一种改进的多目标混合差分进化算法

将差分进化算法（DE）用于多目标优化问题,提出了一种精英保留和进化进程中非支配解集迁移操作的差分进化算法,以保证所求得多目标优化问题Pareto最优解的多样性。采用双群体约束处理技术,构建进化群体的Pareto非支配解外部存档集,并进行基于非支配解集的迁移操作,以增加非支配解的数目和质量。用多个经典测试函数测试的结果表明,与标准DE相比,该方法收敛到问题的Pareto前沿效果良好,能有效保持Pareto最优解多样性与收敛之间的平衡。     

面向双目标应急物资调度的改进差分进化算法

本文对应急物资调度模型的建立及求解该模型的优化算法进行了研究.首先,在资源受限情况下,以配送费用总成本最小和最大缺失损失最小为优化目标,建立了连续消耗问题的多供应点对多受灾点的应急物资调度模型.然后,通过引入DE/best/1变异策略与DE/rand/2变异策略对差分进化算法进行了改进,提出了一种基于双变异策略的改进差分进化算法,将Pareto非支配等级分层与拥挤距离的概念引入到改进差分进化算法中,对约束双目标调度模型进行求解.最后,通过两种不同规模的四组仿真实验,验证了本文提出模型及改进的差分进化算法的可行性和有效性.与基本差分进化算法对比,双变异策略的改进差分进化算法对相同应急物资调度问题进行求解时,得到了更多的Pareto前沿解个数,和较低的应急物资调度配送费用成本与较小的最大缺失损失,同时解分布的广泛性也得到了显著提高.     

一种求解旅行商问题的进化多目标优化方法

为了克服传统小生境(Niching)策略中的参数设置难题,提出一种求解旅行商问题的进化多目标优化方法:建立以路径长度和平均离群距离为目标的双目标优化模型,利用改进非支配排序遗传算法(NSGAII)进行求解.为了在全局探索能力与局部开发能力之间保持平衡,算法中采用一种使路径长度相同的可行解互不占优的评价策略,并通过一种新的离散差分进化算子和简化的2-Opt策略生成候选解.与已有算法的数值试验结果比较表明,求解旅行商问题(TSP)的改进非支配排序遗传算法(NSGAII-TSP)能够更好地保持种群多样性,从而克服局部最优解的吸引并具有更鲁棒的全局探索能力.通过借助特殊的个体评价策略,所提出的算法可以更好地进行全局优化,甚至同时得到多个全局最优解.     

数据驱动选择策略的多目标差分进化算法

针对多目标差分进化算法求解复杂多目标优化问题时,最优解选择策略中非支配排序计算复杂度高的问题,提出一种数据驱动选择策略的多目标差分进化(MODE-DDSS)算法.首先,设计多目标差分进化算法的优化解排序等级评估准则,建立基于评估准则的优化解排序等级评估库;其次,设计基于优化解双向搜索机制和无重复比较机制的数据驱动选择策略,实现优化解的高效搜索和快速排序;最后,构建数据驱动选择策略的多目标差分进化算法,降低算法在最优解选择操作中的时间复杂度,提高算法的寻优效率.实验结果表明,所提出的MODE-DDSS算法能够有效减少最优解在选择过程中的比较次数,提升多目标差分进化算法解决复杂多目标优化问题的寻优效率.     

一种改进的多目标约束优化差分进化算法

提出一种新的多目标优化差分进化算法用于求解约束优化问题.该算法利用佳点集方法初始化个体以维持种群的多样性.将约束优化问题转化为两个目标的多目标优化问题.基于Pareto支配关系,将种群分为Pareto子集和Non-Pareto子集,结合差分进化算法两种不同变异策略的特点,对Non-Pareto子集和Pareto子集分别采用DE/best/1变异策略和DE/rand/1变异策略.数值实验结果表明该算法具有较好的寻优效果.     

基于混合差分进化和alpha约束支配处理的多目标优化算法

针对约束多目标优化问题, 提出了一种基于混合差分进化和alpha约束支配处理的优化算法. 算法在用约束水平度对个体满足约束条件的程度进行定量化表达的同时融入支配关系. 在初期放宽约束水平度, 利用不可行解所携带的有用信息, 增加种群多样性, 在后期紧缩约束水平度, 控制不可行解的比例, 朝可行域方向进化. 同时, 将动态单纯形交叉算子和差分进化结合起来构成一种混合差分进化算法, 提高算法的探索和开发能力. 对6个典型测试函数求解的结果显示, 本文算法无论是在收敛性方面还是解集分散性方面, 与其它算法相比具有很大的优势.     

多目标差分进化在热连轧负荷分配中的应用

提出一种基于差分进化算法的多目标进化算法, 该算法个体的选择是通过非支配排序和拥挤度距离进行综合考虑. 保证了算法收敛到Pareto最优解集的同时, 提高了最优解个体分布的多样性. 通过与非支配排序遗传算法Ⅱ(NSGA Ⅱ)算法进行仿真对比, 结果显示基于拥挤度排序的多目标差分进化算法在收敛性和Pareto最优解集分布的多样性上均优于NSGA Ⅱ算法. 最后将其引入到热连轧负荷分配优化计算中, 给出了目标函数的表达方式, 对多目标进化算法在热连轧负荷分配计算中的应用进行了研究.     

基于分解和差分进化的多目标粒子群优化算法

为了提高多目标优化算法解集的分布性和收敛性,提出一种基于分解和差分进化的多目标粒子群优化算法(dMOPSO-DE).该算法通过提出方向角产生一组均匀的方向向量,确保粒子分布的均匀性;引入隐式精英保持策略和差分进化修正机制选择全局最优粒子,避免种群陷入局部最优Pareto前沿;采用粒子重置策略保证群体的多样性.与非支配排序(NSGA-II)算法、多目标粒子群优化(MOPSO)算法、分解多目标粒子群优化(dMOPSO)算法和分解多目标进化-差分进化(MOEA/D-DE)算法进行比较,实验结果表明,所提出算法在求解多目标优化问题时具有良好的收敛性和多样性.     

动态罚函数法求解约束优化问题

针对罚函数法在求解约束优化问题时罚系数不易选取的问题,提出一种基于动态罚函数的差分进化算法。利用罚函数法将约束优化问题转化为无约束优化问题。为平衡种群的目标函数和约束违反程度,结合[ε]约束法设计了一种动态罚系数策略,其中罚系数随着种群质量和进化代数的改变而改变。采用差分进化算法更新种群直到搜索到最优解。对IEEE CEC 2010和IEEE CEC 2017两组基准测试集进行仿真实验,结果表明提出的算法具有较强的寻优性能。     

基于差分进化粒子群算法的多目标无功优化

针对电力系统有功网损最小、电压水平最好和电压稳定裕度最大的多目标无功优化问题,提出一种基于差分进化的改进多目标粒子群优化算法。该算法通过对Pareto最优解集的差分进化来增加Pareto最优解的多样性,通过拥挤距离来控制精英集中非支配解的分布,以提高对种群空间的均匀采集;采用擂台赛法则构造多目标Pareto最优解集,较大程度的提高了算法的运行效率;自适应惯性权重和加速度因子的动态变化可增强算法的全局搜索能力。将该算法在IEEE14、IEEE30节点标准测试系统上进行了无功优化仿真,结果表明,基于差分进化的改进多目标粒子群优化算法能够在保持Pareto最优解的多样性的同时具有较好的收敛性能,为多目标无功优化提供了一种新的方法。     

Improving the performance of differential evolution algorithm using Cauchy mutation

Differential evolution (DE) is a powerful yet simple evolutionary algorithm for optimization of real-valued, multimodal functions. DE is generally considered as a reliable, accurate and robust optimization technique. However, the algorithm suffers from premature convergence and/or slow convergence rate resulting in poor solution quality and/or larger number of function evaluation resulting in large CPU time for optimizing the computationally expensive objective functions. Therefore, an attempt to speed up DE is considered necessary. This research introduces a modified differential evolution (MDE) that enhances the convergence rate without compromising with the solution quality. The proposed MDE algorithm maintains a failure_counter (FC) to keep a tab on the performance of the algorithm by scanning or monitoring the individuals. Finally, the individuals that fail to show any improvement in the function value for a successive number of generations are subject to Cauchy mutation with the hope of pulling them out of a local attractor which may be the cause of their deteriorating performance. The performance of proposed MDE is investigated on a comprehensive set of 15 standard benchmark problems with varying degrees of complexities and 7 nontraditional problems suggested in the special session of CEC2008. Numerical results and statistical analysis show that the proposed modifications help in locating the global optimal solution in lesser numbers of function evaluation in comparison with basic DE and several other contemporary optimization algorithms.     

An evolving surrogate model-based differential evolution algorithm

Differential evolution (DE) is a simple and effective approach for solving numerical optimization problems. However, the performance of DE is sensitive to the choice of mutation and crossover strategies and their associated control parameters. Therefore, to achieve optimal performance, a time-consuming parameter tuning process is required. In DE, the use of different mutation and crossover strategies with different parameter settings can be appropriate during different stages of the evolution. Therefore, to achieve optimal performance using DE, various adaptation, self-adaptation, and ensemble techniques have been proposed. Recently, a classification-assisted DE algorithm was proposed to overcome trial and error parameter tuning and efficiently solve computationally expensive problems. In this paper, we present an evolving surrogate model-based differential evolution (ESMDE) method, wherein a surrogate model constructed based on the population members of the current generation is used to assist the DE algorithm in order to generate competitive offspring using the appropriate parameter setting during different stages of the evolution. As the population evolves over generations, the surrogate model also evolves over the iterations and better represents the basin of search by the DE algorithm. The proposed method employs a simple Kriging model to construct the surrogate. The performance of ESMDE is evaluated on a set of 17 bound-constrained problems. The performance of the proposed algorithm is compared to state-of-the-art self-adaptive DE algorithms: the classification-assisted DE algorithm, regression-assisted DE algorithm, and ranking-assisted DE algorithm.     

Determining the prices of remanufactured products,capacity of internal workstations and the contracting strategy within queuing framework

This paper studies a remanufacturing facility with several types of incoming nonconforming products and different independent remanufacturing workstations. The workstations have limited capacities so that an outsourcing strategy can be practiced. Each workstation is modeled with an M/M/1/k queuing system considering k as a decision variable. Additionally, a binary decision variable is taken into account to determine the contracting strategy along with some decision variables for the prices of remanufactured products. Thus, a bi-objective mixed-integer nonlinear programming is built to obtain optimal values of the decision variables. The first objective attempts to maximize the total profit and the second minimizes the average length of queuing at workstations. To solve the complex bi-objective mixed-integer nonlinear programming problem, the best out of six multi-objective decision-making (MODM) methods is selected in order to make the bi-objective optimization problem a single-objective one. Afterward, a genetic algorithm (GA) is developed to find a near-optimum solution of the single-objective problem. Besides, all of the important parameters of the algorithm are calibrated using regression analysis. To validate the results obtained, the solutions of some test problems are compared to the ones obtained by the GAMS software. The applicability of the proposed model and the solution procedure are shown with an illustrative example.     

自适应变异差分进化算法估计软测量参数

提出一种自适应变异差分进化算法(ADE),能根据搜索进展情况自适应地确定变异率,使算法在初期保持个体的多样性,避免早熟:在后期逐步降低变异率,保留优良信息,避免最优解遭到破坏,增加搜索到全局最优值的概率．与传统的差分进化算法(DE)相比较,ADE算法的离线性能和在线性能都有较大的改进,搜索到全局最优解的概率获得较大提高,对算法参数的敏感性低．本文将ADE算法应用于对苯二甲酸中对羧基苯甲醛含量软测量模型的参数估计,获得了满意的结果．     

Distributed memetic differential evolution with the synergy of Lamarckian and Baldwinian learning

As a population-based optimizer, the differential evolution (DE) algorithm has a very good reputation for its competence in global search and numerical robustness. In view of the fact that each member of the population is evaluated individually, DE can be easily parallelized in a distributed way. This paper proposes a novel distributed memetic differential evolution algorithm which integrates Lamarckian learning and Baldwinian learning. In the proposed algorithm, the whole population is divided into several subpopulations according to the von Neumann topology. In order to achieve a better tradeoff between exploration and exploitation, the differential evolution as an evolutionary frame is assisted by the Hooke–Jeeves algorithm which has powerful local search ability. We incorporate the Lamarckian learning and Baldwinian learning by analyzing their characteristics in the process of migration among subpopulations as well as in the hybridization of DE and Hooke–Jeeves local search. The proposed algorithm was run on a set of classic benchmark functions and compared with several state-of-the-art distributed DE schemes. Numerical results show that the proposed algorithm has excellent performance in terms of solution quality and convergence speed for all test problems given in this study.     

A novel hybrid DEPS optimized fuzzy PI/PID controller for load frequency control of multi-area interconnected power systems

In this paper, a novel hybrid Differential Evolution (DE) and Pattern Search (PS) optimized fuzzy PI/PID controller is proposed for Load Frequency Control (LFC) of multi-area power system. Initially a two-area non-reheat thermal system is considered and the optimum gains of the fuzzy PI/PID controller are optimized employing a hybrid DE and PS (hDEPS) optimization technique. The superiority of the proposed controller is demonstrated by comparing the results with some recently published modern heuristic optimization techniques such as DE, Bacteria Foraging Optimization Algorithm (BFOA), Genetic Algorithm (GA) and conventional Ziegler Nichols (ZN) based PI controllers for the same interconnected power system. Furthermore, robustness analysis is performed by varying the system parameters and operating load conditions from their nominal values. It is observed that the optimum gains of the proposed controller need not be reset even if the system is subjected to wide variation in loading condition and system parameters. Additionally, the proposed approach is further extended to multi-area multi-source power system with/without HVDC link and the gains of fuzzy PID controllers are optimized using hDEPS algorithm. The superiority of the proposed approach is shown by comparing the results with recently published DE optimized PID controller and conventional optimal output feedback controller for the same power systems. Finally, Reheat turbine, Generation Rate Constraint (GRC) and time delay are included in the system model to demonstrate the ability of the proposed approach to handle nonlinearity and physical constraints in the system model.     

Design of a genetic algorithm for bi-objective unrelated parallel machines scheduling with sequence-dependent setup times and precedence constraints

This paper presents a novel, two-level mixed-integer programming model of scheduling N jobs on M parallel machines that minimizes bi-objectives, namely the number of tardy jobs and the total completion time of all the jobs. The proposed model considers unrelated parallel machines. The jobs have non-identical due dates and ready times, and there are some precedence relations between them. Furthermore, sequence-dependent setup times, which are included in the proposed model, may be different for each machine depending on their characteristics. Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time using traditional approaches or optimization tools is extremely difficult. This paper proposes an efficient genetic algorithm (GA) to solve the bi-objective parallel machine scheduling problem. The performance of the presented model and the proposed GA is verified by a number of numerical experiments. The related results show the effectiveness of the proposed model and GA for small and large-sized problems.     

A memetic algorithm for bi-objective integrated forward/reverse logistics network design

Logistics network design is a major strategic issue due to its impact on the efficiency and responsiveness of the supply chain. This paper proposes a model for integrated logistics network design to avoid the sub-optimality caused by a separate, sequential design of forward and reverse logistics networks. First, a bi-objective mixed integer programming formulation is developed to minimize the total costs and maximize the responsiveness of a logistics network. To find the set of non-dominated solutions, an efficient multi-objective memetic algorithm is developed. The proposed solution algorithm uses a new dynamic search strategy by employing three different local searches. To assess the quality of the novel solution approach, the quality of its Pareto-optimal solutions is compared to those generated by an existing powerful multi-objective genetic algorithm from the recent literature and to exact solutions obtained by a commercial solver.     

基于多种群差分进化的多目标优化算法

针对差分进化算法(Differential Evolution Algorithm,DE)求解多目标优化问题时易陷入局部最优的问题,设计了一种双向搜索机制,它通过对相反进化方向产生的两个子代个体进行评价,来增强DE算法的局部搜索能力;设计了多种群机制,它可令各子群独立进化一定次数再执行全局进化,以完成子群间进化信息的交流,这一方面降低了算法陷入局部最优的风险,另一方面增强了Pareto解集的多样性,使Pareto前沿面的解集分布更为均匀。实验结果表明,相比于NSGA-II等同类算法,所提方法在搜索Pareto最优解时效率更高,并且Pareto最优解集的精度及分布程度比前者更好。     

考虑胜任力水平的研发项目群人力资源调度

在资源受限项目调度问题中,将可更新资源进一步拓展为具有胜任力差异的人力资源,建立考虑胜任力差异的人力资源受限项目调度问题模型,该模型是对传统多模式资源约束项目调度问题（MRCPSP）更接近研发项目群实际的扩展。提出了衡量人员胜任力的参数及估算公式,以多项目总工期和总成本最小化为双目标,建立相应的数学优化模型。按双目标重要性排序,依次对工期最优及成本最优的单目标优化问题求解。根据模型的约束条件将多项目初始网络图转化为几种单项目初始网络图,利用枚举算法给出满足约束条件的可行解集,再设计基于动态规划思想的算法进行分阶段寻优。数值实验表明,考虑了胜任力差异的数学优化模型在求解质量方面具有良好性能。