一种基于合作型协同和ε-占优的多目标微粒群算法

在求解多目标优化问题时,微粒群优化算法有容易陷于局部极值、函数评价次数多和受到维数限制等不足之处.提出了一种基于合作型协同和ε-占优的多目标微粒群算法(cooperative coevolutionary and ε-dominancebased multi-objective particle swarm optimizer,简称CEPSO).依据决策变量分解问题,采用多个子群分别优化各个子问题,并在更新粒子位置时采用均匀分布变异算子防止微粒群早熟收敛;在保存非劣解时,使用<     

MaOEA/d2:一种基于双距离构造的高维多目标进化算法

传统的基于Pareto支配关系的多目标进化算法(MOEA)难以有效求解高维多目标优化问题(MaOP). 提出一种利用PBI效用函数的双距离构造的支配关系, 且无需引入额外的参数. 其次, 利用双距离定义了一种多样性保持方法, 该方法不仅考虑了解个体的双距离, 而且还可以根据优化问题的目标数目自适应地调整多样性占比, 以较好地平衡高维目标解群的收敛性和多样性. 最后, 将基于双距离构造的支配关系和多样性保持方法嵌入到NSGA-II算法框架中, 设计了一种基于双距离的高维多目标进化算法MaOEA/d². 该算法与其他5种代表性的高维多目标进化算法一同在5-、10-、15-和20-目标的DTLZ和WFG基准测试问题上进行了IGD和HV性能测试, 结果表明, MaOEA/d²算法具有较好的收敛性和多样性. 由此表明, MaOEA/d²算法是一种颇具前景的高维多目标进化算法.     

基于全局排序的高维多目标优化研究

目标数超过4的高维多目标优化是目前进化多目标优化领域求解难度最大的问题之一,现有的多目标进化算法求解该类问题时,存在收敛性和解集分布性上的缺陷,难以满足实际工程优化需求.提出一种基于全局排序的高维多目标进化算法GR-MODE,首先,采用一种新的全局排序策略增强选择压力,无需用户偏好及目标主次信息,且避免宽松Pareto支配在排序结果合理性与可信性上的损失;其次,采用Harmonic平均拥挤距离对个体进行全局密度估计,提高现有局部密度估计方法的精确性;最后,针对高维多目标复杂空间搜索需求,设计新的精英选择策略及适应度值评价函数.将该算法与国内外现有的5种高性能多目标进化算法在标准测试函数集DTLZ{1,2, 4,5}上进行对比实验,结果表明,该算法具有明显的性能优势,大幅提升了4~30维高维多目标优化的收敛性和分布性.     

采用放松支配关系的高维多目标微分进化算法

为了提高进化算法在求解高维多目标优化问题时的收敛性和多样性,提出了采用放松支配关系的高维多目标微分进化算法。该算法采用放松的Pareto支配关系,以增加个体的选择压力;采用群体和外部存储器协同进化的方案,并通过混合微分变异算子,生成子代群体;采用基于指标的方法计算个体的适应度并对群体进行更新;采用基于Lp范数（0相似文献   

基于邻域竞赛的多目标优化算法

传统多目标优化算法（Multi-objective evolution algorithms,MOEAs）的基本框架大致分为两部分:首先是收敛性保持,采用Pareto支配方法将种群分成若干非支配层;其次是分布性保持,在临界层中,采用分布性保持机制维持种群的分布性.然而在处理高维优化问题（Many-objective optimization problems,MOPs）（目标维数大于3）时,随着目标维数的增加,种群的收敛性和分布性的冲突加剧,Pareto支配关系比较个体优劣的能力也迅速下降,此时传统的MOEA已不再适用于高维优化问题.鉴于此,本文提出了一种基于邻域竞赛的多目标优化算法（Evolutionary algorithm based on neighborhood competition for multi-objective optimization,NCEA）.NCEA首先将个体的各个目标之和作为个体的收敛性估计;然后,计算当前个体向量与收敛性最好的个体向量之间的夹角,并将其作为当前个体的邻域估计;最后,通过邻域竞赛方法将问题划分为若干个相互关联的子问题并逐步优化.为了验证NCEA的有效性,本文选取5个优秀的算法与NCEA进行对比实验.通过对比实验验证,NCEA具有较强的竞争力,能同时保持良好的收敛性和分布性.     

一种基于分解和协同的高维多目标进化算法

现实中高维多目标优化问题普遍存在，而且其巨大的目标空间使得经典的多目标进化算法面临严峻挑战，提出一种基于分解和协同策略的高维多目标进化算法MaOEA/DCE.该算法利用混合水平正交实验设计方法产生接近于指定规模且均匀分布于聚合系数空间的权重向量，提高种群的分布性；其次，算法将差分进化算子和自适应SBX算子进行协同进化以产生高质量的子代个体，改善算法的收敛性.该算法与另外五种高性能的多目标进化算法在基准测试函数集DTLZ{1，2，4，5}上进行IGD⁺性能指标实验，结果表明MaOEA/DCE在收敛性、多样性和稳定性方面总体具有显著的性能优势.     

基于双极偏好占优的高维目标进化算法

高维目标优化是目前多目标优化领域的研究热点和难点.提出一种占优机制,即双极偏好占优用于处理高维目标优化问题.该占优机制同时考虑决策者的正偏好和负偏好信息,在非支配解之间建立了更加严格的占优关系,能够有效减少种群中非支配解的比例,引导算法向靠近正偏好同时远离负偏好的Pareto最优区域收敛.为检验该方法的有效性,将双极偏好占优融入NSGA-Ⅱ中,形成算法2p-NSGA-Ⅱ,并在2到15目标标准测试函数上进行测试,得到了良好的实验结果.同时,将所提出的占优机制与目前该领域的两种占优机制g占优和r占优进行性能对比,实验结果表明,2p-NSGA-Ⅱ算法无论是在求解精度还是运行效率上,整体上均优于g-NSGA-Ⅱ和r-NSGA-Ⅱ.     

进化信息引导的烟花差分混合多目标算法

烟花算法是一种有效启发式群智能算法,但基本的烟花算法只能解决单目标问题,个体间缺乏信息交流,进化过程中有用信息没有得到充分利用。为提高烟花算法的综合性能,并使其能够应用在多目标优化问题(multi-objective optimization problems,MOPs)上,提出一种基于粒子进化信息引导的自适应多目标烟花差分混合进化算法(multi-objective hybrid optimization algorithm of fireworks and differential guided by evolutioninformation,MOHFWDE)。利用Pareto前沿个体的进化信息引导种群进化,加快算法收敛速度;在烟花算法中引入差分算法的变异算子、交叉算子替换原有高斯变异算子,增强个体间的信息交流。与其他算法进行对比仿真实验,结果表明MOHFWDE具有良好的收敛性、分布性和逼近性。     

一种基于自适应模糊支配的高维多目标粒子群算法

高维多目标优化问题由于具有巨大的目标空间使得一些经典的多目标优化算法面临挑战.提出一种基于自适应模糊支配的高维多目标粒子群算法MAPSOAF,该算法定义了一种自适应的模糊支配关系,通过对模糊支配的阈值自适应变化若干步长,在加强个体间支配能力的同时实现对种群选择压力的精细化控制,以改善算法的收敛性;其次,通过从外部档案集中选取扰动粒子,并在粒子速度更新公式中新增一扰动项以克服粒子群早熟收敛并改善个体分布的均匀性;另外,算法利用简化的Harmonic归一化距离评估个体的密度,在改善种群分布性的同时降低算法的计算代价.该算法与另外五种高性能的多目标进化算法在标准测试函数集DTLZ{1,2,4,5}上进行对比实验,结果表明该算法在收敛性和多样性方面总体上具有较显著的性能优势.     

基于改进K 支配排序的高维多目标进化算法

为提高4目标以上高维多目标优化问题的求解性能,提出一种基于改进K支配排序的高维多目标进化算法(KS-MODE).该算法针对K支配的支配关系和排序方法进行改进,避免循环支配并增强选择压力;设计新的全局密度估计方法提高局部密度估计精确性;设计新的精英选择策略和适应度值评价函数;采用CAO局部搜索算子加速收敛.在4～30个目标标准测试函数上的实验结果表明,KS-MODE能够在保证解集分布性的同时大幅提升收敛性和稳定性,能够有效求解高维多目标优化问题.     

Formulation and parameter selection of multi-objective deterministic particle swarm for simulation-based optimization

Global derivative-free deterministic algorithms are particularly suitable for simulation-based optimization, where often the existence of multiple local optima cannot be excluded a priori, the derivatives of the objective functions are not available, and the evaluation of the objectives is computationally expensive, thus a statistical analysis of the optimization outcomes is not practicable. Among these algorithms, particle swarm optimization (PSO) is advantageous for the ease of implementation and the capability of providing good approximate solutions to the optimization problem at a reasonable computational cost. PSO has been introduced for single-objective problems and several extension to multi-objective optimization are available in the literature. The objective of the present work is the systematic assessment and selection of the most promising formulation and setup parameters of multi-objective deterministic particle swarm optimization (MODPSO) for simulation-based problems. A comparative study of six formulations (varying the definition of cognitive and social attractors) and three setting parameters (number of particles, initialization method, and coefficient set) is performed using 66 analytical test problems. The number of objective functions range from two to three and the number of variables from two to eight, as often encountered in simulation-based engineering problems. The desired Pareto fronts are convex, concave, continuous, and discontinuous. A full-factorial combination of formulations and parameters is investigated, leading to more than 60,000 optimization runs, and assessed by three performance metrics. The most promising MODPSO formulation/parameter is identified and applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions. Its performance is finally compared with four stochastic algorithms, namely three versions of multi-objective PSO and the genetic algorithm NSGA-II.     

Real-time dynamic optimization of batch systems

In this paper a methodology for designing and implementing a real-time optimizing controller for batch processes is proposed. The controller is used to optimize a user-defined cost function subject to a parameterization of the input trajectories, a nominal model of the process and general state and input constraints. An interior point method with penalty function is used to incorporate constraints into a modified cost functional, and a Lyapunov based extremum seeking approach is used to compute the trajectory parameters. The technique is applicable to general nonlinear systems. A precise statement of the numerical implementation of the optimization routine is provided. It is shown how one can take into account the effect of sampling and discretization of the parameter update law in practical situations. A simulation example demonstrates the applicability of the technique.     

Multiobjective optimization of trusses using genetic algorithms

In this paper we propose the use of the genetic algorithm (GA) as a tool to solve multiobjective optimization problems in structures. Using the concept of min–max optimum, a new GA-based multiobjective optimization technique is proposed and two truss design problems are solved using it. The results produced by this new approach are compared to those produced by other mathematical programming techniques and GA-based approaches, proving that this technique generates better trade-offs and that the genetic algorithm can be used as a reliable numerical optimization tool.     

An integrated approach to topology,sizing, and shape optimization

Topology optimization has become very popular in industrial applications, and most FEM codes have implemented certain capabilities of topology optimization. However, most codes do not allow simultaneous treatment of sizing and shape optimization during the topology optimization phase. This poses a limitation on the design space and therefore prevents finding possible better designs since the interaction of sizing and shape variables with topology modification is excluded. In this paper, an integrated approach is developed to provide the user with the freedom of combining sizing, shape, and topology optimization in a single process.     

Effects of dominant wolves in grey wolf optimization algorithm

Bio-inspired computation is one of the emerging soft computing techniques of the past decade. Although they do not guarantee optimality, the underlying reasons that make such algorithms become popular are indeed simplicity in implementation and being open to various improvements. Grey Wolf Optimizer (GWO), which derives inspiration from the hierarchical order and hunting behaviours of grey wolves in nature, is one of the new generation bio-inspired metaheuristics. GWO is first introduced to solve global optimization and mechanical design problems. Next, it has been applied to a variety of problems. As reported in numerous publications, GWO is shown to be a promising algorithm, however, the effects of characteristic mechanisms of GWO on solution quality has not been sufficiently discussed in the related literature. Accordingly, the present study analyses the effects of dominant wolves, which clearly have crucial effects on search capability of GWO and introduces new extensions, which are based on the variations of dominant wolves. In the first extension, three dominant wolves in GWO are evaluated first. Thus, an implicit local search without an additional computational cost is conducted at the beginning of each iteration. Only after repositioning of wolf council of higher-ranks, the rest of the pack is allowed to reposition. Secondarily, dominant wolves are exposed to learning curves so that the hierarchy amongst the leading wolves is established throughout generations. In the final modification, the procedures of the previous extensions are adopted simultaneously. The performances of all developed algorithms are tested on both constrained and unconstrained optimization problems including combinatorial problems such as uncapacitated facility location problem and 0-1 knapsack problem, which have numerous possible real-life applications. The proposed modifications are compared to the standard GWO, some other metaheuristic algorithms taken from the literature and Particle Swarm Optimization, which can be considered as a fundamental algorithm commonly employed in comparative studies. Finally, proposed algorithms are implemented on real-life cases of which the data are taken from the related publications. Statistically verified results point out significant improvements achieved by proposed modifications. In this regard, the results of the present study demonstrate that the dominant wolves have crucial effects on the performance of GWO.     

多元插值全局优化算法及其应用

本文介绍一种多元插值逼近和动态搜索轨迹相结合的全局优化算法.该算法大大减少了目标函数计算次数,寻优收敛速度快,算法稳定,且可获得全局极小,有效地解决了大规模非线性复杂动态系统的参数优化问题.一个具有8个控制参数的电力系统优化控制问题,采用该算法仅访问目标函数78次,便可求得最优控制器参数。     

云搜索优化算法

本文将云的生成、动态运动、降雨和再生成等自然现象与智能优化算法的思想融合,建立了一种新的智能优化算法-云搜索优化算法(CSO)。生成与移动的云可以弥漫于整个搜索空间,这使得新算法具有较强的全局搜索能力;收缩与扩张的云团在形态上会有千奇百态的变化,这使得算法具有较强的局部搜索能力;降雨后产生新的云团可以保持云团的多样性,这也是使搜索避免陷入局优的有效手段。实验表明,基于这三点建立的新算法具有优异的性能,benchmark函数最优值的计算结果以及与已有智能优化算法的比较展现了新算法精确的、稳定的全局求解能力。     

Value Creation in a Network: The Role of Pricing and Revenue Optimization and Enterprise Profit OptimizationTM

The Internet has created a virtual upheaval in the structural features of the supply and demand chains for most businesses. New agents and marketplaces have surfaced. The potential to create value and enhance profitable opportunities has attracted both buyers and sellers to the Internet. Yet, the Internet has proven to be more complex than originally thought. With information comes complexity: the more the information in real time, the greater the difficulty in interpretation and absorption. How can the value-creating potential of the Internet still be realized, its complexity notwithstanding? This paper argues that with the emergence of innovative tools, the expectations of the Internet as a medium for enhanced profit opportunities can still be realized. Creating value on a continuing basis is central to sustaining profitable opportunities. This paper provides an overview of the value creation process in electronic networks, the emergence of the Internet as a viable business communication and collaboration medium, the proclamation by many that the future of the Internet resides in “embedded intelligence”, and the perspectives of pragmatists who point out the other facet of the Internet—its complexity. The paper then reviews some recent new tools that have emerged to address this complexity. In particular, the promise of Pricing and Revenue Optimization (PRO) and Enterprise Profit Optimization^TM (EPO) tools is discussed. The paper suggests that as buyers and sellers adopt EPO, the market will see the emergence of a truly intelligent network—a virtual network—of private and semi-public profitable communities.     

粒子群算法在组合优化问题上的研究与发展

粒子群优化算法是一种新兴的基于群智能搜索的优化技术。该算法简单、易实现、参数少,具有较强的全局优化能力,可有效应用于科学与工程实践中。介绍了算法的基本原理和算法在组合优化上一些改进方法的主要应用形式。最后,对粒子群算法作了一些深入分析并在此基础上对粒子群算法应用于组合优化问题做了一些总结。     

SEO技术研究

为了利用搜索引擎优化SEO（Search Engine Optimization）技术给网站带来高质量的流量并将其转化为商业利益,理解搜索引擎的算法和排名原理十分必要。通过对网站的结构优化、关键词优化、单页优化、防止被搜索引擎惩罚和挽救被惩罚网站等技术的研究,达到提高网站排名,实现网站的价值目的。