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.

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.

融合差分进化和Sine混沌的改进粒子群算法

将差分进化与Sine混沌相结合,提出一种改进的粒子群算法。利用Sine混沌映射对初始种群进行优化,提高了收敛速度;该算法通过引入非同步变化的学习因子的速度更新公式,引入随机惯性权重,使算法能够更好地兼顾全局搜索与局部优化;借鉴差分进化算法中的交叉操作,采用淘汰机制随机搜索策略,提高算法的全局搜索能力,提高算法收敛速度。为了验证融合差分进化和Sine混沌的改进粒子群算法(improved particle swarm optimization algorithm,IPSO)的性能,与基于压缩学习因子的粒子群算法(yield-based particle swarm optimization,YPSO)、自适应加权粒子群算法(self-adaptive particle swarm optimization,SPSO)等PSO相关算法以及蜘蛛蜂优化算法(spider wasp optimization,SWO)、能量谷算法(energy valley algorithm,EVA)等2023年最新算法相比较,验证融合差分进化和Sine混沌的改进粒子群算法(IPSO)的有效性。在不同维度下解决12个常用基准函数,对12个测试函数进行实验,并与其他的几种算法进行比较,实验结果表明,改进后的PSO算法收敛速度快,收敛精度高。

Dynamic multi-objective differential evolution algorithm based on the information of evolution progress

The multi-objective differential evolution(MODE)algorithm is an effective method to solve multi-objective optimization problems.However,in the absence of any information of evolution progress,the optimization strategy of the MODE algorithm still appears as an open problem.In this paper,a dynamic multi-objective differential evolution algorithm,based on the information of evolution progress(DMODE-IEP),is developed to improve the optimization performance.The main contributions of DMODE-IEP are as follows.First,the information of evolution progress,using the fitness values,is proposed to describe the evolution progress of MODE.Second,the dynamic adjustment mechanisms of evolution parameter values,mutation strategies and selection parameter value based on the information of evolution progress,are designed to balance the global exploration ability and the local exploitation ability.Third,the convergence of DMODE-IEP is proved using the probability theory.Finally,the testing results on the standard multi-objective optimization problem and the wastewater treatment process verify that the optimization effect of DMODE-IEP algorithm is superior to the other compared state-of-the-art multi-objective optimization algorithms,including the quality of the solutions,and the optimization speed of the algorithm.

Evolutionary Trajectory Planning for an Industrial Robot

This paper presents a novel general method for computing optimal motions of an industrial robot manipulator （AdeptOne XL robot） in the presence of fixed and oscillating obstacles. The optimization model considers the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacle avoidance. The problem has 6 objective functions, 88 variables, and 21 constraints. Two evolutionary algorithms, namely, elitist non-dominated sorting genetic algorithm （NSGA-II） and multi-objective differential evolution （MODE）, have been used for the optimization. Two methods （normalized weighting objective functions and average fitness factor） are used to select the best solution tradeoffs. Two multi-objective performance measures, namely solution spread measure and ratio of non-dominated individuals, are used to evaluate the Pareto optimal fronts. Two multi-objective performance measures, namely, optimizer overhead and algorithm effort, are used to find the computational effort of the optimization algorithm. The trajectories are defined by B-spline functions. The results obtained from NSGA-II and MODE are compared and analyzed.

Multi-objective optimization for draft scheduling of hot strip mill

A multi-objective optimization model for draft scheduling of hot strip mill was presented, rolling power minimizing, rolling force ratio distribution and good strip shape as the objective functions. A multi-objective differential evolution algorithm based on decomposition （MODE/D）. The two-objective and three-objective optimization experiments were performed respectively to demonstrate the optimal solutions of trade-off. The simulation results show that MODE/D can obtain a good Pareto-optimal front, which suggests a series of alternative solutions to draft scheduling. The extreme Pareto solutions are found feasible and the centres of the Pareto fronts give a good compromise. The conflict exists between each two ones of three objectives. The final optimal solution is selected from the Pareto-optimal front by the importance of objectives, and it can achieve a better performance in all objective dimensions than the empirical solutions. Finally, the practical application cases confirm the feasibility of the multi-objective approach, and the optimal solutions can gain a better rolling stability than the empirical solutions, and strip flatness decreases from （0± 63） IU to （0±45） IU in industrial production.

Multi-objective differential evolution with diversity enhancement

Multi-objective differential evolution (MODE) is a powerful and efficient population-based stochastic search technique for solving multi-objective optimization problems in many scientific and engineering fields. However, premature convergence is the major drawback of MODE, especially when there are numerous local Pareto optimal solutions. To overcome this problem, we propose a MODE with a diversity enhancement (MODE-DE) mechanism to prevent the algorithm becoming trapped in a locally optimal Pareto front. The proposed algorithm combines the current population with a number of randomly generated parameter vectors to increase the diversity of the differential vectors and thereby the diversity of the newly generated offspring. The performance of the MODE-DE algorithm was evaluated on a set of 19 benchmark problem codes available from http://www3.ntu.edu.sg/home/epnsugan/. With the proposed method, the performances were either better than or equal to those of the MODE without the diversity enhancement.

无伴随运动2PRU-PRUR并联机构高维多目标优化设计

设计了一种无伴随运动的面对称一移动两转动2PRU-PRUR并联机构,应用旋量理论分析了机构自由度和运动特性。将末端执行器输出轴设置为偏置形式,可提高姿态能力。采用球面姿态角(方位角和倾摆角)描述该输出轴姿态,并推导出机构逆向位置符号解。以旋量理论为数学工具,给出局部和全域传递性能指标的定义和计算方法。在机构性能评价和工作空间分析的基础上,建立了机构尺度参数昂贵约束高维多目标优化模型,并采用多目标进化算法求解该问题。同时,为提高高维多目标优化算法在解决此模型时的性能,提出了一种矢量角高维多目标差分进化(Vector-angle-based many-objective Differential Evolution,VaDE)算法,可综合平衡个体的收敛性和分布性。应用VaDE求解机构高维多目标优化问题,得到多组Pareto备选解。研究结果可为机构尺度综合和实际应用提供参考。

Differential Evolution-Boosted Sine Cosine Golden Eagle Optimizer with Lévy Flight

Golden eagle optimizer(GEO)is a recently introduced nature-inspired metaheuristic algorithm,which simulates the spiral hunting behavior of golden eagles in nature.Regrettably,the GEO suffers from the challenges of low diversity,slow iteration speed,and stagnation in local optimization when dealing with complicated optimization problems.To ameliorate these deficiencies,an improved hybrid GEO called IGEO,combined with Lévy flight,sine cosine algorithm and differential evolution(DE)strategy,is developed in this paper.The Lévy flight strategy is introduced into the initial stage to increase the diversity of the golden eagle population and make the initial population more abundant;meanwhile,the sine-cosine function can enhance the exploration ability of GEO and decrease the possibility of GEO falling into the local optima.Furthermore,the DE strategy is used in the exploration and exploitation stage to improve accuracy and convergence speed of GEO.Finally,the superiority of the presented IGEO are comprehensively verified by comparing GEO and several state-of-the-art algorithms using(1)the CEC 2017 and CEC 2019 benchmark functions and(2)5 real-world engineering problems respectively.The comparison results demonstrate that the proposed IGEO is a powerful and attractive alternative for solving engineering optimization problems.

3-SRR腿履式调姿救援机器人优化设计与试验

为实现在复杂环境下对处于不同位姿伤员的精准施救及稳定转运,文中提出了一种3-SRR腿履式调姿救援机器人机构,并进行运动学分析、机构优化设计及试验研究。首先,基于闭环矢量法对其进行运动学分析,得到救援机器人运动学反解;然后,基于迭代搜索算法,得到其救援作业空间与姿态空间,并基于单一变量法分析救援机器人机构尺寸参数对救援作业空间的影响;然后,以救援作业空间最大、姿态能力最强为优化目标函数,基于差分进化算法对机构尺寸参数进行优化;最后,研制原理样机并进行调姿能力试验,试验结果证明了方案的可行性与理论分析的正确性,为灾难救援提供一种可行的解决方案。

大规模定制家具加工中心多钻头并行作业的优化

大规模定制家具超高的生产效率与高度个性化的产品两大特征决定了其需要依赖高水平的信息化与自动化组织生产,是家具制造业智能制造的前沿领域。运用数控加工中心开展钻孔作业是调和个性化产品制造过程中的矛盾、实现柔性生产的重要手段。当前,数控钻孔工序因其作业时间长且板件之间差异较大而往往成为制造过程中的瓶颈。为切实提高生产效率,本研究立足生产实际,从钻头与孔的位置关系中寻求突破口,提出了数控加工中心多钻头并行作业优化问题。以优化钻头排列为主要途径,减少下钻次数为核心目标,基于制造大数据与工艺规则挖掘信息并简化建模,采用差分进化算法求解钻头排列方案,进一步通过聚类算法探索出面向未来高自动化水平下的差异化钻头排列,形成了一套具有实际意义与普适性的优化方法。通过理论与实践验证了该方法的有效性,达到了缩减作业时间、提升加工效率的目的。对打通大规模定制家具制造瓶颈、推动定制家具智能制造具有一定的指导意义。

基于改进AOA的联合采购与配送问题研究

针对算术优化算法(AOA)个体信息利用率较低和容易陷入局部最优的缺点,采用信息交换策略并结合正余弦(SCA)算法,设计了基于SCA的改进算术优化算法(EAOA),以提高AOA算法的寻优能力。采用标准测试函数测试EAOA的性能,结果表明EAOA比遗传算法、差分进化算法和标准AOA更有效。针对大规模联合采购与配送协同优化问题的求解,EAOA比遗传算法、差分进化算法和标准AOA得到的总成本更低。

Performance Evaluation and Comparison of Multi - Objective Optimization Algorithms for the Analytical Design of Switched Reluctance Machines

This paper systematically evaluates and compares three well-engineered and popular multi-objective optimization algorithms for the design of switched reluctance machines.The multi-physics and multi-objective nature of electric machine design problems are discussed,followed by benchmark studies comparing generic algorithms(GA),differential evolution(DE)algorithms and particle swarm optimizations(PSO)on a 6/4 switched reluctance machine design with seven independent variables and a strong nonlinear multi-objective Pareto front.To better quantify the quality of the Pareto fronts,five primary quality indicators are employed to serve as the algorithm testing metrics.The results show that the three algorithms have similar performances when the optimization employs only a small number of candidate designs or ultimately,a significant amount of candidate designs.However,DE tends to perform better in terms of convergence speed and the quality of Pareto front when a relatively modest amount of candidates are considered.

考虑舒适性的自动驾驶轨道列车牵引电机节能控制

为提升乘客在自动驾驶轨道列车中的体验感,保证自动驾驶轨道列车的安全运行,提出考虑舒适性的自动驾驶轨道列车牵引电机节能控制技术。构建自动驾驶轨道列车运动学模型,分析牵引和制动电机能耗。依据分析结果建立列车牵引电机节能控制目标函数,并以行驶速度、舒适性、准时性和精确停车设置约束条件。利用混沌算法和蛙跳算法改进标准差分进化算法求解目标函数,获取最优解,实现自动驾驶轨道列车牵引电机节能控制。实验结果表明,所提方法在预期速度跟踪性能、节能性、舒适性、精准停车和准点中表现更为优异,验证了所提方法应用下的自动驾驶轨道列车在满足乘客舒适性要求的基础上,获取了较好的牵引电机节能控制效果。

基于自适应权重调整与差分进化策略的并行式混合蛙跳算法

针对标准混合蛙跳算法(SFLA)在复杂优化问题中出现的收敛速度慢、求解精度不高和运行效率低等问题,提出了一种基于自适应权重调整与差分进化(DE)策略的并行式混合蛙跳算法(P-DE-ASFLA)。在局部搜索过程中,采用邻近学习策略更新子群中的最优个体以加快算法的收敛;采用动态蛙跳规则更新子群中的最差个体以避免算法早熟收敛;在全局搜索过程中,采用DE策略对混合后的种群进行基因更新,增强算法的全局寻优能力。同时基于主从式并行架构,采用多进程技术使子群的局部搜索过程并行化,大幅提高了算法的运行效率。实验结果表明,所提算法在6个标准测试函数中的求解质量和运行效率要远优于标准SFLA和DE算法。

4-PRUR并联机构及其位置分析的差分进化算法

给出1移动3转动(1T3R)对称4-DOF空间4-PRUR并联机构的几何模型,应用螺旋理论分析机构实现1T3R的原理,并讨论输入选取的合理性。根据杆长约束条件,建立机构位置分析的非线性方程组。为改进差分进化算法(Differential evolution,DE)的寻优效率,提出一种基于混沌迁移、最优个体加权处理和群体逃逸策略的自适应双种群差分进化算法(Adaptive differential evolution algorithm with double subpopulations,ADEDS)。将机构位置分析中非线性方程组的求解转化为无约束优化模型,并应用ADEDS求解该问题。数值实例表明,ADEDS能求出并联机构的多组高精度位置正解,并通过位置反解验证位置正解的正确性。

6-CRS并联机器人机构及其位置分析

提出一种新型6-CRS广义Stewart并联机器人机构,建立了其几何模型。应用螺旋理论分别分析了以圆柱副中的转动和线性移动作为主动输入的合理性,研究了相应的机构位置正反解问题。为提高差分进化算法(DE)的寻优效率,将其改进为自适应逃逸差分进化算法(AEDE),可有效克服早熟收敛并提高计算精度。建立了以转动输入为主驱动的机构位置正解非线性方程组,并应用AEDE求其解;推导了以移动输入为主驱动时的位置正解封闭表达式。数值实例表明,AEDE能快速求出以转动输入为主驱动时的全部高精度位置正解,并通过位置反解验证了位置正解的正确性。

工作空间最大化的4-RUP_aR并联机构尺度优化设计

对一种新型3T1R并联机构-4RUPaR并联机构进行工作空间分析和尺度参数优化设计。首先利用解析几何中的坐标变换理论,以机构的杆长作为约束条件,得到了运动学反解方程;然后根据运动学反解方程,建立工作空间的约束条件,通过MATLAB编程实现机构的定姿态工作空间的可视化,并通过"点集"近似表达工作空间的大小;最后采用单一变量分析法得出了并联机构尺度参数与定姿态工作空间的关系。以工作空间最大化作为优化目标,采用差分进化算法求解该优化问题,获得了良好的机构尺度参数,使得并联机构的有效工作空间更大更健壮,也更加符合工程实用要求。

含电压不可行节点的柔性目标无功优化模型

提出一种含电压不可行节点的柔性目标无功优化模型。结合无功优化不可行问题的薄弱节点信息,提出了薄弱区的基本概念,并在基础上构建了柔性目标无功优化模型。该模型包含薄弱区的电压控制模型和非薄弱区的无功优化2个子模型,对应的目标函数分别为电压不可行节点的电压越下限量最少和网损最低,约束条件则在传统的无功优化模型上更新电压不可行节点的电压幅值安全下限值。采用代表薄弱区与非薄弱区种群先后更新策略的协同进化算法求解所建模型,通过63节点厂站模拟系统进行仿真分析,验证了所提方法的有效性。

并联机构位置正解的人工蜂群和牛顿组合算法

将智能优化算法与数值迭代方法有机组合,构造一种并联机构位置正解求解的通用算法——混合人工蜂群和Newton迭代(Hybrid artificial bee colony and Newton iteration,HABC-Newton)算法。将差分进化(Differential evolution,DE)算法融入人工蜂群(Artificial bee colony,ABC)算法,形成一种能快速收敛到问题近优解的混合人工蜂群(Hybrid ABC,HABC)算法,再以该近优解为初值,应用Newton-Шамарский迭代法求出高精度位置正解。以4自由度4-SPS-CU并联机构正运动学分析为例,阐述基于HABC-Newton算法的并联机构正运动学分析方法。为了验证算法的有效性和普适性,给出4-SPS-CU、3-RRR两种耦合并联机构位置正解的数值算例。结果表明,HABC-Newton算法能以较少计算开销求得并联机构的全部高精度位置正解。还比较了HABC-Newton、ABC、DE和粒子群算法求并联机构位置正解的性能,数值实验显示,HABC-Newton算法的精度、稳健性和计算效率高于对比算法。