多目标量子编码遗传算法

如何使算法快速收敛到真正的Pareto前沿,并保持解集在前沿分布的均匀性是多目标优化算法重点研究解决的问题。该文提出一种基于量子遗传算法的多目标优化算法,利用量子遗传算法的高效全局搜索能力,在整个解空间内快速搜索多目标函数的Pareto最优解,利用量子遗传算法维持解集多样性的特点,使搜索到的Pareto最优解在前沿均匀分布。通过求解带约束的多目标函数优化问题,对该文算法的多目标优化性能进行了考察,并与NSGAII,PAES,MOPSO和Ray-Tai-Seows算法等知名多目标优化算法进行比较,结果证明了该文算法的有效性和先进性。     

利用冲突信息降维的进化高维目标优化算法

进化多目标优化算法求解高维目标优化问题面临收敛能力、计算复杂度、决策以及Pareto前沿的可视化等困难，其根本原因是目标空间维数高。目标降维通过丢弃冗余目标，为缓解高维目标优化求解困难提供一种新思路。本文提出利用冲突信息降维的分解进化高维目标优化算法（CIOR-MOEA/D）。该方法通过衡量目标在近似解集上体现的冲突性，构造问题的冲突信息矩阵，对该矩阵进行特征分析，确定目标的重要性程度，实现维数约简，并利用分解进化多目标优化算法（MOEA/D）对重要子目标集合进行分解进化,从而得到问题的近似解集。实验结果表明,本文提出的目标降维算法在降维的准确性与鲁棒性上均表现突出，能够有效地处理冗余高维目标优化问题。      

一种非均匀分布问题分布性维护方法

 几乎所有多目标进化算法(multi-objective optimization evolutionary algorithm,MOEA)都是针对Pareto最优面为均匀分布问题而言.然而现实中很多问题Pareto最优面是非均匀分布的,决策者希望得到一个与Pareto最优面分布类似的解集.现存算法并不能有效解决该问题.对此,提出一种针对于非均匀分布多目标优化问题的维护方法(non-uniformly diversity maintenance method,NUDMM).该方法定义一个反映个体分布"规则"程度的指标——杂乱度,并设计一种降低种群杂乱度的方法,在未知Pareto最优面分布规律情况下有效剔除造成种群混乱的个体.通过与NSGA-II和SPEA2在不同维数下8个非均匀函数上对比实验,表明NUDMM在有效保持问题真实分布的同时,具有良好的收敛性.     

Geometrical Design of Plate-Fin Heat Sinks Using Hybridization of MOEA and RSM

The work in this paper is aimed at demonstrating the practical multiobjective optimization of plate-fin heat sinks and the superiority of using a combined response surface method and multiobjective evolutionary optimizer over solely using the evolutionary optimizer. The design problem assigned is to minimize a heat sink junction temperature and fan pumping power. Design variables determine a heat sink geometry and inlet air velocity. Design constraints are given in such a way that the maximum and minimum fin heights are properly limited. Function evaluation is carried out by using finite volume analysis software. Two multiobjective evolutionary optimization strategies, real-code strength Pareto evolutionary algorithm with and without the use of a response surface technique, are implemented to explore the Pareto optimal front. The optimum results obtained from both design approaches are compared and discussed. It is illustrated that the multiobjective evolutionary technique is a powerful tool for the multiobjective design of electronic air-cooled heat sinks. With the same design conditions and an equal number of function evaluations, the multiobjective optimizer in association with the response surface technique totally outperforms the other. The design parameters affecting the diversity of the Pareto front include fin thickness, fin height distribution, and inlet air velocity while the plate base thickness and the total number of fins of the non-dominated solutions tend to approach certain values.     

Connectivity constrained wireless sensor deployment using multiobjective evolutionary algorithms and fuzzy decision making

Deployment of sensor nodes is an important issue in designing sensor networks. The sensor nodes communicate with each other to transmit their data to a high energy communication node which acts as an interface between data processing unit and sensor nodes. Optimization of sensor node locations is essential to provide communication for a longer duration. An energy efficient sensor deployment based on multiobjective particle swarm optimization algorithm is proposed here and compared with that of non-dominated sorting genetic algorithm. During the process of optimization, sensor nodes move to form a fully connected network. The two objectives i.e. coverage and lifetime are taken into consideration. The optimization process results in a set of network layouts. A comparative study of the performance of the two algorithms is carried out using three performance metrics. The sensitivity analysis of different parameters is also carried out which shows that the multiobjective particle swarm optimization algorithm is a better candidate for solving the multiobjective problem of deploying the sensors. A fuzzy logic based strategy is also used to select the best compromised solution on the Pareto front.     

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Pareto多目标优化的光纤Bragg光栅传感网络的波长分配

针对现有波分复用(WDM)的光纤Bragg光栅(FBG) 传感网络的复用瓶颈,运用Pareto多 目标优化理论,建立了基于带宽重叠技术的FBG传感网络优化模型。通过非支配排序遗传算 法Ⅱ(NSGA-Ⅱ)进化算法求解Pareto 最优曲线,为网络中的每个FBG传感器合理地分配Bragg波长的工作范围,以最小的光谱重叠 程度换取 光源带宽资源的最大节约。仿真和实验结果表明,得到Pareto最优曲线为不同程度的光 谱重叠找到了最优的Bragg波长配置方案,有效地提高了FBG传感网络的WDM能力。     

基于分解的多目标进化算法的异构无线网络业务接入控制

异构无线网络接入控制问题包含多个优化目标,现有算法考虑不全面且多是将其转换为单目标求解,限制了各目标的相对关系,无法适应不同的实际需求。该文提出一种直接采用多目标进化算法的接入控制算法。首先将优化目标扩展为3个,分别是最小化阻塞率、最小化占用总资源和负载均衡;其次引入基于分解的多目标进化算法(MOEA/D)并设计进化策略,进行初步寻优;最后通过非支配排序得到Pareto最优解集,即最佳接入方案。仿真结果表明,所提算法可以提高各优化目标的求解精度,从而提高业务接入成功率和网络资源利用率,并且为决策者提供多种接入方案,可根据实际需求进行最优选择。     

Elitist nondominated sorting genetic algorithm based RF IC optimizer

An optimization tool for radio frequency integrated circuits (RFICs) based on an elitist nondominated sorting genetic algorithm is introduced. It casts RF circuit synthesis as a multi-objective optimization problem and produces multiple solutions along the Pareto optimal front. Optimization is followed by sensitivity assessment wherein Monte Carlo simulations are performed for the Pareto points with respect to process, voltage, and temperature variations. The tool is validated in the synthesis of a 5.2-GHz direct-conversion receiver front-end that includes a common-gate differential low-noise amplifier, I/Q down-conversion mixers, and a quadrature voltage-controlled oscillator in a 250-nm SiGe BiCMOS process.     

高维多目标优化问题融入决策者偏好的集合进化优化方法

高维多目标优化问题普遍存在且非常重要,但是,已有的解决方法却很少.本文提出一种有效解决该问题的融入决策者偏好的集合进化优化方法,该方法首先基于决策者给出的每个目标的偏好区域,将原优化问题的目标函数转化为期望函数;然后,以原优化问题的多个解形成的集合为新的决策变量,以超体积和决策者期望满足度为新的目标函数,将优化问题转化为2目标优化问题;最后,采用多目标集合进化优化方法求解,得到满足决策者偏好且收敛性和分布性均衡的Pareto优化解集.将所提方法应用于4个基准高维多目标优化问题,并与其他2种方法比较,实验结果验证了所提方法的优越性.     

基于可分解的多目标进化算法的PDN阻抗的优化

频率的电源分配网络设计是一个多目标优化问题。应用多目标进化算法优化电源分配网络的阻抗,其中去耦电容的个数和种类成为了PDN中两个需要优化的目标函数,这使得PDN中的输入阻抗,在截止频率内小于目标阻抗以达到设计要求。为解决这个问题,应用可分解的多目标进化算法,同时优化这两个目标,以获得期望的Pareto Front(PF)。实验证明,该设计方法易于实现,且效果良好、稳定性强。优化的PDN的输入阻抗满足设计要求并且优化的去耦电容的个数和种类逼近PF。     

基于权值向量的偏好多目标优化方法

偏好多目标优化方法是多目标优化领域的一个重要分支,其主要目的是仅搜索Pareto前沿面上部分区域内决策者感兴趣的解.基于MOEA/D算法根据预先设定的均匀分布的权值向量搜索Pareto最优前沿面的思想,本文提出了一种基于权值向量的偏好多目标优化方法,该方法通过引入具有偏好信息的权值向量,使算法仅搜索偏好点附近的解.仿真实验结果表明,与现有偏好多目标优化算法相比,本文方法具有支持多偏好点、偏好区域大小可控、偏好点位置无特别要求及偏好解具有更好收敛性的优势.     

用多目标进化算法搜索MOPs的鲁棒Pareto最优解

 搜索鲁棒Pareto最优解是多目标进化算法(MOEA)研究的一个重要方面.目前,优化"原目标函数"的传统MOEA与基于"有效目标函数"的MOEA (Eff-MOEA)在搜索鲁棒Pareto最优解时都易丢失某些性质的解.为解决这一缺陷,本文定义了一种新的鲁棒Pareto最优解,提出了一种新的搜索鲁棒Pareto最优解的MOEA(MOEA/R),MOEA/R将多目标鲁棒优化问题(MROP)转化成两目标问题来优化,一个目标为解的质量,另一个目标为解的鲁棒性,每一目标均对应一子优化问题.通过与NSGA-Ⅱ及Eff-MOEA的对比分析,结果表明MOEA/R的结果较好,更重要的是本文探索了一种新的搜索鲁棒Pareto最优解的思想.     

多目标混沌进化算法

设计了多目标混沌进化算法(MCEA),在每一代遗传操作和外部档案调整完成之后,该算法从外部档案中随机选择部分个体,对这些个体的拷贝进行混沌搜索,以产生更多非劣解.将强度Pareto进化算法(SPEA)和SPEA2分别与基于Logistic映射的混沌搜索结合而产生的MCEAs应用于一些复杂多目标优化问题,计算结果表明,混沌的加入,明显改善了多目标进化算法(MOEA)各方面的性能.     

Analog circuit synthesis performing fast Pareto frontier exploration and analysis through 3D graphs

This paper presents a technique for performing analog design synthesis at circuit level providing feedback to the designer through the exploration of the Pareto frontier. A modified simulated annealing which is able to perform crossover with past anchor points when a local minimum is found which is used as the optimization algorithm on the initial synthesis procedure. After all specifications are met, the algorithm searches for the extreme points of the Pareto frontier in order to obtain a non-exhaustive exploration of the Pareto front. Finally, multi-objective particle swarm optimization is used to spread the results and to find a more accurate frontier. Piecewise linear functions are used as single-objective cost functions to produce a smooth and equal convergence of all measurements to the desired specifications during the composition of the aggregate objective function. To verify the presented technique two circuits were designed, which are: a Miller amplifier with 96 dB Voltage gain, 15.48 MHz unity gain frequency, slew rate of 19.2 V/μs with a current supply of 385.15 μA, and a complementary folded cascode with 104.25 dB Voltage gain, 18.15 MHz of unity gain frequency and a slew rate of 13.370 MV/μs. These circuits were synthesized using a 0.35 μm technology. The results show that the method provides a fast approach for good solutions using the modified SA and further good Pareto front exploration through its connection to the particle swarm optimization algorithm.     

Multi‐objective optimization for channel allocation in mobile computing using NSGA‐II

Efficient channel allocation to mobile hosts aims to minimize the number of blocked hosts and is of utmost importance in a mobile computing network. Also, to achieve highly reliable data transmission, wireless mobile networks require efficient and reliable link connectivity regardless of terminal mobility, and thus reliable traffic performance. A mobile network consists of mobile nodes, base stations, links, etc. that are often prone to failure. The multi‐objective optimization problem (MOP), does not offer one best solution with respect to all the objectives. The aim is to determine the trade‐off surface, which is a set of non‐dominated solution points known as Pareto‐optimal. The two objectives addressed in this paper are to minimize the number of blocked hosts while maximizing the reliability of the data transmission. A multi‐objective optimization is carried out to optimize both objectives simultaneously. The elitist NSGA‐II (non‐dominated sorting genetic algorithm) has been used as an evolutionary optimization technique to solve this problem. A population of efficient solutions results when the termination condition is satisfied. Also the Pareto‐optimal fronts obtained provide a wide range of trade‐off operating conditions from which an appropriate operating point may be selected by the decision maker. The experimental results are presented and analyzed for overall evaluation of the performance of the proposed work. Further, comparison of the results with the two recent earlier models reveals that the proposed work performs better in serving mobile hosts as it caters to two objectives simultaneously. Copyright © 2010 John Wiley & Sons, Ltd.     

多目标混合蛙跳算法中改进的种群分割方法

种群分割方法是混合蛙跳算法最重要的组成部分之一,直接影响算法的性能。针对多目标混合蛙跳算法,提出一种新的种群分割方法。该方法将代表潜在最优区域的非支配个体集合通过聚类的方式划分族群,目的是使不同族群在不同区域进行局部搜索,避免算法早熟。被支配个体则根据其与非支配个体集合的近似度分配到族群中,并通过随机加入其他族群个体的方式提高本族群的多样性。实验结果表明,本文的方法在提高多目标混合蛙跳算法的收敛性和收敛速度方面都具有优势,而且对于目标个数较多的优化问题（最多10个目标）仍能获得令人满意的结果。      

Comparison of QMC-based yield-aware pareto front techniques for multi-objective robust analog synthesis

This paper focuses on the implementation of different techniques for the integration of yield estimation in the synthesis loop of analog integrated circuits (ICs). MOEA/D (Multi-Objective Evolutionary Algorithm with Decomposition) is considered to be a very powerful multi-objective optimization algorithm. For the consideration of yield, several techniques are discussed and three different yield-aware Pareto front (PF) generation techniques have been implemented on the MOEA/D optimizer. The implemented yield-aware PF techniques are compared by designing a fully-differential folded-cascode amplifier with different number of objectives. In order to embed the variation effects into the optimization loop, the statistical analysis of the circuit has been carried out by using a Quasi Monte Carlo (QMC) technique. The results suggest that especially two of these techniques look promising for high dimensional robust optimization of analog circuits.     

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.