the effectiveness and feasibility of the proposed frame work, various case studies are presented for conventional and wind-thermal power system considering the provision of spinning reserves.