Trigonometric Differential Evolution Research Articles

Optimization of Dynamic Systems: A Comparative Study of Two Modified Differential Evolution Algorithms

Differential Evolution (DE) is a novel, efficient, effective and robust evolutionary optimization technique. DE algorithm is gaining popularity for solving complex optimization problems encountered in many engineering disciplines. This paper deals with the application and performance evaluation of two modified versions of DE [named as Modified Differential Evolution (MDE) and Trigonometric Differential Evolution (TDE)]. Three algorithms have been used for solving five dynamic optimization problems encountered in chemical engineering. Results indicate that MDE algorithm outperformed DE and TDE algorithms for solving problems with small number of control stages. But TDE algorithm is found to be faster and efficient than MDE and DE algorithms particularly for problems involving large number of control stages.

Reverse engineering genetic networks using nonlinear saturation kinetics

A gene regulatory network (GRN) represents a set of genes along with their regulatory interactions. Cellular behavior is driven by genetic level interactions. Dynamics of such systems show nonlinear saturation kinetics which can be best modeled by Michaelis-Menten (MM) and Hill equations. Although MM equation is being widely used for modeling biochemical processes, it has been applied rarely for reverse engineering GRNs. In this paper, we develop a complete framework for a novel model for GRN inference using MM kinetics. A set of coupled equations is first proposed for modeling GRNs. In the coupled model, Michaelis-Menten constant associated with regulation by a gene is made invariant irrespective of the gene being regulated. The parameter estimation of the proposed model is carried out using an evolutionary optimization method, namely, trigonometric differential evolution (TDE). Subsequently, the model is further improved and the regulations of different genes by a given gene are made distinct by allowing varying values of Michaelis-Menten constants for each regulation. Apart from making the model more relevant biologically, the improvement results in a decoupled GRN model with fast estimation of model parameters. Further, to enhance exploitation of the search, we propose a local search algorithm based on hill climbing heuristics. A novel mutation operation is also proposed to avoid population stagnation and premature convergence. Real life benchmark data sets generated in vivo are used for validating the proposed model. Further, we also analyze realistic in silico datasets generated using GeneNetweaver. The comparison of the performance of proposed model with other existing methods shows the potential of the proposed model.

Inferring gene regulatory networks using a time-delayed mass action model.

This paper demonstrates a new time-delayed mass action model which applies a set of delay differential equations (DDEs) to represent the dynamics of gene regulatory networks (GRNs). The mass action model is a classical model which is often used to describe the kinetics of biochemical processes, so it is fit for GRN modeling. The ability to incorporate time-delayed parameters in this model enables different time delays of interaction between genes. Moreover, an efficient learning method which employs population-based incremental learning (PBIL) algorithm and trigonometric differential evolution (TDE) algorithm TDE is proposed to automatically evolve the structure of the network and infer the optimal parameters from observed time-series gene expression data. Experiments on three well-known motifs of GRN and a real budding yeast cell cycle network show that the proposal can not only successfully infer the network structure and parameters but also has a strong anti-noise ability. Compared with other works, this method also has a great improvement in performances.

Novel Coordination of DOCRs using Trigonometric Differential Evolution Algorithm

The coordination of directional overcurrent relays (DOCRs) has been formulated with different optimization algorithms (deterministic, heuristic, swarm, and evolutionary). The surge of studying coordination problem using heuristic, swarm and evolutionary optimization methods became popular. Because the coordination optimization problem is highly complex and non-linear, some algorithms may result in undesired operation time of DOCRs and also violation of coordination constraints. Therefore, the primary objective is to focus on the use of Trigonometric Differential Evolution (Tri-DE) algorithm in solving complex and non-linear DOCR coordination. The secondary objective is to improve the Trigonometric Differential Evolution algorithm in the coordination problem and compare it with the original Tri-DE algorithm.

Kinetic Parameter Estimation Using Modified Differential Evolution

For the development of mathematical models in chemical engineering, the parameter estimation methods are very important as design, optimization and advanced control of chemical processes depend on values of model parameters obtained from experimental data. Nonlinearity in models makes the estimation of parameter more difficult and more challenging. This paper presents an evolutionary computation approach for solving such problems. In this work, a modified version of Differential Evolution (DE) algorithm [named Modified Differential evolution (MDE)] is used to solve a kinetic parameter estimation problem from chemical engineering field. The computational efficiency of MDE is compared with that of original DE and Trigonometric Differential Evolution (TDE). Results indicate that performance of MDE algorithm is better than that of DE and TDE.

Parent-centric differential evolution algorithm for global optimization problems

Differential evolution (DE) is a population based evolutionary search algorithm widely used for solving optimization problems. In the present article we investigate the application of parent-centric approach on the performance of classical DE, without tampering with the basic structure of DE. The parent-centric approach is embedded in the mutation phase of DE. We propose two versions of (DE) called differential evolution with parent-centric crossover (DEPCX) and differential evolution with probabilistic parent-centric crossover (ProDEPCX) in order to improve the performance of classical DE. The proposed algorithms are validated on a test bed of ten benchmark functions and the numerical results are compared with basic DE and a modified version called trigonometric differential evolution (TDE). Empirical analysis of numerical results on the benchmark problems show that the performance of proposed versions is either at par or better in comparison to TDE and basic DE in terms of convergence rate and quality of fitness function value.

Optimization of dynamic systems: A trigonometric differential evolution approach

In many chemical engineering applications, one frequently encounters dynamic optimization problems. The solution of these types of problems is usually very difficult due to their highly nonlinear, multidimensional and multimodal nature. In fact, several deterministic techniques have been proposed to solve these problems but difficulties related to ease of implementation, global convergence, and good computational efficiency have been frequently found. Recently, evolutionary algorithms (EAs) are gaining popularity for solving complex problems encountered in many engineering disciplines. They are found to be robust and more likely to locate global optimum as compared to several deterministic (gradient based) optimization methods. This paper deals with the application and evaluation of one such algorithm called trigonometric differential evolution (TDE) algorithm for solving dynamic optimization problems encountered in chemical engineering. This is a modified version of differential evolution (DE) which provides enhanced convergence speed. Both DE and TDE algorithms have been applied to seven dynamic optimization problems (five optimal control problems and two kinetic parameter estimation problems) taken from recent literature. The obtained numerical simulation results indicate better performance of TDE as compared to that of DE particularly for problems involving large number of control stages.

Optimizing object classification under ambiguity/ignorance: application to the credit rating problem

A nascent technique for object classification is employed to exposit the classification of US banks to their financial strength ratings, presented by the Moody's Investors Services. The classification technique primarily utilized, called CaRBS (classification and ranking belief simplex), allows for the presence of ignorance to be inherent. The modern constrained optimization method, trigonometric differential evolution (TDE), is adopted to configure a CaRBS system. Two different objective functions are considered with TDE to measure the level of optimization achieved, which utilize differently the need to reduce ambiguity and/or ignorance inherently during the optimization process. The appropriateness of the CaRBS system to analyse incomplete data is also highlighted, with no requirement to impute any missing values or remove objects with missing values inherent. Comparative results are also presented using the well-known multivariate discriminant analysis and neural network models. The findings in this study identify a novel dimension to the issue of object classification optimization, with the discernment between the concomitant notions of ambiguity and ignorance. Copyright © 2005 John Wiley & Sons, Ltd.