Use Of Differential Evolution Research Articles

Two-level optimization by differential evolution in decision tree learning algorithm

Decision tree learning algorithms have a long history, but they are still popular due to their efficiency. Tree construction starts at the root and continues to each leaf node, creating a “near-optimal” tree. One of the key steps in creating a decision tree is the selection of a feature to split at each root node, which affects the classification accuracy. This process can be quite labor intensive. The article proposes a new approach to constructing decision trees based on the use of differential evolution for two-level tree optimization. Differential evolution works in two stages: at the first level, a feature is selected for separation, and at the second level, the threshold value for this feature is optimized. The results of the work were tested on several examples of classification problems.

Feature Descriptor based on Differential Evolution for Visual Navigation in Dynamic Environments

This work proposes to use a teach-and-repeat method to navigate in an outdoor environment. Instead of using state-of-the-art feature point descriptors to match the current images to the database, we rely on the Generated Binary Robust Independent Elementary Features (GRIEF), a model robust to changes in illumination and weather. These descriptors are obtained via a training process employing evolutionary methods and binary comparison tests. The objective is to obtain visual feature descriptors designed for a given task. For the teach-and-repeat task, they are trained to optimize the estimate of the robot heading error with respect to a learned path. In this work, we propose to investigate how Differential Evolution (DE) can improve the performance of the GRIEF in terms of the convergence rate during the training phase and of fitness score. The new approach, named GRIEF-DE, is trained with the Michigan data set, made of pictures of an outdoor environment with significant changes in appearance caused by seasonal weather variations and illumination, and compared with the original GRIEF. The proposed model was applied to 4 different data sets and the experimental results suggest that the use of Differential Evolution improves the training performance as well as the estimation of the robot orientation with respect to the path of reference.

On training non-uniform fuzzy partitions for function approximation using differential evolution: A study on fuzzy transform and fuzzy projection

This paper focuses on the use of differential evolution to improve the approximation properties of function approximation models based on fuzzy partitions. Two cases are considered: Fuzzy transform and Fuzzy projection, and the design of hybrid evolutionary fuzzy systems, is studied. Even though function approximation techniques based on fuzzy partitions have been well studied, few papers consider the problem of centroid selection of the basis functions. Thus, in most cases uniform fuzzy partitions are considered. By using an evolutionary algorithm a systematic approach on the selection of the partition, is provided. The optimisation problem involves the determination of the model parameters, which in our case are the fuzzy partition’s membership functions’ locations. The proposed method is tested on the scattered data approximation problem, in a regression sense, that is given a set of sparse data the latent function is approximated. Numerical studies on one and two-dimensional test functions demonstrate that the evolutionary algorithm based fuzzy projection displays high performance in terms of approximation error. Moreover, the proposed approach shows high approximation capabilities with a small number of basis functions. Comparison results, with uniform fuzzy partition models, neural networks and support vector machines, are provided.

Development of ANFIS technique for estimation of CO2 solubility in amino acids and study on impact of input parameters

ANFIS (Adaptive neuro fuzzy inference system) modeling of CO2 capture using chemical absorbent was carried out in this study to correlate the solubility of CO2 to the solvent and operational parameters. In the ANFIS model, the input parameters including temperature, pressure, and physio-chemical properties of the solvent were considered, while the loading of CO2 in the absorbent was considered as the sole target output to be predicted by the model. Indeed, we developed a machine learning based model for predicting the CO2 loading capacity in amino acid salt solutions as the chemical absorbent of carbon dioxide. This model uses a metaheuristic optimized ANFIS based on a wide range of amino acids. This study's novel part is the use of Differential Evolution (DE) and Firefly Algorithm (FA) metaheuristics in order to solve hyper-parameter tuning of ANFIS as an optimization problem based on differential evolution. Accordingly, the optimized ANFIS model has an R2 score of 0.9520 for the test data and a score of 0.9841 for the training data. This indicates that the proposed model is both general and accurate in terms of its predictions for CO2 loading in amino acid salt solutions. The MAPE and RMSE error rates are also 1.17E-01, respectively, while the MAPE error rate is 1.14E-01.

Approximate Analytical Solution of Unstable Ordinary Differential Equation Using Differential Evolution Algorithm

The application of evolutionary optimization algorithms in problem solving is currently gaining wide popularity. Use of Differential Evolution (DE) algorithm in obtaining analytically approximate solution of unstable second–order initial value Ordinary Differential Equation (ODE) is presented in this work. The methodology involves solving an associated problem of optimization with constrains to get an analytically approximate solution for the ODE under consideration. Three test cases were used to demonstrate the efficiency of our method. In comparison with other methods discussed in the literature, our method gave significant improvement on the accuracy of the obtained results.

A differential evolution algorithm for estimating mobile channel parameters [formula omitted

The statistical modeling of mobile radio signals requires the estimation of parameters that describe the probability distribution that hypothetically models this channel, so that this probabilistic model guarantees a good adjustment to the experimental data. This article proposes the use of differential evolution (DE) algorithms for estimating parameters of the α−η−μ fading channel, and to compare these to the traditional method of moments (MM) and maximum likelihood estimation (MLE) method. These traditional parameter estimation methods use nonlinear numerical methods, and the solution, if found, may be the optimal value, an approximation of the optimal value, or a local maximum. The authors demonstrate through comparative experiments using the MM and the MLE method that the DE algorithm for the proposed estimation demands a lower run time. In addition, it presents the error performance measured by the mean square error (MSE), near or above, as well as high robustness measured by the statistical analysis. Essentially, this algorithm always finds acceptable physical estimations with a good goodness of fit to experimental data. This estimating DE algorithm along with its proposed fitness function are original contributions of this paper. The received signal samples, used in the experiments of this paper, were randomly generated by the α−η−μ fading simulator, which is another contribution of this paper. This proposed α−η−μ fading simulator is based on the Clarke and Gans fading model and expands the generation range of current simulators, from μ integer multiples of 0.5, to μ integer multiples of 0.25.

Detection of Glaucoma in Retinal Images Based on Multiobjective Approach

Glaucoma is one of the major causes of blindness. Glaucoma is a condition due to increased pressure within the eyeball, causing progressive, irreversible and gradual loss of sight. It can be prevented only detection in disc ratio (CDR), ratio of blood vessel area in interior and superior side of the blood vessel in the nasal temporal side extracted from retinal fundus images. Reducing the number of features and reducing the error rate are two conflicting objectives. The proposed methodology aims to explore the use of Differential Evolution based multi objective feature selection technique to select a subset of features which minimize both our conflicting objectives. The performance of selected subset of features has been evaluated using KNN classification technique. It has been observed that said extracted subset of five features, KNN classification achieved better accuracy than any other subset of features.

Systemically modeling the relationship between climate change and wheat aphid abundance

Climate change influences all living beings. Wheat aphids deplete the nutritional value of wheat and affect the production of wheat in changing climate. In this study, we attempt to explain the ecological mechanisms of how climate change affects wheat aphids by simulating the relationship between climate and the abundance of wheat aphids, which will not only aid in improving wheat aphid forecasting and the effectiveness of prevention and treatment, but also help mitigate food crises. Fuzzy cognitive maps (FCM) are an effective tool for portraying complex systems. Using Sitobion avenae and climatological data collected in China, we made use of differential evolution (DE) algorithms to construct FCM models that directly illustrate the effect of climate on wheat aphid abundance. The relationships among climate and wheat aphids at different growth stages (I–III instar larvae, IV instar larvae with wings, IV instar larvae without wings, adult with wings, adult without wings) were established. The analysis results from the FCM models show that temperature positively influences wheat aphids most. Moreover, these models can be used to determine the numerical value of each climate factor and the abundance of wheat aphids quantitatively. Furthermore, the two overall relationship models between climate and wheat aphids were constructed and the experimental results show that natural enemies and highest daily temperature affect wheat aphids most. Natural enemies and highest daily temperature exert negative and positive impacts on wheat aphids respectively. Some interrelationships among wheat aphids at all growth stages and the internal relationships among climate factors were also shown.

Differential Evaluation Based Secure Ad-Hoc Protocol for Vanets

VANET is a special category of MANETs which is composed of moving vehicles, acting as nodes. Vehicular Ad-hoc Networks is aimed at increasing inter-vehicular communication, so that information collected in a vehicle can be shared with other vehicle users, with the aim of improving driving experience. Many studies have indicated that appropriate attack algorithms are essential to provide secure operation of a network. It has been observed that the use of optimum or sub-optimum values are ignored while detecting the wormhole attacks in VANETs. The use of differential evolution is ignored in existing literature which can find optimum values for attack detection based VANETs. It has been observed that the proposed technique outperforms existing techniques in terms of packet collision and throughput.

Solving constrained optimisation problems using the improved imperialist competitive algorithm and Deb’s technique

ABSTRACTIn this paper, an improved imperialist competitive algorithm called I-ICA is proposed for solving constrained optimisation problems. In I-ICA, the use of differential evolution (DE)/rand/1 mutation operator at assimilation step enhances the population diversity. Also, the binomial crossover operator improves the speed of convergence to optimal solution by distributing good information among solutions. Furthermore, Deb’s rules were applied for handling constrains. Examinations were done on 24 well-known functions and 5 engineering design problems. The comparison of I-ICA with basic ICA and 22 state-of-the-art algorithms shows I-ICA’s superiority in terms of the rate of convergence and quality of the obtained solution.

A review of the recent use of Differential Evolution for Large-Scale Global Optimization: An analysis of selected algorithms on the CEC 2013 LSGO benchmark suite

Abstract This paper gives a review of recent extensions of the Differential Evolution (DE) algorithm for use in Large-Scale Global Optimization (LSGO) and presents an empirical analysis of DE-based and some other state-of-the-art algorithms for LSGO on the CEC 2013 LSGO benchmark suite. Since witnessing the first successful applications of DE for a wide variety of optimization problems in the early nineties, researchers have developed several new algorithms in this field. In this paper, we are especially interested in algorithms for solving LSGO. As LSGO is one of the most active research lines, not only in DE, but in many evolutionary and meta-heuristic algorithms, we discuss general approaches for dealing with LSGO first. The main focus of the paper is DE. We review its basic algorithm and discuss several extensions used for coping with large-scale problems. This paper has two main objectives: (1) To propose, from a theoretical point of view, the grouping of DE mechanisms for dealing with LSGO into nine groups, and (2) To evaluate sixteen recently proposed algorithms for LSGO empirically. Many benchmark suites were designed with the aim of providing a suitable evaluation platform for testing and comparing large-scale optimization algorithms. In this paper, the CEC 2013 LSGO benchmark suite was chosen for comparison, because it resembles the following features of real-world problems: Non-uniform subcomponent sizes; imbalance in the contribution of subcomponents; and functions with interdependent overlapping subcomponents. The performances of state-of-the-art algorithms are compared, and the algorithms are ranked using three different metrics, which evaluate the performance from different perspectives. The conducted research shows that DE is among the best algorithms for LSGO on the CEC 2013 LSGO benchmark suite, especially when used with other mechanisms for dealing with large numbers of variables. Finally, the analysis has shown that there is still some room for further improvements in DE towards the solution of LSGO problems.

Temperature influence analysis on parameter estimation of induction motors using differential evolution

Three-phase induction motors are widely used in industry due to their low cost and ruggedness compared with other electromechanical conversion machines, as the direct cur-rent motors, for example. Systems and control drives (DTC, FOC and V/f) are applied in industry, so it is important to know the electrical and mechanical parameters of the machine, such as, stator and rotor resistances, stator and rotor leakage inductance and magnetizing inductance, moment of inertia and friction coefficients. However, parameters like stator and rotor resistances suffer influences throughout its use due to external factors, such as temperature, which impairs the machine efficiency. In the search for a method to find these parameters, even with the changes provided by the temperature influence, this work proposes the use of differential evolution for the estimation of the parameters using as input the curve of a single phase stator current. Tests were realized using four different temperature values, and for each one it was assigned a corresponding input, in order to analyze the temperature influence on stator and rotor resistance. The results presented show that it is possible to estimate the motor electrical and mechanical parameters even with the changes provided by the temperature influences.

A general method for parameter estimation in light-response models.

Selecting appropriate initial values is critical for parameter estimation in nonlinear photosynthetic light response models. Failed convergence often occurs due to wrongly selected initial values when using currently available methods, especially the kind of local optimization. There are no reliable methods that can resolve the conundrum of selecting appropriate initial values. After comparing the performance of the Levenberg–Marquardt algorithm and other three algorithms for global optimization, we develop a general method for parameter estimation in four photosynthetic light response models, based on the use of Differential Evolution (DE). The new method was shown to successfully provide good fits (R2 > 0.98) and robust parameter estimates for 42 datasets collected for 21 plant species under the same initial values. It suggests that the DE algorithm can efficiently resolve the issue of hyper initial-value sensitivity when using local optimization methods. Therefore, the DE method can be applied to fit the light-response curves of various species without considering the initial values.

Decoupling Control of Penicillin Fermentation Processes Based on MLS-SVM Inversion

Specific to typical multi-variable, strong-coupling and nonlinear penicillin fermentation process, by combination of an inverse system method and a support vector machine theory, a nonlinear robust decoupling control method based on MLS-SVM inversion is proposed. Firstly, a dynamic system model is developed based on material balance relation of fed-batch fermentation process, and existence of inverse system is analyzed. Secondly, an inverse model has been developed offline by use of fitting capacity of MLS-SVM; online correction was made by use of differential evolution (DE) algorithm on the basis of deviation information. Finally, to connect the inverse model and original system in serial into a compound pseudo-linear system, and based on characteristics of pseudo-linear system, introduce internal model controller for closed-loop control of the system. Simulation result shows that such control method can realize dynamic decoupling control of penicillin fermentation process; the system boasts very strong parameter robustness and good resistance against interference

Empirical Comparison of Differential Evolution Variants for Industrial Controller Design

AbstractTo be cost-effective, most commercial off-the-shelf industrial controllers have low system order and a predefined internal structure. When operating in an industrial environment, the system output is often specified by a reference model, and the control system must closely match the model's response. In this context, a valid controller design solution must satisfy the application specifications, fit the controller's configuration and meet a model matching criterion. This paper proposes a method of solving the design problem using bilinear matrix inequality formulation, and the use of Differential Evolution (DE) algorithms to solve the resulting optimization problem. The performance of the proposed method is demonstrated by comparing a set of ten DE variants. Extensive statistical analysis shows that the variants best/1/{bin, exp} and rand-to-best/1/{bin, exp} are effective in terms of mean best objective function value, average number of function evaluations, and objective function value progression.

Incorporating Objective Function Information Into the Feasibility Rule for Constrained Evolutionary Optimization.

When solving constrained optimization problems by evolutionary algorithms, an important issue is how to balance constraints and objective function. This paper presents a new method to address the above issue. In our method, after generating an offspring for each parent in the population by making use of differential evolution (DE), the well-known feasibility rule is used to compare the offspring and its parent. Since the feasibility rule prefers constraints to objective function, the objective function information has been exploited as follows: if the offspring cannot survive into the next generation and if the objective function value of the offspring is better than that of the parent, then the offspring is stored into a predefined archive. Subsequently, the individuals in the archive are used to replace some individuals in the population according to a replacement mechanism. Moreover, a mutation strategy is proposed to help the population jump out of a local optimum in the infeasible region. Note that, in the replacement mechanism and the mutation strategy, the comparison of individuals is based on objective function. In addition, the information of objective function has also been utilized to generate offspring in DE. By the above processes, this paper achieves an effective balance between constraints and objective function in constrained evolutionary optimization. The performance of our method has been tested on two sets of benchmark test functions, namely, 24 test functions at IEEE CEC2006 and 18 test functions with 10-D and 30-D at IEEE CEC2010. The experimental results have demonstrated that our method shows better or at least competitive performance against other state-of-the-art methods. Furthermore, the advantage of our method increases with the increase of the number of decision variables.

Optimized weights of document keywords for auto-reply accuracy

A Taguchi-crossover differential evolution (TCDE) algorithm is proposed to optimize weights of document keywords for auto-reply accuracy. The proposed TCDE algorithm combines the use of differential evolution for exploring the optimal feasible region in macro-space with the use of the Taguchi method for exploiting the optimal solution in micro-space. For learning purpose, an answer needs to be exactly given for a specific query. Notably, teachers give a problem answer to elementary students who need to have the clear and accurate solution for learning according to their queries. This study shows the TCDE which integrates a cosine similarity measure and an evaluation function to successfully find the best weights of document keywords for auto-reply accuracy. Performance comparisons confirm that the TCDE algorithm outperforms existing methods presented in the literature in finding the best weights of document keywords and obtaining accurate answers.

Optimizing Mobile Robot Path Planning and Navigation by Use of Differential Evolution

Optimizing Mobile Robot Path Planning and Navigation by Use of Differential Evolution

Differential-Evolution-Based Optimization of the Dynamic Response for Parallel Operation of Inverters With No Controller Interconnection

In this paper, the use of differential evolution (DE), a global search technique inspired by evolutionary theory, to find the parameters that are required to achieve optimum dynamic response of parallel operation of inverters with no interconnection among the controllers is proposed. Basically, in order to reach such a goal, the system is modeled in a certain way that the slopes of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> - ω and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> curves are the parameters to be tuned. Such parameters, when properly tuned, result in system's eigenvalues located in positions that assure the system's stability and oscillation-free dynamic response with minimum settling time. This paper describes the modeling approach and provides an overview of the motivation for the optimization and a description of the DE technique. Simulation and experimental results are also presented, and they show the viability of the proposed method.

Identification of Nolinear Systems Using Inceremnetal and Diffusion Differential Evolution Algorithms

The paper investigates on the use of Differential Evolution (DE) for training the system identification model particularly when the measurement data are available at different sensor nodes. Under such situation the conventional DE algorithms cannot be applied directly. Hence in this paper two distributed learning algorithms known as incremental DE (IDE) and diffusion DE (DDE) have been developed to meet the requirements. The identification of nonlinear plants under different noise conditions has been obtained through simulation study and the results have been compared with distributed PSO algorithms. The performance of the proposed algorithms in terms of convergence rate and minimum mean squared error indicate that the distributed DE algorithms exhibit superior performance compared to its PSO counter parts.