基于拟态物理学的约束多目标共轭梯度混合算法

在拟态物理学优化算法APO的基础上,将一种基于序值的无约束多目标算法RMOAPO的思想引入到约束多目标优化领域中.提出一种基于拟态物理学的约束多目标共轭梯度混合算法CGRMOAPA.算法采取外点罚函数法作为约束问题处理技术,并借鉴聚集函数法的思想,将约束多目标优化问题转化为单目标无约束优化问题,最终利用共轭梯度法进行求解.通过与CRMOAPO、MOGA、NSGA-II的实验对比,表明了算法CGRMOAPA具有较好的分布性能,也为约束多目标优化问题的求解提供了一种新的思路.     

NSGA-II算法在农业水保措施配置优化中的应用

农业水保措施的配置要考虑其生态效益和经济效益.不同水保措施组合方案有其相应的生态和经济效益,如何配置使综合效益最佳是一个最优化问题.分析了农业水保措施配置最优化需要考虑的两个目标,并将其公式化,建立了水保措施配置优化模型,并应用NSGA-II多目标遗传算法求解该模型.最后,以甘肃天水市罗玉沟流域的水保措施配置为例,进行了初步应用.结果表明,采用NSGA-II算法在水保措施配置优化模型求解时,计算效率较高,优化结果稳定,具有一定的应用价值.     

考虑序列设置时间的混合流水车间多目标调度研究

基于混合流水车间多品种的特性,序列设置时间和工序跳跃是很多车间在调度时需要考虑的两个重要问题,论文充分考虑这两种生产约束,建立了以最大完工时间和负荷均衡指标为双目标的混合流水车间多目标调度数学模型,并运用改进的NSGA-II算法对基于实际企业生产数据假设的算例进行仿真求解,结果表明求解的调度方案符合实际需求,能够为企业的实际调度提供有效的方案。     

加工时间可控单机加权总完工时间Pareto优化研究

针对单机环境最优化加权总完工时间问题,当工件加工时间可通过分配资源进行压缩时,研究对工件的加工次序和时间压缩量的优化,从而权衡调度性能目标和资源成本目标。调度性能目标为压缩后工件的加权总完工时间,资源成本目标为工件压缩量的线性函数。此问题复杂性已被证明为NP-hard,为弥补较少有研究从Pareto优化角度求解该问题有效前沿的不足,针对经典NSGA-II求解时易早熟收敛的特点,采用算法混合方式进行优化方法研究。融合归档式多目标模拟退火算法跳出局部极值的优势,启用外部存档策略提升种群的多样性,采用主从模式的并行结构提升求解效率。最后为检验优化方法的有效性,一方面通过对Benchmark测试函数ZDT1-6的求解,表明混合算法对不同结构和形状目标函数兼具普适性和有效性;另一方面结合问题特点设计有效编码方式,针对随机生成算例进行求解。通过分析有效前沿收敛性和多样性,验证了所提方法对于优化加工时间可控单机加权总完工时间问题的有效性。     

基于改进NSGA-II算法的多级服务设施备用覆盖选址决策模型

为了应对跨区域突发事件过程中受灾点服务差异化需求的问题,建立了应急储备设施点的多级备用覆盖选址决策模型,即一个需求点由多个应急设施提供不同质量水平的服务,并考虑设施繁忙状态下由其他设施点提供服务的状况,使模型更加符合实际应用。首次通过设计分段的染色体编码方式改进NSGA-II算法提升运算效率以更好地解决多目标选址决策问题,将改进方法下得到的Pareto解分布与NSGA-II算法下的仿真结果进行对比分析,结合设施点的部署策略得到不同的空间布局方案。证明了模型的可行性及改进NSGA-II算法在解决设施点多目标选址决策问题时的有效性。     

基于Epsilon约束法的短纤维生产调度的双目标优化研究

针对短纤维生产行业实际,本文综合考虑客户的需求差异、客户的重要程度、纤维生产设备的准备时间以及交货期差异等因素,研究连续需求下的短纤维生产排序优化问题。首先,本文建立双目标整数规划模型,即最小化客户订单总延迟和最小化机器总准备时间;其次,设计Epsilon约束算法并调用CPLEX精确求解调度方案,即帕累托前沿;最后设计非支配排序的遗传算法(NSGA-II)求解大规模生产下的调度优化方案。通过实验,证明该整数规划模型和算法对解决多客户连续需求问题具有实际价值,进而可以为短纤维生产企业提供参考。     

基于混沌集群智能优化算法的多目标粗糙集属性约减

针对管理实践及大数据处理过程中具有多决策属性的粗糙集属性约减问题,将条件属性依赖度与知识分辨度进行结合构建属性权重,分别建立针对不同决策属性的约减目标函数,引入帕累托最优思想,将基于多决策属性的粗糙集属性约减问题转化为离散多目标优化问题。针对该问题的结构设计了具有集群智能优化思想的元胞自动机求解算法,在算法中引入基于个体的非支配解集平衡局部最优与全局最优的关系,引入混沌遗传算子增加种群多样性。以某铁路局设备安全风险处理数据为案例构建多决策属性粗糙集决策表进行优化计算并进行管理决策分析。研究发现:(1)相对于传统的NSGA-II与MO-cell算法,本文提出的算法具有更强的多目标属性挖掘性能;(2)帕累托最优思想可以较好地解释多决策属性粗糙集在管理实践中的意义。     

基于NSGA-II的应急生产任务多目标优化模型及算法研究

重大突发事件发生后,若灾区的应急物资需求不能通过调用储备得到满足,则应急生产将成为灾区应急物资供应的重要保障手段。本文研究重大突发事件发生后应急物资生产任务的优化问题,重点关注原材料生产能力变化对完成应急生产任务的影响,以应急生产任务完成时间最短、完成成本最低为决策目标,研究了包含多个供应商、多个制造商以及单个受灾点的应急物资生产任务多目标规划模型。运用在求解多目标规划问题时具有众多优势的非支配排序多目标遗传算法(NSGA-II)对模型进行求解。通过算例分析,NSGA-II可以得到较好的Pareto前沿,并且可以根据不同情况给出最优的应急物资生产和原材料保障方案。本文的研究还表明,要想更快完成应急生产任务,需要做好原材料、资金、电力、交通等各种要素的配套保障工作。     

灾情巡视问题的蚁群两目标优化算法研究

分析目前灾情巡视问题求解方法存在的缺陷,归纳出灾情巡视问题两目标优化模型.针对灾情巡视问题模型特点,引入蚁群算法和多目标优化理论,提出两个灾情巡视问题的蚁群两目标优化算法:算法1将灾情巡视问题的道路网络转化为完全图,增加m-1个(m为巡视组数)虚拟巡视起点,将灾情巡视两目标优化问题转化为单旅行商两目标优化问题,然后使用蚁群算法和多目标优化理论进行迭代求解.算法2使用一只蚂蚁寻找一个子回路,m个子回路构成一个灾情巡视可行方案,采用罚函数法和多目标优化理论构建增广两目标优化评价函数,使用g组,共g×m只蚂蚁共同协作来发现灾情巡视问题的最优解.算法特点:①算法1将灾情巡视两目标优化问题转化为单旅行商两目标优化问题,可以充分利用已有蚁群算法求解单旅行商问题的研究成果;②两个算法引入蚁群算法,提高了算法效率;③两个算法克服目前灾情巡视问题的求解方法不严密性缺陷;④两目标优化算法可以为用户提供多个满足约束条件的Pareto组合解,扩大了用户选择范围,增强了算法的适用性.算法测试表明:灾情巡视问题的蚁群两目标优化算法是完全可行和有效的.     

基于成本和加班时长的双目标家庭护理人员调度问题

人口老龄化程度的持续加重使得家庭医疗护理服务逐渐发展。本文针对家庭护理人员调度优化问题,考虑医患的技能匹配、加班费用、加班时长和工作量分配的均衡性等因素,设定最大技能偏差和工作时长,建立了最小化运营成本和最小化最大加班时长的双目标混合整数规划模型。设计了改进的NSGA-II和SPEA-II算法对问题进行求解,数值实验表明:最大加班时长越长,运营成本越小;最大技能偏差和医护人员早到惩罚对目标的影响明显;小规模算例中两算法均表现良好,大中型规模算例中改进SPEA-II的效率更高。     

双目标可重入混合流水车间调度问题的离散灰狼优化算法

可重入混合流水车间调度问题普遍存在于许多高科技制造产业中,如半导体晶圆制造和TFT-LCD面板生产过程等,但目前关于可重入调度问题的相关研究还比较少。本文设计了一种改进多目标灰狼优化算法(IMOGWO)解决最小化最大完工时间和总拖期时间最小的可重入混合流水车间调度问题,针对该问题特点对基本灰狼优化算法进行了一系列改进操作。通过对小规模测试问题基准算例的数值实验,验证了所设计的IMOGWO算法求解该调度问题的有效性。实验结果表明IMOGWO算法在非劣解的收敛性和支配性方面显著优于已有的NSGA-II和MOGWO算法,在解的分布性指标方面IMOGWO稍微优于其他两种算法。     

Improving the non-dominated sorting genetic algorithm using a gene-therapy method for multi-objective optimization

The non-dominate sorting genetic algorithmic-II (NSGA-II) is an effective algorithm for finding Pareto-optimal front for multi-objective optimization problems. To further enhance the advantage of the NSGA-II, this study proposes an evaluative-NSGA-II (E-NSGA-II) in which a novel gene-therapy method incorporates into the crossover operation to retain superior schema patterns in evolutionary population and enhance its solution capability. The merit of each select gene in a crossover chromosome is estimated by exchanging the therapeutic genes in both mating chromosomes and observing their fitness differentiation. Hence, the evaluative crossover operation can generate effective genomes based on the gene merit without explicitly analyzing the solution space. Experiments for nine unconstrained multi-objective benchmarks and four constrained problems show that E-NSGA-II can find Pareto-optimal solutions in all test cases with better convergence and diversity qualities than several existing algorithms.     

A multi-objective simulated-annealing algorithm for scheduling in flowshops to minimize the makespan and total flowtime of jobs

In this paper, we consider the problem of permutation flowshop scheduling with the objectives of minimizing the makespan and total flowtime of jobs, and present a Multi-Objective Simulated-annealing Algorithm (MOSA). Two initial sequences are obtained by using simple and fast existing heuristics, supplemented by the implementation of three improvement schemes. Each of the two resultant sequences corresponds to a possible non-dominated solution containing the minimum value of one objective function. These sequences, taken one at a time, are given as the starting sequences to the MOSA. The MOSA seeks to obtain non-dominated solutions through the implementation of a simple probability function that attempts to generate solutions on the Pareto-optimal front. The probability function selects probabilistically a particular objective function, considering which the algorithm uncovers non-dominated solutions. Moreover, the probability function is varied in such a way that the entire objective-function space is covered uniformly so as to obtain as many non-dominated and well-dispersed solutions as possible. The parameters in the proposed MOSA are determined after conducting a pilot study. Two variants of the proposed algorithm, called MOSA-I and MOSA-II, with different parameter settings with respect to the temperature and epoch length, are considered in the performance evaluation of algorithms. In order to evaluate MOSA-I and MOSA-II, we have made use of 90 benchmark problems provided by Taillard [Eur. J. Operation. Res. 64 (1993) 278]. After an extensive literature survey, the following flowshop multi-objective scheduling algorithms have been identified as benchmark procedures: (a) MOGLS (Multi-Objective Genetic Local Search) by Ishibuchi and Murata [IEEE Trans. Syst., Man, Cybernet. C: Appl. Rev. 28 (1998) 392]; (b) Elitist Non-dominated sorting Genetic Algorithm (ENGA) by Bagchi [Multi-Objective Scheduling by Genetic Algorithms, Kluwer Academic Publishers, 1999]; (c) GPW (Gradual Priority Weighting) approach by Chang, Hsieh and Lin [Int. J. Prod. Econ. 79 (2002) 171]; and (d) a posteriori approach based heuristic by Framinan, Leisten and Ruiz-Usano [Eur. J. Operation. Res. 141 (2002) 559]. The non-dominated sets obtained from each of the existing benchmark algorithms and the proposed MOSA-I and MOSA-II are compared, and subsequently combined to obtain a net non-dominated front. It is found that most of the solutions in the net non-dominated front are yielded by MOSA-I and MOSA-II. In addition, it is noteworthy that both MOSA-I and MOSA-II require less computational effort than the MOGLS, ENGA and GPW.     

基于改进NSGA-II算法的云制造服务组合优化研究

云制造任务日趋复杂,与基于云制造的云服务组合优化问题相关的指标日益增多,需要综合考虑各个评价指标,从海量备选云服务中筛选出最优服务组合。本文针对云制造的特点,从线上、线下两方面构建了云制造服务评价指标体系;为了更好地处理高维多目标优化问题并消除实际问题中的量纲影响,本文利用改进的α支配策略代替帕累托支配改进NSGA-II算法,提出了基于nα支配的NSGA-II算法。最后,本文通过一个电机制造案例验证了提出算法的可行性,并通过与标准NSGA-II算法、r-NSGA-II算法和基于模糊支配的NSGA-II算法对比,证明了提出算法得到的解集更优、更小,能够大大减小后续组合优选的计算量。     

CFD modeling and multi-objective optimization of cyclone geometry using desirability function,artificial neural networks and genetic algorithms

The low-mass loading gas cyclone separator has two performance parameters, the pressure drop and the collection efficiency (cut-off diameter). In this paper, a multi-objective optimization study of a gas cyclone separator has been performed using the response surface methodology (RSM) and CFD data. The effects of the inlet height, the inlet width, the vortex finder diameter and the cyclone total height on the cyclone performance have been investigated. The analysis of design of experiment shows a strong interaction between the inlet dimensions and the vortex finder diameter. No interaction between the cyclone height and the other three factors was observed. The desirability function approach has been used for the multi-objective optimization. A new set of geometrical ratios (design) has been obtained to achieve the best performance. A numerical comparison between the new design and the Stairmand design confirms the superior performance of the new design. As an alternative approach for applying RSM as a meta-model, two radial basis function neural networks (RBFNNs) have been used. Furthermore, the genetic algorithms technique has been used instead of the desirability function approach. A multi-objective optimization study using NSGA-II technique has been performed to obtain the Pareto front for the best performance cyclone separator.     

Convex hull-based multi-objective evolutionary computation for maximizing receiver operating characteristics performance

The receiver operating characteristics (ROC) analysis has gained increasing popularity for analyzing the performance of classifiers. In particular, maximizing the convex hull of a set of classifiers in the ROC space, namely ROCCH maximization, is becoming an increasingly important problem. In this work, a new convex hull-based evolutionary multi-objective algorithm named ETriCM is proposed for evolving neural networks with respect to ROCCH maximization. Specially, convex hull-based sorting with convex hull of individual minima (CH-CHIM-sorting) and extreme area extraction selection (EAE-selection) are proposed as a novel selection operator. Empirical studies on 7 high-dimensional and imbalanced datasets show that ETriCM outperforms various state-of-the-art algorithms including convex hull-based evolutionary multi-objective algorithm (CH-EMOA) and non-dominated sorting genetic algorithm II (NSGA-II).     

公交网络时刻表再协同设计的多目标优化模型

为了改善公交服务质量,公交运营者试图调整现有时刻表的发车时间,使不同线路的车次协同到达换乘站点以方便乘客换乘。针对此场景,研究了公交时刻表重新协同设计问题,提出了求解该问题的多目标模型。模型考虑了对发车间隔灵敏的乘客需求、灵活的车次协同到站方式和发车时间的规则性,分析了该多目标模型的特征和计算复杂性,表明本文研究的问题是NP-hard问题,且它的帕累托最优前沿是非凸的,设计了基于非支配排序的遗传算法求解模型。算例表明,与枚举算法相比,提出的求解算法在较短的时间内可获得高质量的帕累托解。     

FEMOEA: a fast and efficient multi-objective evolutionary algorithm

A multi-objective evolutionary algorithm which can be applied to many nonlinear multi-objective optimization problems is proposed. Its aim is to quickly obtain a fixed size Pareto-front approximation. It adapts ideas from different multi-objective evolutionary algorithms, but also incorporates new devices. In particular, the search in the feasible region is carried out on promising areas (hyperspheres) determined by a radius value, which decreases as the optimization procedure evolves. This mechanism helps to maintain a balance between exploration and exploitation of the search space. Additionally, a new local search method which accelerates the convergence of the population towards the Pareto-front, has been incorporated. It is an extension of the local optimizer SASS and improves a given solution along a search direction (no gradient information is used). Finally, a termination criterion has also been proposed, which stops the algorithm if the distances between the Pareto-front approximations provided by the algorithm in three consecutive iterations are smaller than a given tolerance. To know how far two of those sets are from each other, a modification of the well-known Hausdorff distance is proposed. In order to analyze the algorithm performance, it has been compared to the reference algorithms NSGA-II and SPEA2 and the state-of-the-art algorithms MOEA/D and SMS-EMOA. Several quality indicators have been considered, namely, hypervolume, average distance, additive epsilon indicator, spread and spacing. According to the computational tests performed, the new algorithm, named FEMOEA, outperforms the other algorithms.     

计及客户满意度的电动汽车物流配送路径规划与充放电管理

物流配送作为一种盈利型社会服务性行业,配送服务时间对客户满意度具有重要影响。论文考虑电动汽车(electric vehicle, EV)在配送途中和回到配送中心两个阶段,以物流配送成本最低和客户平均满意度最高为目标,构建了一种EV在换电模式下计及客户满意度的物流配送路径规划与充放电管理多目标优化模型,其中物流配送成本包括换电成本、车辆损耗成本以及慢速充放电成本。最后,以A-n29节点VRP基准测试系统插入四座换电站节点为例进行数值仿真,采用非支配排序遗传算法(Non-dominated sorting genetic algorithm, NSGA-II)对所提多目标优化模型进行求解,结果验证了所提方法的可行性和有效性。此外,论文进一步考查了EV慢速充放电管理对配电系统的影响,并对EV发车时间作了参数灵敏度分析,为管理者提供一些参考。