基于余弦距离的多目标粒子群优化算法

针对粒子群优化算法具有的个体分布不均匀以及重复个体较多等缺陷,提出了一种基于余弦距离的多目标粒子群优化算法,该算法根据外部精英存储策略,利用余弦距离排挤机制来选取最分散的粒子,扩大 Pareto最优解集的收敛性和多样性,增强算法的全局寻优能力。通过采用标准多目标优化问题ZDTl～ZDT3进行仿真实验与粒子群算法、混沌粒子群算法、基于拥挤距离的多目标优化算法对比表明,该算法在Pareto前沿的收敛性和多样性方面均优于基于拥挤距离排挤机制,并具有较高的效率     

基于粒子群优化的地震应急物资多目标调度算法

合理高效地优化调度救灾物资对提升地震应急救援效果具有重要意义。地震应急需要同时兼顾时效性、公平性和经济性等相互冲突的多个调度目标。该文对地震应急物资调度问题建立了带约束的3目标优化模型，并设计了基于进化状态评估的自适应多目标粒子群优化算法(AMOPSO/ESE)来求解Pareto最优解集。然后根据“先粗后精”的决策行为模式提出了由兴趣最优解集和邻域最优解集构成的Pareto前沿来辅助决策过程。仿真表明该算法能有效地获得优化调度方案，与其他算法相比，所得Pareto解集在收敛性和多样性上具有性能优势。     

多策略差分进化的元胞多目标粒子群算法

为了增加Pareto解集的多样性,平衡多目标优化的全局搜索和局部寻优的能力,提出一种多策略差分进化的元胞多目标粒子群算法.该算法在分析粒子群优化原理基础上,将元胞自动机理论融入粒子群算法,研究粒子种群的交流结构和信息传递机制.为了避免粒子飞行速度过快陷入局部收敛,提出一种限制粒子飞行速度的策略,并引入一种多策略差分进化选择算子增加对粒子的扰动.实验证明,该算法相对于比较算法,有更好的收敛性和多样性.     

基于动态交换策略的快速多目标粒子群优化算法研究

本文提出了一种基于动态交换策略的快速多目标粒子群优化算法,通过把初始种群分割成Pareto和Non_Pareto集合,并在迭代过程中对Pareto解集进行动态调整,从而较好地完成了多目标优化算法对Pareto解集的搜索和逼近.实验和应用实例均表明了该算法的有效性和快速性,并通过性能指标ER的计算验证了本算法优于某些同类的多目标优化算法.     

基于MODPSO-SA算法的多AUV任务分配

提出一种基于Pareto解集的多目标模拟退火粒子群算法(MODPSO-SA),用于解决自主水下机器人(AUV)协同任务分配问题.为避免粒子群算法陷入局部最优,加入改进的模拟退火技术,形成一种新的多目标局部搜索策略.仿真结果表明,MODPSO-SA算法能够得出多组合理Pareto解集,可以有效解决多AUV任务分配问题.     

城市道路交叉口信号配时多目标优化方法研究

针对目前交叉口信号配时优化目标单一、综合运行效率不高的问题,提出一种交叉口信号配时多目标优化方法。考虑绿灯时间、周期长度和饱和度等约束条件,通过加权系数法定义代价函数,使交叉口的延误时间、停车次数和通行能力在某种程度上达到最优。基于免疫克隆算法在处理多目标问题中具有最优解分布宽广性、均匀性好等特点,引入环境变异算子,提出环境变异免疫克隆算法对模型求解,增强了算法的全局搜索能力,提高了解的质量。仿真结果表明,与传统配时方法和改进粒子群算法相比,该文方法能有效减少信号交叉口的延误时间和停车次数,提高交叉口的运行效率。     

改进偏好多目标优化算法在直流偏磁抑制装置优化配置中的应用

基于偏好的多目标优化算法能够定向搜索符合决策者需求的Pareto解集,是多目标优化算法与工程实际联系最为紧密的方法之一。为准确地将决策者偏好需求反映到最终Pareto解集,提出一种偏好映射点动态更新策略,通过动态更新偏好映射点来降低算法对初始参考点位置的依赖。为实现输出Pareto解数目可调可控,引入偏好解集过滤器,使得算法能够得到解集数目符合决策者要求、分布均匀的Pareto解。最后,利用所提算法求解ZDT系列测试函数和浙北区域直流偏磁抑制装置优化配置问题。结果表明,所提算法能有效收敛至决策者偏好对应的Pareto解集,可以为直流偏磁抑制装置优化配置工程实际问题提供符合决策者需求的优秀候选方案。     

改进的多目标粒子群算法优化设计及应用

针对粒子群算法存在易陷入局部最优点的缺点,提出了一种改进的带变异算子的多目标粒子群优化算法。采用非支配排序策略和动态加权法选择最优粒子,引导种群飞行,提高帕累托(Pareto)最优解的多样性。与其他优化算法相比,该算法易于实现并且计算速度更快。通过计算Pareto前沿最优解设计最佳多层电磁吸收体,在吸收体的厚度与反射系数之间取得最佳折衷。通过对反射系数函数与吸收体厚度函数测试验证,该算法能够在保持优化解多样性的同时具有较好的收敛性。     

一种基于粒子群算法的螺旋迭代模型研究

实际工程优化过程中,对于多个目标的优化与求解最优值是值得研究的一个问题。文章基于粒子群算法研究多目标优化问题,实现二维多目标搜索,运用粒子群多目标求解模型迭代实现动态多目标搜索,最终得到非劣解在目标空间中的分布,构成了Pareto面,得到非劣解集,在实际问题中,提供最优解的备选,为工程实践优化和筛选最优解问题提供参考依据。     

基于粒子群算法的钻进参数多目标优化

为了使钻进过程达到最优,提出了基于机械钻速、钻头寿命和钻头比能的钻进参数多目标优化模型。参考典型的多目标优化进化算法NSGA-Ⅱ,提出了一种多目标粒子群算法(MOPSO)。采用一个钻进参数优化实例对优化模型和算法进行检验,得到分布均匀的Pareto最优解,一些最优解与传统的钻进参数单目标优化的解近似;讨论了算法中的种群规模、迭代次数和外部档案规模三个参数,得到一组兼顾解质量和计算时间的参数值,其计算时间的统计结果证明模型和算法满足钻进参数动态优化的要求。     

一种基于多样性信息和收敛度的多目标粒子群优化算法

为了提高多目标粒子群算法优化解的多样性和收敛性,提出了一种基于多样性信息和收敛度的多目标粒子群优化算法（Multiobjective Particle Swarm Optimization based on the Diversity Information and Convergence Degree,dicdMOPSO）.首先,利用非支配解多样性信息评估知识库中最优解的分布状态,设计出一种全局最优解选择机制,平衡了种群的进化过程,提高了非支配解的多样性和收敛性;其次,基于种群多样性信息设计出一种飞行参数调整机制,增强了粒子的全局探索能力和局部开发能力,获得了多样性和收敛性较好的种群.最后,将dicdMOPSO应用于标准测试函数测试,实验结果表明,dicdMOPSO与其他多目标算法相比不仅获得了多样性较高的可行解,而且能够较快的收敛到Pareto前沿.     

基于IMOPSO算法的多目标多聚焦图像融合

目前的多聚焦图像融合方法对于融合模型的建立主要依赖于经验,其参数配置存在主观性.提出了一种基于IMOPSO算法的多目标多聚焦图像融合方法,简化了多聚焦图像融合模型,克服了参数配置对经验的依赖性.首先给出了多聚焦图像融合有效的评价指标,然后构造了统一的小波域多聚焦图像融合模型,最后以模型参数作为决策变量,采用IMOPSO算法进行多目标优化搜索.IMOPSO算法不但引入变异算子以避免早熟,而且引入拥挤算子,使Pareto优解尽可能均匀分布于Pareto前端,并采用一种新的自适应惯性权重提高寻优能力.实验结果表明,IMOPSO算法具有更快的收敛速度和更好的寻优能力,同时基于该算法的融合方法也实现了Pareto最优多聚焦图像融合.     

Multiobjective optimization design of Yagi-Uda antenna

An optimization method, such as the steepest gradient methods, could not easily obtain globally optimum solutions for devising antenna design parameters that allow the antenna to simultaneously improve multiple performances such as gain, sidelobe level, and input impedance. The genetic algorithm (GA) is suitable for empirically solving optimization problems and is effective in designing an antenna. In particular, this method can solve the multiobjective optimization problem using various Pareto-optimal solutions in an extremely efficient manner. In this paper, the Pareto GA, by which various Pareto-optimal solutions for each objective function (performance) can be obtained in a single trial of a numerical simulation and which enables the selection of parameters in accordance with the design requirement, is applied to the multiobjective optimization design of the Yagi-Uda antenna. The effectiveness of the Pareto GA was demonstrated by comparing the performances obtained by the Pareto GA with those of the previously reported values, which were obtained by the conventional GA, and with the values of the design benchmark reference.     

基于模糊C均值聚类的锦标赛选择机制与多目标优化研究

本文提出了一种用于多目标优化的进化算法--基于模糊C均值聚类的进化算法（A Fuzzy C-Means Clustering Based Evolutionary Algorithm,FCEA）.在算法的迭代过程中,先利用模糊C均值聚类算法寻找种群的分布结构,通过对每一代种群进行模糊划分,获得每个个体隶属于每一类的隶属度,然后本文设计了一种基于隶属度的锦标赛选择算子,用于从整个种群中选择相似个体进行重组,引导算法进行搜索.实验结果表明,基于隶属度的锦标赛选择算子的应用能够提升算法的性能,与MOEA/D-DE、NSGAⅡ、SPEA2、SMS-EMOA等先进的优化算法进行比较的结果表明,FCEA在求解具有复杂Pareto前沿的多目标优化问题（GLT系列）时具有一定的竞争力.     

Multiobjective programming using uniform design and genetic algorithm

The notion of Pareto-optimality is one of the major approaches to multiobjective programming. While it is desirable to find more Pareto-optimal solutions, it is also desirable to find the ones scattered uniformly over the Pareto frontier in order to provide a variety of compromise solutions to the decision maker. We design a genetic algorithm for this purpose. We compose multiple fitness functions to guide the search, where each fitness function is equal to a weighted sum of the normalized objective functions and we apply an experimental design method called uniform design to select the weights. As a result, the search directions guided by these fitness functions are scattered uniformly toward the Pareto frontier in the objective space. With multiple fitness functions, we design a selection scheme to maintain a good and diverse population. In addition, we apply the uniform design to generate a good initial population and design a new crossover operator for searching the Pareto-optimal solutions. The numerical results demonstrate that the proposed algorithm can find the Pareto-optimal solutions scattered uniformly over the Pareto frontier.     

自适应分解式多目标粒子群优化算法

为了提高多目标粒子群优化算法解的分布性,文中提出了一种自适应分解式多目标粒子群优化算法（Adaptive Multiobjective Particle Swarm Optimization based on Decomposed Archive,AMOPSO-DA）.首先,设计了一种基于优化解空间分布信息的外部档案更新策略,有效提升了AMOPSO-DA的空间搜索能力;其次,提出了一种基于粒子进化方向信息的飞行参数调整方法,有效平衡了AMOPSO-DA的探索和开发能力.最后,将提出的AMOPSO-DA应用于多目标优化问题,实验结果表明,文中提出的AMOPSO-DA能够获得分布性较好的优化解.     

Multiobjective genetic optimization of diagnostic classifiers withimplications for generating receiver operating characteristiccurves

It is well understood that binary classifiers have two implicit objective functions (sensitivity and specificity) describing their performance. Traditional methods of classifier training attempt to combine these two objective functions (or two analogous class performance measures) into one so that conventional scalar optimization techniques can be utilized. This involves incorporating a priori information into the aggregation method so that the resulting performance of the classifier is satisfactory for the task at hand. We have investigated the use of a niched Pareto multiobjective genetic algorithm (GA) for classifier optimization. With niched Pareto GA's, an objective vector is optimized instead of a scalar function, eliminating the need to aggregate classification objective functions. The niched Pareto GA returns a set of optimal solutions that are equivalent in the absence of any information regarding the preferences of the objectives. The a priori knowledge that was used for aggregating the objective functions in conventional classifier training can instead be applied post-optimization to select from one of the series of solutions returned from the multiobjective genetic optimization. We have applied this technique to train a linear classifier and an artificial neural network (ANN), using simulated datasets. The performances of the solutions returned from the multiobjective genetic optimization represent a series of optimal (sensitivity, specificity) pairs, which can be thought of as operating points on a receiver operating characteristic (ROC) curve. All possible ROC curves for a given dataset and classifier are less than or equal to the ROC curve generated by the niched Pareto genetic optimization.     

Designing resilient networks using multicriteria metaheuristics

The paper deals with the design of resilient networks that are fault tolerant against link failures. Usually, fault tolerance is achieved by providing backup paths, which are used in case of an edge failure on a primary path. We consider this task as a multiobjective optimization problem: to provide resilience in networks while minimizing the cost subject to capacity constraint. We propose a stochastic approach, which can generate multiple Pareto solutions in a single run. The feasibility of the proposed method is illustrated by considering several network design problems using a single weighted average of objectives and a direct multiobjective optimization approach using the Pareto dominance concept.     

Pareto-Based Multiobjective Machine Learning: An Overview and Case Studies

Machine learning is inherently a multiobjective task. Traditionally, however, either only one of the objectives is adopted as the cost function or multiple objectives are aggregated to a scalar cost function. This can be mainly attributed to the fact that most conventional learning algorithms can only deal with a scalar cost function. Over the last decade, efforts on solving machine learning problems using the Pareto-based multiobjective optimization methodology have gained increasing impetus, particularly due to the great success of multiobjective optimization using evolutionary algorithms and other population-based stochastic search methods. It has been shown that Pareto-based multiobjective learning approaches are more powerful compared to learning algorithms with a scalar cost function in addressing various topics of machine learning, such as clustering, feature selection, improvement of generalization ability, knowledge extraction, and ensemble generation. One common benefit of the different multiobjective learning approaches is that a deeper insight into the learning problem can be gained by analyzing the Pareto front composed of multiple Pareto-optimal solutions. This paper provides an overview of the existing research on multiobjective machine learning, focusing on supervised learning. In addition, a number of case studies are provided to illustrate the major benefits of the Pareto-based approach to machine learning, e.g., how to identify interpretable models and models that can generalize on unseen data from the obtained Pareto-optimal solutions. Three approaches to Pareto-based multiobjective ensemble generation are compared and discussed in detail. Finally, potentially interesting topics in multiobjective machine learning are suggested.