Variant Of Differential Evolution Algorithm Research Articles

Cε-LDE: A lightweight variant of differential evolution algorithm with combined ε constrained method and Lévy flight for constrained optimization problems

Differential evolution (DE) algorithm is popular to tackle real-world optimization problems. The standard DE, however, is not able to solve constrained optimization problems (COPs) for their complicated linear or nonlinear constraints. The transformation of constraints, which is realized via constraint handling technique, has a great impact on dealing with constrained algorithms. In this paper, a lightweight and efficient variant of DE named Cε-LDE is proposed to solve constrained single-objective optimization problems. This study firstly introduces a combined constraint handling method, which is designed based on the difference and relationship between two different ε constrained methods and balances infeasible solution and feasible solution with rules from the perspective of probability allocation. In addition, an extra control parameter is redefined in terms of different initial ε level in consideration of the complexity and diversity of COPs. On the other hand, DE evolves by opposition-based learning initialization and modifications on mutation operator and crossover rate selection, respectively. Mutation strategies frequently named rand/1 and best/1 are adopted and Lévy flight is added to the mutation strategy as a multiplier with scale factor F for a long jump. The crossover rate CR tends to be a larger or smaller stochastic value according to the pros and cons of the selected vector. A set of 28 problems under different dimension settings (D = 10, 30, 50 and 100) used for the CEC 2017 Competition is employed to evaluate the performance of the proposed Cε-LDE. The computational results demonstrate the effectiveness and superiority of the proposed combined ε constrained method. A comparative study of Cε-LDE with state-of-art algorithms is conducted on the obtained experimental results under the rules of CEC 2017 Competition. The ranking outcomes reveal that Cε-LDE is equipped with high competitiveness. Furthermore, the applications in several standard real-life engineering problems verify the effectiveness and practicability of the proposed scheme.

Statistical analysis based reactive power optimization using improved differential evolutionary algorithm

AbstractThis study presents a novel improved differential evolutionary (IDE) algorithm for optimizing reactive power management (RPM) problems. The effectiveness of IDE algorithm is tested on different unimodal and multimodal benchmark functions. The objective function of the RPM is considered as the minimization of active power losses. Initially, the power flow analysis approach is employed to detect the optimal position of flexible AC transmission system (FACTS) devices. The proposed method is used to determine the optimal value of control variables such as generator's reactive power generation, transformer tap settings, and reactive power sources. Furthermore, the efficacy of the IDE approach is compared with other promising optimization methods such as variants of differential evolution algorithm, moth flame optimization (MFO), brainstorm‐based optimization algorithm (BSOA), and particle swarm optimization (PSO) on various IEEE standard test bus (i.e., IEEE‐30, ‐57, ‐118, and ‐300) systems with active and reactive loading incorporating FACTS devices. A Static VAR compensator (SVC) for shunt compensation and a thyristor‐controlled series compensator (TCSC) for series compensation were used as FACTS devices. The proposed IDE method significantly reduces the active power loss, that is, 55.65% in IEEE 30, 39.68% in IEEE 57, 16.32% in IEEE 118, and 8.56% in IEEE 300 bus system at nominal loading. Finally, the statistical analysis such as Wilcoxon signed‐rank test (WSRT) and ANOVA test were thoroughly analysed to demonstrate the firmness and accuracy of the proposed technique.

Adaptive Dimensional Learning with a Tolerance Framework for the Differential Evolution Algorithm

The Differential Evolution (DE) algorithm, which is an efficient optimization algorithm, has been used to solve various optimization problems. In this paper, adaptive dimensional learning with a tolerance framework for DE is proposed. The population is divided into an elite subpopulation, an ordinary subpopulation, and an inferior subpopulation according to the fitness values. The ordinary and elite subpopulations are used to maintain the current evolution state and to guide the evolution direction of the population, respectively. The inferior subpopulation learns from the elite subpopulation through the dimensional learning strategy. If the global optimum is not improved in a specified number of iterations, a tolerance mechanism is applied. Under the tolerance mechanism, the inferior and elite subpopulations implement the restart strategy and the reverse dimensional learning strategy, respectively. In addition, the individual status and algorithm status are used to adaptively adjust the control parameters. To evaluate the performance of the proposed algorithm, six state-of-the-art DE algorithm variants are compared on the benchmark functions. The results of the simulation show that the proposed algorithm outperforms other variant algorithms regarding function convergence rate and solution accuracy.

Optimum Design of Steel Frames Using Different Variants of Differential Evolution Algorithm

Optimum Design of Steel Frames Using Different Variants of Differential Evolution Algorithm

An adaptive mutation strategy for differential evolution algorithm based on particle swarm optimization

Differential evolution (DE) algorithm is a very effective algorithm used for solving wide range of optimization problems. However, the performance of DE is dependent on the control parameters and to choose the right parameter value and tuning of these parameters is a challenging task. Therefore, a novel variant of differential evolution algorithm based on particle swarm optimization (DEPSO) is proposed to improve the overall performance of Differential evolution algorithm. In our proposed approach, we are using DE mutation strategy during the initial phase of evolution and therefore enlarge its search space possibly to the extent that helps in finding more encouraging results and thus avoid premature convergence. During the subsequent phase of evolution process, this value of sigmoid function reduces with the increase of number of iterations. In this scenario, there is a greater probability of operating PSO mutation strategy and thus this sigmoid function helps in improving the precision and convergence speed. The Performance of our proposed algorithm is tested with 10 benchmark test functions on 50 and 25 dimensions set, also tested with 11 test functions on 30- and 100-dimension test functions. We have also tested our proposed algorithm with 8 test functions on high dimension set as 500- and 1000-dimensions. The performance comparison shows that our proposed variant is giving significant improvement in convergence speed and thus avoiding premature convergence. Average performance of DEPSO is better than classical DE, PSO and other algorithms in comparison.

Differential Evolution Algorithm Based on Ensemble of Constraint Handling Techniques and Multi-Population Framework

Aimed at improving the insufficient search ability of constraint differential evolution with single constraint handling technique when solving complex optimization problem, this paper proposes a constraint differential evolution algorithm based on ensemble of constraint handling techniques and multi-population framework, called ECMPDE. First, handling three improved variants of differential evolution algorithms are dynamically matched with two constraint handling techniques through the constraint allocation mechanism. Each combination includes three variants with corresponding constraint handling technique and these combinations are in the set. Second, the population is divided into three smaller subpopulations and one larger reward subpopulation. Then a combination with three constraint algorithms is randomly selected from the set, and the three constraint algorithms are run in three sub-populations respectively. According to the improvement of fitness value, the optimal constraint algorithm is selected to run on the reward sub-population, which can share information and close cooperation among populations. In order to verify the effectiveness of the proposed algorithm, 12 standard constraint optimization problems and 10 engineering constraint optimization problems are tested. The experimental results show that ECMPDE is an effective algorithm for solving constraint optimization problems.

Rose pattern for heliostat field optimization with a dynamic speciation‐based mutation differential evolution

Concentrated solar power technology is one of the most promising technologies in energy field. Arguably, the heliostat field layout is a crucial component in solar power tower system. Numerous studies have been developed for heliostat field optimization. However, most of the existing layouts which utilize radial staggered patterns are based on only two or four variables, leading to relatively rigid modes due to strong configuration constraints. In this article, we propose a new method called rose layout, which divides the regular radial staggered pattern into six sectors and they are optimized separately. Therefore, the radial increments between consecutive rows are not restricted to zones or rows, only relevant to which sector they belong to. This arrangement is more flexible and also efficient. Furthermore, a new differential evolution algorithm with a dynamic speciation-based mutation strategy (DSM-DE) is developed to solve this high-dimensional problem. In order to validate the proposed rose pattern and DSM-DE, three sets of comparative experiments were carried out. The first set of tests were operated with the conventional four optimization variables, the second series optimized total 43 radial increments between consecutive rows, whereas the third series employed the rose layout. All sets of cases were optimized by four competitive variants of differential evolution algorithm, ie, JADE, SHADE, EB-LSHADE, and DSM-DE. Experimental results verified that the rose layout can obtain higher overall optical efficiency and less land coverage than previous methods and DSM-DE is superior to other DE variants for this high-dimensional problem. The heliostat field studied in this article is simulated in Qinghai, China. By integrating rose layout with DSM-DE, the field unweighted efficiency progressed from 44.386% to 53.972%, and the annual weighted efficiency reached 59.091%, which was 0.318% higher than the 43-variable optimization.

Differential Evolution Based on Node Strength

In this paper, three novel algorithms for optimisation based on the differential evolution algorithm are devised. The main idea behind those algorithms stems from the observation that differential evolution dynamics can be modelled via complex networks. In our approach, the individuals of the population are modelled by the nodes and the relationships between them by the directed lines of the graph. Subsequent analysis of non-trivial topological features further influence the process of parent selection in the mutation step and replace the traditional approach which is not reflecting the complex relationships between individuals in the population during evolution. This approach represents a general framework which can be applied to various kinds of differential evolution algorithms. We have incorporated this framework with the three well-performing variants of differential evolution algorithms to demonstrate the effectiveness of our contribution with respect to the convergence rate. Two well-known benchmark sets (including 49 functions) are used to evaluate the performance of the proposed algorithms. Experimental results and statistical analysis indicate that the enhanced algorithms perform better or at least comparable to their original versions.

Population-based sampling methods for geological well testing

In this paper, the application of a population-based sampling algorithm, i.e., differential evolution, in the geological well testing of a multi-layered faulted reservoir model is discussed. In this sense, the available multiple well test datasets are used to calibrate the geological model parameters rather than fitting simplified analytical models. In the exercise studied in this paper, the parameter space includes a range of geostatistical, petrophysical, and structural parameters. The differential evolution algorithm starts with an initial random population from the ranges of input variables and progresses with successive evaluation of the static models’ transient tests. The static models’ input parameters are perturbed to generate new populations, which can finally match the truth model well test derivative with lower misfits. The ensemble of population models (samples) along with the misfit values are used to highlight the value of well test data in reducing the uncertainty in the parameter space. A Bayesian framework is employed to implement the Markov chain Monte Carlo (McMC) methods to estimate the posterior distributions of the parameters. The results are confirmed by the sample-based Sobol sensitivity indices, which rank the influential parameters. To reduce the computational cost of the McMC and sensitivity indices, a cross-validated proxy model (i.e., Multivariate Adaptive Regression Spline) is constructed. The effect of different variants of differential evolution algorithm on the geological well test matching is also discussed. This paper provides a workflow for quantitative integration of well test data into the reservoir characterization workflow.

Self-Adaptive Differential Evolution Algorithm With Zoning Evolution of Control Parameters and Adaptive Mutation Strategies.

The performance of the differential evolution (DE) algorithm is significantly affected by the choice of mutation strategies and control parameters. Maintaining the search capability of various control parameter combinations throughout the entire evolution process is also a key issue. A self-adaptive DE algorithm with zoning evolution of control parameters and adaptive mutation strategies is proposed in this paper. In the proposed algorithm, the mutation strategies are automatically adjusted with population evolution, and the control parameters evolve in their own zoning to self-adapt and discover near optimal values autonomously. The proposed algorithm is compared with five state-of-the-art DE algorithm variants according to a set of benchmark test functions. Furthermore, seven nonparametric statistical tests are implemented to analyze the experimental results. The results indicate that the overall performance of the proposed algorithm is better than those of the five existing improved algorithms.

Chemical process dynamic optimization based on the differential evolution algorithm with an adaptive scheduling mutation strategy

To solve chemical process dynamic optimization problems, a differential evolution algorithm integrated with adaptive scheduling mutation strategy (ASDE) is proposed. According to the evolution feedback information, ASDE, with adaptive control parameters, adopts the round-robin scheduling algorithm to adaptively schedule different mutation strategies. By employing an adaptive mutation strategy and control parameters, the real-time optimal control parameters and mutation strategy are obtained to improve the optimization performance. The performance of ASDE is evaluated using a suite of 14 benchmark functions. The results demonstrate that ASDE performs better than four conventional differential evolution (DE) algorithm variants with different mutation strategies, and that the whole performance of ASDE is equivalent to a self-adaptive DE algorithm variant and better than five conventional DE algorithm variants. Furthermore, ASDE was applied to solve a typical dynamic optimization problem of a chemical process. The obtained results indicate that ASDE is a feasible and competitive optimizer for this kind of problem.

Optimization methodology based on neural networks and self-adaptive differential evolution algorithm applied to an aerobic fermentation process

The determination of the optimal neural network topology is an important aspect when using neural models. Due to the lack of consistent rules, this is a difficult problem, which is solved in this paper using an evolutionary algorithm namely Differential Evolution. An improved, simple, and flexible self-adaptive variant of Differential Evolution algorithm is proposed and tested. The algorithm included two initialization strategies (normal distribution and normal distribution combined with the opposition based principle) and a modified mutation principle. Because the methodology contains new elements, a specific name has been assigned, SADE-NN-1. In order to determine the most influential inputs of the models, a sensitivity analysis was applied. The case study considered in this work refer to the oxygen mass transfer coefficient in stirred bioreactors in the presence of n-dodecane as oxygen vector. The oxygen transfer in the fermentation broths has a significant influence on the growth of cultivated microorganism, the accurate modeling of this process being an important problem that has to be solved in order to optimize the aerobic fermentation process.The neural networks predicted the mass transfer coefficients with high accuracy, which indicates that the proposed methodology had a good performance. The same methodology, with a few modifications, and with the best neural network models, was used for determining the optimal conditions for which the mass transfer coefficient is maximized.A short review of the differential evolution methodology is realized in the first part of this article, presenting the main characteristics and variants, with advantages and disadvantages, and fitting in the modifications proposed within the existing directions of research.

Stratified Sampling Differential Evolution Algorithm for Global Optimization Problem

Differential Evolution (DE) is one kind of evolution algorithm, which based on difference of individuals. DE has exhibited good performance on optimization problem. However, when a local optimal solution is reached with classical Differential Evolution, all individuals in the population gather around it, and escaping from these local optima becomes difficult. To avoid premature convergence of DE, we present in this paper a novel variant of DE algorithm, called SSDE, which uses the stratified sampling method to replace the random sampling method. The proposed SSDE algorithm is compared with some variant DE. The numerical results show that our approach is robust, competitive and fast.

Stratified Sampling Differential Evolution Algorithm for Global Optimization Problem

Differential Evolution (DE) is one kind of evolution algorithm, which based on difference of individuals. DE has exhibited good performance on optimization problem. However, when a local optimal solution is reached with classical Differential Evolution, all individuals in the population gather around it, and escaping from these local optima becomes difficult. To avoid premature convergence of DE, we present in this paper a novel variant of DE algorithm, called SSDE, which uses the stratified sampling method to replace the random sampling method. The proposed SSDE algorithm is compared with some variant DE. The numerical results show that our approach is robust, competitive and fast.