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.

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.

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.

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%).

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 differential evolution algorithm for resource-constrained project scheduling problem

An improved differential evolution（IDE）algorithm that adopts a novel mutation strategy to speed up the convergence rate is introduced to solve the resource-constrained project scheduling problem（RCPSP）with the objective of minimizing project duration Activities priorities for scheduling are represented by individual vectors and a senal scheme is utilized to transform the individual-represented priorities to a feasible schedule according to the precedence and resource constraints so as to be evaluated.To investigate the performance of the IDE-based approach for the RCPSP,it is compared against the meta-heuristic methods of hybrid genetic algorithm（HGA）,particle swarm optimization（PSO） and several well selected heuristics.The results show that the proposed scheduling method is better than general heuristic rules and is able to obtain the same optimal result as the HGA and PSO approaches but more efficient than the two algorithms.

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.

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.

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

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

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.

A hybrid differential evolution algorithm for meta-task scheduling in grids

Task scheduling is one of the core steps to effectively exploit the capabilities of heterogeneous re-sources in the grid.This paper presents a new hybrid differential evolution(HDE)algorithm for findingan optimal or near-optimal schedule within reasonable time.The encoding scheme and the adaptation ofclassical differential evolution algorithm for dealing with discrete variables are discussed.A simple but ef-fective local search is incorporated into differential evolution to stress exploitation.The performance of theproposed HDE algorithm is showed by being compared with a genetic algorithm(GA)on a known staticbenchmark for the problem.Experimental results indicate that the proposed algorithm has better perfor-mance than GA in terms of both solution quality and computational time,and thus it can be used to de-sign efficient dynamic schedulers in batch mode for real grid systems.

Global Optimum-Based Search Differential Evolution

In this paper, a global optimum-based search strategy is proposed to alleviate the situation that the differential evolution(DE) usually sticks into a stagnation, especially on complex problems. It aims to reconstruct the balance between exploration and exploitation, and improve the search efficiency and solution quality of DE. The proposed method is activated by recording the number of recently consecutive unsuccessful global optimum updates. It takes the feedback from the global optimum,which makes the search strategy not only refine the current solution quality, but also have a change to find other promising space with better individuals. This search strategy is incorporated with various DE mutation strategies and DE variations. The experimental results indicate that the proposed method has remarkable performance in enhancing search efficiency and improving solution quality.

Improved gravitational search algorithm based on free search differential evolution

This paper presents an improved gravitational search algorithm （IGSA） as a hybridization of a relatively recent evolutionary algorithm called gravitational search algorithm （GSA）, with the free search differential evolution （FSDE）. This combination incorporates FSDE into the optimization process of GSA with an attempt to avoid the premature convergence in GSA. This strategy makes full use of the exploration ability of GSA and the exploitation ability of FSDE. IGSA is tested on a suite of benchmark functions. The experimental results demonstrate the good performance of IGSA.

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.

A Preliminary Application of the Differential Evolution Algorithm to Calculate the CNOP

A projected skill is adopted by use of the differential evolution (DE) algorithm to calculate a conditional nonlinear optimal perturbation (CNOP). The CNOP is the maximal value of a constrained optimization problem with a constraint condition, such as a ball constraint. The success of the DE algorithm lies in its ability to handle a non-differentiable and nonlinear cost function. In this study, the DE algorithm and the traditional optimization algorithms used to obtain the CNOPs are compared by analyzing a theoretical grassland ecosystem model and a dynamic global vegetation model. This study shows that the CNOPs generated by the DE algorithm are similar to those by the sequential quadratic programming (SQP) algorithm and the spectral projected gradients (SPG2) algorithm. If the cost function is non-differentiable, the CNOPs could also be caught with the DE algorithm. The numerical results suggest the DE algorithm can be employed to calculate the CNOP, especially when the cost function is non-differentiable.

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.

Solving Ordinary Differential Equations with Evolutionary Algorithms

In this paper, the authors show that the general linear second order ordinary Differential Equation can be formulated as an optimization problem and that evolutionary algorithms for solving optimization problems can also be adapted for solving the formulated problem. The authors propose a polynomial based scheme for achieving the above objectives. The coefficients of the proposed scheme are approximated by an evolutionary algorithm known as Differential Evolution (DE). Numerical examples with good results show the accuracy of the proposed method compared with some existing methods.

Discrete differential evolution algorithm for integer linear bilevel programming problems

A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.

Steady Fault Characteristic Analysis of a Missile Power System Based on a Differential Evolution Algorithm

The differential evolution (DE) algorithm is applied to solving themodels''equations of a whole missile power system, and the steady fault characteristics of the wholesystem are analyzed. The DE algorithm is robust, requires few control variables, is easy to use andlends itself very well to parallel computation. Calculation results indicate that the DE algorithmsimulates faults of a missile power system very well.