Unfolding neutron spectra from water-pumping-injection multilayered concentric sphere neutron spectrometer using self-adaptive differential evolution algorithm

A self-adaptive differential evolution neutron spectrum unfolding algorithm(SDENUA)is established in this study to unfold the neutron spectra obtained from a water-pumping-injection multilayered concentric sphere neutron spectrometer(WMNS).Specifically,the neutron fluence bounds are estimated to accelerate the algorithm convergence,and the minimum error between the optimal solution and input neutron counts with relative uncertainties is limited to 10^(-6)to avoid unnecessary calculations.Furthermore,the crossover probability and scaling factor are self-adaptively controlled.FLUKA Monte Carlo is used to simulate the readings of the WMNS under(1)a spectrum of Cf-252 and(2)its spectrum after being moderated,(3)a spectrum used for boron neutron capture therapy,and(4)a reactor spectrum.Subsequently,the measured neutron counts are unfolded using the SDENUA.The uncertainties of the measured neutron count and the response matrix are considered in the SDENUA,which does not require complex parameter tuning or an a priori default spectrum.The results indicate that the solutions of the SDENUA agree better with the IAEA spectra than those of MAXED and GRAVEL in UMG 3.1,and the errors of the final results calculated using the SDENUA are less than 12%.The established SDENUA can be used to unfold spectra from the WMNS.

An Immune Self-adaptive Differential Evolution Algorithm with Application to Estimate Kinetic Parameters for Homogeneous Mercury Oxidation

A new version of differential evolution(DE) algorithm,in which immune concepts and methods are applied to determine the parameter setting,named immune self-adaptive differential evolution(ISDE),is proposed to improve the performance of the DE algorithm.During the actual operation,ISDE seeks the optimal parameters arising from the evolutionary process,which enable ISDE to alter the algorithm for different optimization problems and improve the performance of ISDE by the control parameters' self-adaptation.The performance of the proposed method is studied with the use of nine benchmark problems and compared with original DE algorithm and other well-known self-adaptive DE algorithms.The experiments conducted show that the ISDE clearly outperforms the other DE algorithms in all benchmark functions.Furthermore,ISDE is applied to develop the kinetic model for homogeneous mercury(Hg) oxidation in flue gas,and satisfactory results are obtained.

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.

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.

Strengthened Dominance Relation NSGA-Ⅲ Algorithm Based on Differential Evolution to Solve Job Shop Scheduling Problem

The job shop scheduling problem is a classical combinatorial optimization challenge frequently encountered in manufacturing systems.It involves determining the optimal execution sequences for a set of jobs on various machines to maximize production efficiency and meet multiple objectives.The Non-dominated Sorting Genetic Algorithm Ⅲ(NSGA-Ⅲ)is an effective approach for solving the multi-objective job shop scheduling problem.Nevertheless,it has some limitations in solving scheduling problems,including inadequate global search capability,susceptibility to premature convergence,and challenges in balancing convergence and diversity.To enhance its performance,this paper introduces a strengthened dominance relation NSGA-Ⅲ algorithm based on differential evolution(NSGA-Ⅲ-SD).By incorporating constrained differential evolution and simulated binary crossover genetic operators,this algorithm effectively improves NSGA-Ⅲ’s global search capability while mitigating pre-mature convergence issues.Furthermore,it introduces a reinforced dominance relation to address the trade-off between convergence and diversity in NSGA-Ⅲ.Additionally,effective encoding and decoding methods for discrete job shop scheduling are proposed,which can improve the overall performance of the algorithm without complex computation.To validate the algorithm’s effectiveness,NSGA-Ⅲ-SD is extensively compared with other advanced multi-objective optimization algorithms using 20 job shop scheduling test instances.The experimental results demonstrate that NSGA-Ⅲ-SD achieves better solution quality and diversity,proving its effectiveness in solving the multi-objective job shop scheduling problem.

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.

Furnace Temperature Curve Optimization Model Based on Differential Evolution Algorithm

When soldering electronic components onto circuit boards,the temperature curves of the reflow ovens across different zones and the conveyor belt speed significantly influence the product quality.This study focuses on optimizing the furnace temperature curve under varying settings of reflow oven zone temperatures and conveyor belt speeds.To address this,the research sequentially develops a heat transfer model for reflow soldering,an optimization model for reflow furnace conditions using the differential evolution algorithm,and an evaluation and decision model combining the differential evolution algorithm with the Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)method.This approach aims to determine the optimal furnace temperature curve,zone temperatures of the reflow oven,and the conveyor belt speed.

Classification-based self-adaptive differential evolution and its application in multi-lateral multi-issue negotiation

Multi-lateral multi-issue negotiations are the most complex realistic negotiation problems. Automated ap- proaches have proven particularly promising for complex ne- gotiations and previous research indicates evolutionary com- putation could be useful for such complex systems. To im- prove the efficiency of realistic multi-lateral multi-issue ne- gotiations and avoid the requirement of complete informa- tion about negotiators, a novel negotiation model based on art improved evolutionary algorithm p-ADE is proposed. The new model includes a new multi-agent negotiation protocol and strategy which utilize p-ADE to improve the negotia- tion efficiency by generating more acceptable solutions with stronger suitability for all the participants. Where p-ADE is improved based on the well-known differential evolution （DE）, in which a new classification-based mutation strategy DE/rand-to-best/pbest as well as a dynamic self-adaptive pa- rameter setting strategy are proposed. Experimental results confirm the superiority of p-ADE over several state-of-the-art evolutionary optimizers. In addition, the p-ADE based multi- agent negotiation model shows good performance in solving realistic multi-lateral multi-issue negotiations.

Differential Evolution Algorithm Based Self-adaptive Control Strategy for Fed-batch Cultivation of Yeast

In the fed-batch cultivation of Saccharomyces cerevisiae,excessive glucose addition leads to increased ethanol accumulation,which will reduce the efficiency of glucose utilization and inhibit product synthesis.Insufficient glucose addition limits cell growth.To properly regulate glucose feed,a different evolution algorithm based on self-adaptive control strategy was proposed,consisting of three modules(PID,system identification and parameter optimization).Performance of the proposed and conventional PID controllers was validated and compared in simulated and experimental cultivations.In the simulation,cultivation with the self-adaptive control strategy had a more stable glucose feed rate and concentration,more stable ethanol concentration around the set-point(1.0 g·L^(-1)),and final biomass concentration of 34.5 g-DCW·L^(-1),29.2%higher than that with a conventional PID control strategy.In the experiment,the cultivation with the self-adaptive control strategy also had more stable glucose and ethanol concentrations,as well as a final biomass concentration that was 37.4%higher than that using the conventional strategy.

An Enhanced Adaptive Differential Evolution Approach for Constrained Optimization Problems

Effective constrained optimization algorithms have been proposed for engineering problems recently.It is common to consider constraint violation and optimization algorithm as two separate parts.In this study,a pbest selection mechanism is proposed to integrate the current mutation strategy in constrained optimization problems.Based on the improved pbest selection method,an adaptive differential evolution approach is proposed,which helps the population jump out of the infeasible region.If all the individuals are infeasible,the top 5%of infeasible individuals are selected.In addition,a modified truncatedε-level method is proposed to avoid trapping in infeasible regions.The proposed adaptive differential evolution approach with an improvedεconstraint processmechanism(IεJADE)is examined on CEC 2006 and CEC 2010 constrained benchmark function series.Besides,a standard IEEE-30 bus test system is studied on the efficiency of the IεJADE.The numerical analysis verifies the IεJADE algorithm is effective in comparisonwith other effective algorithms.

Multiple Elite Individual Guided Piecewise Search-Based Differential Evolution

The differential evolution(DE)algorithm relies mainly on mutation strategy and control parameters'selection.To take full advantage of top elite individuals in terms of fitness and success rates,a new mutation operator is proposed.The control parameters such as scale factor and crossover rate are tuned based on their success rates recorded over past evolutionary stages.The proposed DE variant,MIDE,performs the evolution in a piecewise manner,i.e.,after every predefined evolutionary stages,MIDE adjusts its settings to enrich its diversity skills.The performance of the MIDE is validated on two different sets of benchmarks:CEC 2014 and CEC 2017(special sessions&competitions on real-parameter single objective optimization)using different performance measures.In the end,MIDE is also applied to solve constrained engineering problems.The efficiency and effectiveness of the MIDE are further confirmed by a set of experiments.

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.

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.

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%).

Equation governing the probability density evolution of multi-dimensional linear fractional differential systems subject to Gaussian white noise

Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian property.The recently developed globally-evolving-based generalized density evolution equation(GE-GDEE),which is a unified partial differential equation(PDE)governing the transient probability density function(PDF)of a generic path-continuous process,including non-Markovian ones,provides a feasible tool to solve this problem.In the paper,the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is established.In particular,it is proved that in the GE-GDEE corresponding to the state-quantities of interest,the intrinsic drift coefficient is a time-varying linear function,and can be analytically determined.In this sense,an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original highdimensional linear fractional differential system can be constructed such that their transient PDFs are identical.Specifically,for a multi-dimensional linear fractional differential system,if only one or two quantities are of interest,GE-GDEE is only in one or two dimensions,and the surrogate system would be a one-or two-dimensional linear integer-order system.Several examples are studied to assess the merit of the proposed method.Though presently the closed-form intrinsic drift coefficient is only available for linear stochastic fractional differential systems,the findings in the present paper provide a remarkable demonstration on the existence and eligibility of GE-GDEE for the case that the original high-dimensional system itself is non-Markovian,and provide insights for the physical-mechanism-informed determination of intrinsic drift and diffusion coefficients of GE-GDEE of more generic complex nonlinear systems.

Okumura Hata Propagation Model Optimization in 400 MHz Band Based on Differential Evolution Algorithm: Application to the City of Bertoua

Propagation models are the foundation for radio planning in mobile networks. They are widely used during feasibility studies and initial network deployment, or during network extensions, particularly in new cities. They can be used to calculate the power of the signal received by a mobile terminal, evaluate the coverage radius, and calculate the number of cells required to cover a given area. This paper takes into account the standard k factors model and then uses the differential evolution algorithm to set up a propagation model adapted to the physical environment of the Cameroonian cities of Bertoua. Drive tests were made on the LTE TDD network in the city of Bertoua. Differential evolution algorithm is used as the optimization algorithm to deduct a propagation model which fits the environment of the considered town. The calculation of the root mean square error between the actual data from the drive tests and the prediction data from the implemented model allows the validation of the obtained results. A comparative study made between the RMSE value obtained by the new model and those obtained by the Okumura Hata and free space models, allowed us to conclude that the new model obtained is better and more representative of our local environment than the Okumura Hata currently used. The implementation shows that Differential evolution can perform well and solve this kind of optimization problem;the newly obtained models can be used for radio planning in the city of Bertoua in Cameroon.

Improved Adaptive Differential Evolution Algorithm for the Un-Capacitated Facility Location Problem

The differential evolution algorithm is an evolutionary algorithm for global optimization and the un-capacitated facility location problem (UFL) is one of the classic NP-Hard problems. In this paper, combined with the specific characteristics of the UFL problem, we introduce the activation function to the algorithm for solving UFL problem and name it improved adaptive differential evolution algorithm (IADEA). Next, to improve the efficiency of the algorithm and to alleviate the problem of being stuck in a local optimum, an adaptive operator was added. To test the improvement of our algorithm, we compare the IADEA with the basic differential evolution algorithm by solving typical instances of UFL problem respectively. Moreover, to compare with other heuristic algorithm, we use the hybrid ant colony algorithm to solve the same instances. The computational results show that IADEA improves the performance of the basic DE and it outperforms the hybrid ant colony algorithm.

Self-adapting control parameters modifieddifferential evolution for trajectoryplanning of manipulators

Control parameters of original differential evolution （DE） are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE for different optiinization problems. According to the relative position of two different individual vectors selected to generate a difference vector in the searching place, a self-adapting strategy for the scale factor F of the difference vector is proposed. In terms of the convergence status of the target vector in the current population, a self-adapting crossover probability constant CR strategy is proposed. Therefore, good target vectors have a lower CFI while worse target vectors have a large CFI. At the same time, the mutation operator is modified to improve the convergence speed. The performance of these proposed approaches are studied with the use of some benchmark problems and applied to the trajectory planning of a three-joint redundant manipulator. Finally, the experiment results show that the proposed approaches can greatly improve robustness and convergence speed.