Deep Structure Optimization for Incremental Hierarchical Fuzzy Systems Using Improved Differential Evolution Algorithm

The optimization of the rule base of a fuzzy logic system (FLS) based on evolutionary algorithm has achievednotable results. However, due to the diversity of the deep structure in the hierarchical fuzzy system (HFS) and thecorrelation of each sub fuzzy system, the uncertainty of the HFS’s deep structure increases. For the HFS, a largenumber of studies mainly use fixed structures, which cannot be selected automatically. To solve this problem, thispaper proposes a novel approach for constructing the incremental HFS. During system design, the deep structureand the rule base of the HFS are encoded separately. Subsequently, the deep structure is adaptively mutated basedon the fitness value, so as to realize the diversity of deep structures while ensuring reasonable competition amongthe structures. Finally, the differential evolution (DE) is used to optimize the deep structure of HFS and theparameters of antecedent and consequent simultaneously. The simulation results confirm the effectiveness of themodel. Specifically, the root mean square errors in the Laser dataset and Friedman dataset are 0.0395 and 0.0725,respectively with rule counts of rules is 8 and 12, respectively.When compared to alternative methods, the resultsindicate that the proposed method offers improvements in accuracy and rule counts.

Operational optimization of copper flotation process based on the weighted Gaussian process regression and index-oriented adaptive differential evolution algorithm

Concentrate copper grade(CCG)is one of the important production indicators of copper flotation processes,and keeping the CCG at the set value is of great significance to the economic benefit of copper flotation industrial processes.This paper addresses the fluctuation problem of CCG through an operational optimization method.Firstly,a density-based affinity propagationalgorithm is proposed so that more ideal working condition categories can be obtained for the complex raw ore properties.Next,a Bayesian network(BN)is applied to explore the relationship between the operational variables and the CCG.Based on the analysis results of BN,a weighted Gaussian process regression model is constructed to predict the CCG that a higher prediction accuracy can be obtained.To ensure the predicted CCG is close to the set value with a smaller magnitude of the operation adjustments and a smaller uncertainty of the prediction results,an index-oriented adaptive differential evolution(IOADE)algorithm is proposed,and the convergence performance of IOADE is superior to the traditional differential evolution and adaptive differential evolution methods.Finally,the effectiveness and feasibility of the proposed methods are verified by the experiments on a copper flotation industrial process.

Modified Differential Evolution Algorithm for Solving Dynamic Optimization with Existence of Infeasible Environments

Dynamic constrained optimization is a challenging research topic in which the objective function and/or constraints change over time.In such problems,it is commonly assumed that all problem instances are feasible.In reality some instances can be infeasible due to various practical issues,such as a sudden change in resource requirements or a big change in the availability of resources.Decision-makers have to determine whether a particular instance is feasible or not,as infeasible instances cannot be solved as there are no solutions to implement.In this case,locating the nearest feasible solution would be valuable information for the decision-makers.In this paper,a differential evolution algorithm is proposed for solving dynamic constrained problems that learns from past environments and transfers important knowledge from them to use in solving the current instance and includes a mechanism for suggesting a good feasible solution when an instance is infeasible.To judge the performance of the proposed algorithm,13 well-known dynamic test problems were solved.The results indicate that the proposed algorithm outperforms existing recent algorithms with a margin of 79.40%over all the environments and it can also find a good,but infeasible solution,when an instance is infeasible.

Research on Rosenbrock Function Optimization Problem Based on Improved Differential Evolution Algorithm

The Rosenbrock function optimization belongs to unconstrained optimization problems, and its global minimum value is located at the bottom of a smooth and narrow valley of the parabolic shape. It is very difficult to find the global minimum value of the function because of the little information provided for the optimization algorithm. According to the characteristics of the Rosenbrock function, this paper specifically proposed an improved differential evolution algorithm that adopts the self-adaptive scaling factor F and crossover rate CR with elimination mechanism, which can effectively avoid premature convergence of the algorithm and local optimum. This algorithm can also expand the search range at an early stage to find the global minimum of the Rosenbrock function. Many experimental results show that the algorithm has good performance of function optimization and provides a new idea for optimization problems similar to the Rosenbrock function for some problems of special fields.

An Efficient Differential Evolution for Truss Sizing Optimization Using AdaBoost Classifier

Design constraints verification is the most computationally expensive task in evolutionary structural optimization due to a large number of structural analyses thatmust be conducted.Building a surrogatemodel to approximate the behavior of structures instead of the exact structural analyses is a possible solution to tackle this problem.However,most existing surrogate models have been designed based on regression techniques.This paper proposes a novel method,called CaDE,which adopts a machine learning classification technique for enhancing the performance of the Differential Evolution(DE)optimization.The proposed method is separated into two stages.During the first optimization stage,the original DE is implemented as usual,but all individuals produced in this phase are stored as inputs of the training data.Based on design constraints verification,these individuals are labeled as“safe”or“unsafe”and their labels are saved as outputs of the training data.When collecting enough data,an AdaBoost model is trained to evaluate the safety state of structures.This model is then used in the second stage to preliminarily assess new individuals,and unpromising ones are rejected without checking design constraints.This method reduces unnecessary structural analyses,thereby shortens the optimization process.Five benchmark truss sizing optimization problems are solved using the proposed method to demonstrate its effectiveness.The obtained results show that the CaDE finds good optimal designs with less structural analyses in comparison with the original DE and four other DE variants.The reduction rate of five examples ranges from 18 to over 50%.Moreover,the proposed method is applied to a real-size transmission tower design problem to exhibit its applicability in practice.

Multi-objective Optimization of a Parallel Ankle Rehabilitation Robot Using Modified Differential Evolution Algorithm

Dimensional synthesis is one of the most difficult issues in the field of parallel robots with actuation redundancy. To deal with the optimal design of a redundantly actuated parallel robot used for ankle rehabilitation, a methodology of dimensional synthesis based on multi-objective optimization is presented. First, the dimensional synthesis of the redundant parallel robot is formulated as a nonlinear constrained multi-objective optimization problem. Then four objective functions, separately reflecting occupied space, input/output transmission and torque performances, and multi-criteria constraints, such as dimension, interference and kinematics, are defined. In consideration of the passive exercise of plantar/dorsiflexion requiring large output moment, a torque index is proposed. To cope with the actuation redundancy of the parallel robot, a new output transmission index is defined as well. The multi-objective optimization problem is solved by using a modified Differential Evolution（DE） algorithm, which is characterized by new selection and mutation strategies. Meanwhile, a special penalty method is presented to tackle the multi-criteria constraints. Finally, numerical experiments for different optimization algorithms are implemented. The computation results show that the proposed indices of output transmission and torque, and constraint handling are effective for the redundant parallel robot; the modified DE algorithm is superior to the other tested algorithms, in terms of the ability of global search and the number of non-dominated solutions. The proposed methodology of multi-objective optimization can be also applied to the dimensional synthesis of other redundantly actuated parallel robots only with rotational movements.

A Hybrid Differential Evolution Algorithm Integrated with Particle Swarm Optimization

To implement self-adaptive control parameters,a hybrid differential evolution algorithm integrated with particle swarm optimization( PSODE) is proposed. In the PSODE, control parameters are encoded to be a symbiotic individual of original individual,and each original individual has its own symbiotic individual. Differential evolution( DE) operators are used to evolve the original population. And,particle swarm optimization( PSO) is applied to co-evolving the symbiotic population. Thus,with the evolution of the original population in PSODE, the symbiotic population is dynamically and self-adaptively adjusted and the realtime optimum control parameters are obtained. The proposed algorithm is compared with some DE variants on nine functions. The results show that the average performance of PSODE is the best.

A new parameter setting-based modified differential evolution for function optimization

The population-based efficient iterative evolutionary algorithm(EA)is differential evolution(DE).It has fewer control parameters but is useful when dealing with complex problems of optimization in the real world.A great deal of progress has already been made and implemented in various fields of engineering and science.Nevertheless,DE is prone to the setting of control parameters in its performance evaluation.Therefore,the appropriate adjustment of the time-consuming control parameters is necessary to achieve optimal DE efficiency.This research proposes a new version of the DE algorithm control parameters and mutation operator.For the justifiability of the suggested method,several benchmark functions are taken from the literature.The test results are contrasted with other literary algorithms.

Novel Adaptive Memory Event-Triggered-Based Fuzzy Robust Control for Nonlinear Networked Systems via the Differential Evolution Algorithm

This article mainly investigates the fuzzy optimization robust control issue for nonlinear networked systems characterized by the interval type-2(IT2)fuzzy technique under a differential evolution algorithm.To provide a more reasonable utilization of the constrained communication channel,a novel adaptive memory event-triggered(AMET)mechanism is developed,where two event-triggered thresholds can be dynamically adjusted in the light of the current system information and the transmitted historical data.Sufficient conditions with less conservative design of the fuzzy imperfect premise matching(IPM)controller are presented by introducing the Wirtinger-based integral inequality,the information of membership functions(MFs)and slack matrices.Subsequently,under the IPM policy,a new MFs intelligent optimization technique that takes advantage of the differential evolution algorithm is first provided for IT2 TakagiSugeno(T-S)fuzzy systems to update the fuzzy controller MFs in real-time and achieve a better system control effect.Finally,simulation results demonstrate that the proposed control scheme can obtain better system performance in the case of using fewer communication resources.

Optimization of Electrocardiogram Classification Using Dipper Throated Algorithm and Differential Evolution

Electrocardiogram(ECG)signal is a measure of the heart’s electrical activity.Recently,ECG detection and classification have benefited from the use of computer-aided systems by cardiologists.The goal of this paper is to improve the accuracy of ECG classification by combining the Dipper Throated Optimization(DTO)and Differential Evolution Algorithm(DEA)into a unified algorithm to optimize the hyperparameters of neural network(NN)for boosting the ECG classification accuracy.In addition,we proposed a new feature selection method for selecting the significant feature that can improve the overall performance.To prove the superiority of the proposed approach,several experimentswere conducted to compare the results achieved by the proposed approach and other competing approaches.Moreover,statistical analysis is performed to study the significance and stability of the proposed approach using Wilcoxon and ANOVA tests.Experimental results confirmed the superiority and effectiveness of the proposed approach.The classification accuracy achieved by the proposed approach is(99.98%).

An Improved Differential Evolution for Optimization of Chemical Process

微分进化(DE ) 是一个进化优化方法，它成功地在许多实际盒子中被使用了。然而，特别，当过去常优化计算联盟者时， DE 包含大计算时间昂贵的客观功能。克服这个困难，免疫的概念基于种痘被用来帮助增殖优秀模式并且制止退化现象。为了改进决定的疫苗，一个新疫苗的自治获得方法，和一个方法的有效性，种痘的概率被建议。另外，为动态地修改搜索空间的一个方法被建议提高收敛到真全球最佳的可能性。实验证明改进 DE 显著地比古典 DE 更好表现。

A Hybrid Algorithm Based on Differential Evolution and Group Search Optimization and Its Application on Ethylene Cracking Furnace

To find the optimal operational condition when the properties of feedstock changes in the cracking furnace online,a hybrid algorithm named differential evolution group search optimization(DEGSO) is proposed,which is based on the differential evolution(DE) and the group search optimization(GSO).The DEGSO combines the advantages of the two algorithms:the high computing speed of DE and the good performance of the GSO for preventing the best particle from converging to local optimum.A cooperative method is also proposed for switching between these two algorithms.If the fitness value of one algorithm keeps invariant in several generations and less than the preset threshold,it is considered to fall into the local optimization and the other algorithm is chosen.Experiments on benchmark functions show that the hybrid algorithm outperforms GSO in accuracy,global searching ability and efficiency.The optimization of ethylene and propylene yields is illustrated as a case by DEGSO.After optimization,the yield of ethylene and propylene is increased remarkably,which provides the proper operational condition of the ethylene cracking furnace.

An Adaptive Differential Evolution Algorithm to Solve Constrained Optimization Problems in Engineering Design

Differential evolution (DE) algorithm has been shown to be a simple and efficient evolutionary algorithm for global optimization over continuous spaces, and has been widely used in both benchmark test functions and real-world applications. This paper introduces a novel mutation operator, without using the scaling factor F, a conventional control parameter, and this mutation can generate multiple trial vectors by incorporating different weighted values at each generation, which can make the best of the selected multiple parents to improve the probability of generating a better offspring. In addition, in order to enhance the capacity of adaptation, a new and adaptive control parameter, i.e. the crossover rate CR, is presented and when one variable is beyond its boundary, a repair rule is also applied in this paper. The proposed algorithm ADE is validated on several constrained engineering design optimization problems reported in the specialized literature. Compared with respect to algorithms representative of the state-of-the-art in the area, the experimental results show that ADE can obtain good solutions on a test set of constrained optimization problems in engineering design.

Hybrid particle swarm optimization with differential evolution and chaotic local search to solve reliability-redundancy allocation problems

In order to solve reliability-redundancy allocation problems more effectively,a new hybrid algorithm named CDEPSO is proposed in this work,which combines particle swarm optimization (PSO) with differential evolution (DE) and a new chaotic local search.In the CDEPSO algorithm,DE provides its best solution to PSO if the best solution obtained by DE is better than that by PSO,while the best solution in the PSO is performed by chaotic local search.To investigate the performance of CDEPSO,four typical reliability-redundancy allocation problems were solved and the results indicate that the convergence speed and robustness of CDEPSO is better than those of PSO and CPSO (a hybrid algorithm which only combines PSO with chaotic local search).And,compared with the other six improved meta-heuristics,CDEPSO also exhibits more robust performance.In addition,a new performance was proposed to more fairly compare CDEPSO with the same six improved meta-heuristics,and CDEPSO algorithm is the best in solving these problems.

Chemical process dynamic optimization based on hybrid differential evolution algorithm integrated with Alopex

To solve dynamic optimization problem of chemical process (CPDOP), a hybrid differential evolution algorithm, which is integrated with Alopex and named as Alopex-DE, was proposed. In Alopex-DE, each original individual has its own symbiotic individual, which consists of control parameters. Differential evolution operator is applied for the original individuals to search the global optimization solution. Alopex algorithm is used to co-evolve the symbiotic individuals during the original individual evolution and enhance the fitness of the original individuals. Thus, control parameters are self-adaptively adjusted by Alopex to obtain the real-time optimum values for the original population. To illustrate the whole performance of Alopex-DE, several varietal DEs were applied to optimize 13 benchmark functions. The results show that the whole performance of Alopex-DE is the best. Further, Alopex-DE was applied to solve 4 typical CPDOPs, and the effect of the discrete time degree on the optimization solution was analyzed. The satisfactory result is obtained.

Solving chemical dynamic optimization problems with ranking-based differential evolution algorithms

Dynamic optimization problems(DOPs) described by differential equations are often encountered in chemical engineering. Deterministic techniques based on mathematic programming become invalid when the models are non-differentiable or explicit mathematical descriptions do not exist. Recently, evolutionary algorithms are gaining popularity for DOPs as they can be used as robust alternatives when the deterministic techniques are invalid. In this article, a technology named ranking-based mutation operator(RMO) is presented to enhance the previous differential evolution(DE) algorithms to solve DOPs using control vector parameterization. In the RMO, better individuals have higher probabilities to produce offspring, which is helpful for the performance enhancement of DE algorithms. Three DE-RMO algorithms are designed by incorporating the RMO. The three DE-RMO algorithms and their three original DE algorithms are applied to solve four constrained DOPs from the literature. Our simulation results indicate that DE-RMO algorithms exhibit better performance than previous non-ranking DE algorithms and other four evolutionary algorithms.

Harmony search algorithm with differential evolution based control parameter co-evolution and its application in chemical process dynamic optimization

A modified harmony search algorithm with co-evolutional control parameters(DEHS), applied through differential evolution optimization, is proposed. In DEHS, two control parameters, i.e., harmony memory considering rate and pitch adjusting rate, are encoded as a symbiotic individual of an original individual(i.e., harmony vector). Harmony search operators are applied to evolving the original population. DE is applied to co-evolving the symbiotic population based on feedback information from the original population. Thus, with the evolution of the original population in DEHS, the symbiotic population is dynamically and self-adaptively adjusted, and real-time optimum control parameters are obtained. The proposed DEHS algorithm has been applied to various benchmark functions and two typical dynamic optimization problems. The experimental results show that the performance of the proposed algorithm is better than that of other HS variants. Satisfactory results are obtained in the application.

Multi-objective optimization of p-xylene oxidation process using an improved self-adaptive differential evolution algorithm

The rise in the use of global polyester fiber contributed to strong demand of the Terephthalic acid(TPA).The liquid-phase catalytic oxidation of p-xylene(PX)to TPA is regarded as a critical and efficient chemical process in industry[1].PX oxidation reaction involves many complex side reactions,among which acetic acid combustion and PX combustion are the most important.As the target product of this oxidation process,the quality and yield of TPA are of great concern.However,the improvement of the qualified product yield can bring about the high energy consumption,which means that the economic objectives of this process cannot be achieved simultaneously because the two objectives are in conflict with each other.In this paper,an improved self-adaptive multi-objective differential evolution algorithm was proposed to handle the multi-objective optimization problems.The immune concept is introduced to the self-adaptive multi-objective differential evolution algorithm(SADE)to strengthen the local search ability and optimization accuracy.The proposed algorithm is successfully tested on several benchmark test problems,and the performance measures such as convergence and divergence metrics are calculated.Subsequently,the multi-objective optimization of an industrial PX oxidation process is carried out using the proposed immune self-adaptive multi-objective differential evolution algorithm(ISADE).Optimization results indicate that application of ISADE can greatly improve the yield of TPA with low combustion loss without degenerating TA quality.

Optimal Static State Estimation Using hybrid Particle Swarm-Differential Evolution Based Optimization

In this paper, swarm optimization hybridized with differential evolution (PSO-DE) technique is proposed to solve static state estimation (SE) problem as a minimization problem. The proposed hybrid method is tested on IEEE 5-bus, 14-bus, 30-bus, 57-bus and 118-bus standard test systems along with 11-bus and 13-bus ill-conditioned test systems under different simulated conditions and the results are compared with the same, obtained using standard weighted least square state estimation (WLS-SE) technique and general particle swarm optimization (GPSO) based technique. The performance of the proposed optimization technique for SE, in terms of minimum value of the objective function and standard deviations of minimum values obtained in 100 runs, is found better as compared to the GPSO based technique. The statistical error analysis also shows the superiority of the proposed PSO-DE based technique over the other two techniques.