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.

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.

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.

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.

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.

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.

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.

Microwave shock motivating the Sr substitution of 2D porous GdFeO_(3) perovskite for highly active oxygen evolution

The incorporation of partial A-site substitution in perovskite oxides represents a promising strategy for precisely controlling the electronic configuration and enhancing its intrinsic catalytic activity.Conventional methods for A-site substitution typically involve prolonged high-temperature processes.While these processes promote the development of unique nanostructures with highly exposed active sites,they often result in the uncontrolled configuration of introduced elements.Herein,we present a novel approach for synthesizing two-dimensional(2D)porous GdFeO_(3) perovskite with A-site strontium(Sr)substitution utilizing microwave shock method.This technique enables precise control of the Sr content and simultaneous construction of 2D porous structures in one step,capitalizing on the advantages of rapid heating and cooling(temperature~1100 K,rate~70 K s^(-1)).The active sites of this oxygen-rich defect structure can be clearly revealed through the simulation of the electronic configuration and the comprehensive analysis of the crystal structure.For electrocatalytic oxygen evolution reaction application,the synthesized 2D porous Gd_(0.8)Sr_(0.2)FeO_(3) electrocatalyst exhibits an exceptional overpotential of 294 mV at a current density of 10 mA cm^(-2)and a small Tafel slope of 55.85 mV dec^(-1)in alkaline electrolytes.This study offers a fresh perspective on designing crystal configurations and the construction of nanostructures in perovskite.

High-speed penetration of ogive-nose projectiles into thick concrete targets:Tests and a projectile nose evolution model

The majority of the projectiles used in the hypersonic penetration study are solid flat-nosed cylindrical projectiles with a diameter of less than 20 mm.This study aims to fill the gap in the experimental and analytical study of the evolution of the nose shape of larger hollow projectiles under hypersonic penetration.In the hypersonic penetration test,eight ogive-nose AerMet100 steel projectiles with a diameter of 40 mm were launched to hit concrete targets with impact velocities that ranged from 1351 to 1877 m/s.Severe erosion of the projectiles was observed during high-speed penetration of heterogeneous targets,and apparent localized mushrooming occurred in the front nose of recovered projectiles.By examining the damage to projectiles,a linear relationship was found between the relative length reduction rate and the initial kinetic energy of projectiles in different penetration tests.Furthermore,microscopic analysis revealed the forming mechanism of the localized mushrooming phenomenon for eroding penetration,i.e.,material spall erosion abrasion mechanism,material flow and redistribution abrasion mechanism and localized radial upsetting deformation mechanism.Finally,a model of highspeed penetration that included erosion was established on the basis of a model of the evolution of the projectile nose that considers radial upsetting;the model was validated by test data from the literature and the present study.Depending upon the impact velocity,v0,the projectile nose may behave as undistorted,radially distorted or hemispherical.Due to the effects of abrasion of the projectile and enhancement of radial upsetting on the duration and amplitude of the secondary rising segment in the pulse shape of projectile deceleration,the predicted DOP had an upper limit.

Carbon Emission Effects Driven by Evolution of Chinese Dietary Structure from 1987 to 2020

Exploring carbon emission effects based on the evolution of residents’ dietary structure to achieve the carbon neutrality goal and mitigate climate change is an important task.This study took China as the research object(data excluding Hong Kong,Macao and Taiwan) and used the carbon emission coefficient method to quantitatively measure the food carbon emissions from 1987–2020,then analyzed the carbon emission effects under the evolution of dietary structure.The results showed that during the study period,the Chinese dietary structure gradually changed to a high-carbon consumption pattern.The dietary structure of urban residents developed to a balanced one,while that of rural residents developed to a high-quality one.During the study period,the per capita food carbon emissions and total food consumption of Chinese showed an increasing trend.The per capita food carbon emissions of residents in urban and rural showed an overall upward trend.The total food carbon emissions in urban increased significantly,while that in rural increased first and then decreased.The influence of beef and mutton on carbon emissions is the highest in dietary structure.Compared with the balanced dietary pattern,the food carbon emissions of Chinese residents had not yet reached the peak,but were evolving to a high-carbon consumption pattern.

Tuning electronic structure of RuO_(2)by single atom Zn and oxygen vacancies to boost oxygen evolution reaction in acidic medium

The poor stability of RuO_(2)electrocatalysts has been the primary obstacles for their practical application in polymer electrolyte membrane electrolyzers.To dramatically enhance the durability of RuO_(2)to construct activity-stability trade-off model is full of significance but challenging.Herein,a single atom Zn stabilized RuO_(2)with enriched oxygen vacancies(SA Zn-RuO_(2))is developed as a promising alternative to iridium oxide for acidic oxygen evolution reaction(OER).Compared with commercial RuO_(2),the enhanced Ru–O bond strength of SA Zn-RuO_(2)by forming Zn-O-Ru local structure motif is favorable to stabilize surface Ru,while the electrons transferred from Zn single atoms to adjacent Ru atoms protects the Ru active sites from overoxidation.Simultaneously,the optimized surrounding electronic structure of Ru sites in SA ZnRuO_(2)decreases the adsorption energies of OER intermediates to reduce the reaction barrier.As a result,the representative SA Zn-RuO_(2)exhibits a low overpotential of 210 mV to achieve 10 mA cm^(-2)and a greatly enhanced durability than commercial RuO_(2).This work provides a promising dual-engineering strategy by coupling single atom doping and vacancy for the tradeoff of high activity and catalytic stability toward acidic OER.

Damage evolution of rock-encased-backfill structure under stepwise cyclic triaxial loading

Rock-encased-backfill(RB)structures are common in underground mining,for example in the cut-andfill and stoping methods.To understand the effects of cyclic excavation and blasting activities on the damage of these RB structures,a series of triaxial stepwise-increasing-amplitude cyclic loading experiments was conducted with cylindrical RB specimens(rock on outside,backfill on inside)with different volume fractions of rock(VF=0.48,0.61,0.73,and 0.84),confining pressures(0,6,9,and 12 MPa),and cyclic loading rates(200,300,400,and 500 N/s).The damage evolution and meso-crack formation during the cyclic tests were analyzed with results from stress-strain hysteresis loops,acoustic emission events,and post-failure X-ray 3D fracture morphology.The results showed significant differences between cyclic and monotonic loadings of RB specimens,particularly with regard to the generation of shear microcracks,the development of stress memory and strain hardening,and the contact forces and associated friction that develops along the rock-backfill interface.One important finding is that as a function of the number of cycles,the elastic strain increases linearly and the dissipated energy increases exponentially.Also,compared with monotonic loading,the cyclic strain hardening characteristics are more sensitive to rising confining pressures during the initial compaction stage.Another finding is that compared with monotonic loading,more shear microcracks are generated during every reloading stage,but these microcracks tend to be dispersed and lessen the likelihood of large shear fracture formation.The transition from elastic to plastic behavior varies depending on the parameters of each test(confinement,volume fraction,and cyclic rate),and an interesting finding was that the transformation to plastic behavior is significantly lower under the conditions of 0.73 rock volume fraction,400 N/s cyclic loading rate,and 9 MPa confinement.All the findings have important practical implications on the ability of backfill to support underground excavations.

Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.