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.

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.

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.

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.

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.

A Multi-Stage Differential-Multifactorial Evolutionary Algorithm for Ingredient Optimization in the Copper Industry

Ingredient optimization plays a pivotal role in the copper industry,for which it is closely related to the concentrate utilization rate,stability of furnace conditions,and the quality of copper production.To acquire a practical ingredient plan,which should exhibit long duration time with sufficient utilization and feeding stability for real applications,an ingredient plan optimization model is proposed in this study to effectively guarantee continuous production and stable furnace conditions.To address the complex challenges posed by this integer programming model,including multiple coupling feeding stages,intricate constraints,and significant non-linearity,a multi-stage differential-multifactorial evolution algorithm is developed.In the proposed algorithm,the differential evolutionary(DE)algorithm is improved in three aspects to efficiently tackle challenges when optimizing the proposed model.First,unlike traditional time-consuming serial approaches,the multifactorial evolutionary algorithm is utilized to optimize multiple complex models contained in the population of evolutionary algorithm caused by the feeding stability in a parallel manner.Second,a repair algorithm is employed to adjust infeasible ingredient lists in a timely manner.In addition,a local search strategy taking feedback from the current optima and considering the different positions of global optimum is developed to avoiding premature convergence of the differential evolutionary algorithm.Finally,the simulation experiments considering different planning horizons using real data from the copper industry in China are conducted,which demonstrates the superiority of the proposed method on feeding duration and stability compared with other commonly deployed approaches.It is practically helpful for reducing material cost as well as increasing production profit for the copper industry.

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.

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.

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.

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.

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%).

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.

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.

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.

Differential evolution algorithm for hybrid flow-shop scheduling problems

Aiming at the hybrid flow-shop （HFS） scheduling that is a complex NP-hard combinatorial problem with wide engineering background, an effective algorithm based on differential evolution （DE） is proposed. By using a special encoding scheme and combining DE based evolutionary search and local search, the exploration and exploitation abilities are enhanced and well balanced for solving the HFS problems. Simulation results based on some typical problems and comparisons with some existing genetic algorithms demonstrate the proposed algorithm is effective, efficient and robust for solving the HFS problems.

Deformable Catalytic Material Derived from Mechanical Flexibility for Hydrogen Evolution Reaction

Deformable catalytic material with excellent flexible structure is a new type of catalyst that has been applied in various chemical reactions,especially electrocatalytic hydrogen evolution reaction(HER).In recent years,deformable catalysts for HER have made great progress and would become a research hotspot.The catalytic activities of deformable catalysts could be adjustable by the strain engineering and surface reconfiguration.The surface curvature of flexible catalytic materials is closely related to the electrocatalytic HER properties.Here,firstly,we systematically summarized self-adaptive catalytic performance of deformable catalysts and various micro–nanostructures evolution in catalytic HER process.Secondly,a series of strategies to design highly active catalysts based on the mechanical flexibility of lowdimensional nanomaterials were summarized.Last but not least,we presented the challenges and prospects of the study of flexible and deformable micro–nanostructures of electrocatalysts,which would further deepen the understanding of catalytic mechanisms of deformable HER catalyst.

A continuous and long-term in-situ stress measuring method based on fiber optic. Part I: Theory of inverse differential strain analysis

A method for in-situ stress measurement via fiber optics was proposed. The method utilizes the relationship between rock mass elastic parameters and in-situ stress. The approach offers the advantage of long-term stress measurements with high spatial resolution and frequency, significantly enhancing the ability to measure in-situ stress. The sensing casing, spirally wrapped with fiber optic, is cemented into the formation to establish a formation sensing nerve. Injecting fluid into the casing generates strain disturbance, establishing the relationship between rock mass properties and treatment pressure.Moreover, an optimization algorithm is established to invert the elastic parameters of formation via fiber optic strains. In the first part of this paper series, we established the theoretical basis for the inverse differential strain analysis method for in-situ stress measurement, which was subsequently verified using an analytical model. This paper is the fundamental basis for the inverse differential strain analysis method.

Mg/MgO interfaces as efficient hydrogen evolution cathodes causing accelerated corrosion of additive manufactured Mg alloys:A DFT analysis

The corrosion rates of additive-manufactured Mg alloys are higher than their as-cast counterparts,possibly due to increased kinetics for the hydrogen evolution reaction on secondary phases,which may include oxide inclusions.Scanning Kelvin Probe Force Microscopy demonstrated that MgO inclusions could act as cathodes for Mg corrosion,but their low conductivity likely precludes this.However,the density of state calculations through density functional theory using hybrid HSE06 functional revealed overlapping electronic states at the Mg/MgO interface,which facilitates electron transfers and participates in redox reactions.Subsequent determination of the hydrogen absorption energy at the Mg/MgO interface reveals it to be an excellent catalytic site,with HER being found to be a factor of 23x more efficient at the interface than on metallic Mg.The results not only support the plausibility of the Mg/MgO interface being an effective cathode to the adjacent anodic Mg matrix during corrosion but also contribute to the understanding of the enhanced cathodic activities observed during the anodic dissolution of magnesium.

Precisely Control Relationship between Sulfur Vacancy and H Absorption for Boosting Hydrogen Evolution Reaction

Ef fective and robust catalyst is the core of water splitting to produce hydrogen.Here, we report an anionic etching method to tailor the sulfur vacancy(VS) of NiS_(2) to further enhance the electrocatalytic performance for hydrogen evolution reaction(HER). With the VS concentration change from 2.4% to 8.5%, the H* adsorption strength on S sites changed and NiS_(2)-VS 5.9% shows the most optimized H* adsorption for HER with an ultralow onset potential(68 m V) and has long-term stability for 100 h in 1 M KOH media. In situ attenuated-total-reflection Fourier transform infrared spectroscopy(ATR-FTIRS) measurements are usually used to monitor the adsorption of intermediates. The S-H* peak of the Ni S_(2)-VS 5.9% appears at a very low voltage, which is favorable for the HER in alkaline media. Density functional theory calculations also demonstrate the Ni S_(2)-VS 5.9% has the optimal |ΔG^(H*)| of 0.17 e V. This work offers a simple and promising pathway to enhance catalytic activity via precise vacancies strategy.

Valence electronic engineering of superhydrophilic Dy-evoked Ni-MOF outperforming RuO_(2) for highly efficient electrocatalytic oxygen evolution

Tackling the problem of poor conductivity and catalytic stability of pristine metal-organic frameworks(MOFs) is crucial to improve their oxygen evolution reaction(OER) performance.Herein,we introduce a novel strategy of dysprosium(Dy) doping,using the unique 4f orbitals of this rare earth element to enhance electrocatalytic activity of MOFs.Our method involves constructing Dy-doped Ni-MOF(Dy@Ni-MOF) nanoneedles on carbon cloth via a Dy-induced valence electronic perturbation approach.Experiments and density functional theory(DFT) calculations reveal that Dy doping can effectively modify the electronic structure of the Ni active centers and foster a strong electronic interaction between Ni and Dy.The resulting benefits include a reduced work function and a closer proximity of the d-band center to the Fermi level,which is conducive to improving electrical conductivity and promoting the adsorption of oxygen-containing intermediates.Furthermore,the Dy@Ni-MOF achieves superhydrophilicity,ensuring effective electrolyte contact and thus accelerating reaction kinetics,Ex-situ and in-situ analysis results manifest Dy_(2)O_(3)/NiOOH as the actual active species.Therefore,Dy@Ni-MOF shows impressive OER performance,significantly surpassing Ni-MOF.Besides,the overall water splitting device with Dy@NiMOF as an anode delivers a low cell voltage of 1.51 V at 10 mA cm^(-2) and demonstrates long-term stability for 100 h,positioning it as a promising substitute for precious metal catalysts.