Improved NSGA-Ⅱ Multi-objective Genetic Algorithm Based on Hybridization-encouraged Mechanism

To improve performances of multi-objective optimization algorithms,such as convergence and diversity,a hybridization-encour-aged mechanism is proposed and realized in elitist nondominated sorting genetic algorithm (NSGA-Ⅱ).This mechanism uses the nor-malized distance to evaluate the difference among genes in a population.Three possible modes of crossover operators-"Max Distance","Min-Max Distance",and "Neighboring-Max"-are suggested and analyzed.The mode of "Neighboring-Max",which not only takes advantage of hybridization but also improves the distribution of the population near Pareto optimal front,is chosen and used in NSGA-II on the basis of hybridization-encouraged mechanism (short for HEM-based NSGA-Ⅱ).To prove the HEM-based algorithm,several problems are studied by using standard NSGA-II and the presented method.Different evaluation criteria are also used to judge these algorithms in terms of distribution of solutions,convergence,diversity,and quality of solutions.The numerical results indicate that the application of hybridization-encouraged mechanism could effectively improve the performances of genetic algorithm.Finally,as an example in engineering practices,the presented method is used to design a longitudinal flight control system,which demonstrates the obtainability of a reasonable and correct Pareto front.     

基于改进多目标布谷鸟搜索算法的翼型气动优化设计

布谷鸟搜索（CS）算法是一种新型的受自然现象启发的元启发式智能优化算法，其强大的全局搜索能力和收敛速度受到了广泛关注。多目标布谷鸟搜索（MOCS）算法是一种在单目标布谷鸟算法基础上发展的可以直接求解Pareto解集的多目标优化算法。针对原始MOCS算法的不足，采用一系列措施以提高算法的收敛精度、收敛速度以及解的均匀性：通过引入非支配排序与拥挤距离来改进解的适应度评估；通过改进随机游走策略来提高局部搜索能力；通过引入改进的自适应丢弃概率策略来提高算法的收敛速度；加入档案管理机制，提高解的均匀性。典型的多目标数值算例结果表明，改进的MOCS算法相较于当前主流的NSGA-Ⅱ算法拥有更快的收敛速度和更高的收敛精度。以RAE2822双目标升阻比优化设计为例，将改进的MOCS算法应用于多目标气动优化中，改进的MOCS算法共获得64个Pareto解，优化后的翼型气动性能有明显的提升，设计者可以根据自己的偏好选取不同的Pareto解。对于气动优化问题，改进的MOCS算法与目前主流的NSGA-Ⅱ相比，收敛速度更快。     

Research of low boom and low drag supersonic aircraft design

Sonic boom reduction will be an issue of utmost importance in future supersonic transport, due to strong regulations on acoustic nuisance. The paper describes a new multi-objective optimization method for supersonic aircraft design. The method is developed by coupling Seebass–George–Darden(SGD) inverse design method and multi-objective genetic algorithm.Based on the method, different codes are developed. Using a computational architecture, a conceptual supersonic aircraft design environment(CSADE) is constructed. The architecture of CSADE includes inner optimization level and out optimization level. The low boom configuration is generated in inner optimization level by matching the target equivalent area distribution and actual equivalent area distribution. And low boom/low drag configuration is generated in outer optimization level by using NSGA-II multi-objective genetic algorithm to optimize the control parameters of SGD method and aircraft shape. Two objective functions, low sonic boom and low wave drag, are considered in CSADE. Physically reasonable Pareto solutions are obtained from the present optimization. Some supersonic aircraft configurations are selected from Pareto front and the optimization results indicate that the swept forward wing configuration has benefits in both sonic boom reduction and wave drag reduction. The results are validated by using computational fluid dynamics(CFD) analysis.     

Pareto基因算法多目标翼型优化设计

 基于 Pareto最优解的定义,通过构造新型的联赛式选择复制等算子而发展了一种适合于求解多目标优化设计的 Pareto基因算法。通过等级法来正确识别每一代中近 Pareto波阵面的解,从而消除选择误差达到快速收敛的目的。为提高解的分布性:采用小生境技术解决了基因材料多样性损失问题;采用常规实数编码方式配合平均交叉算子解决了编码端点效应问题。将所发展的方法应用于多目标翼型优化设计中,获得了理想的 Pareto波阵面,为决策者提供了一个可选的有效解数据库。     

高超声速飞行器后体/尾喷管一体化设计

采用实数编码、小生境技术、稳态复制策略、多目标定级排序技术,改进了标准遗传算法,建立了多目标遗传算法,并将其应用于高超声速飞行器后体/尾喷管的一体化设计,以尾喷管的推力、升力和附加俯仰力矩系数为性能目标,得到了优化问题的Pareto最优前沿面,优化结果显示了设计变量与性能目标之间的关系,并提出了建议的外形方案。该优化算法可进一步推广应用于包含更加精确的流动模型的优化设计当中。     

Interference-free wind tunnel testing of jet propelled missiles

Wind tunnel evaluation of the aerodynamic interaction effects between plume and the external flow past the missile body including the wake boundary (“slipstream”) over powered flight envelopes of rocket propelled vehicles can be greatly facilitated — or even made possible — by a methodology replacing the hot propellant by cold, inert gases. Model nozzle design is based on the second order matching of plume geometry and first order modeling of plume stiffness. Since modeled nozzles will have larger throat radii than the prototypes, one can use sting-supported, sting-fed model installations thus eliminating aerodynamic interference effects due to struts. The concepts of simulated altitude and simulated full-scale Reynolds Number greatly reduce wind tunnel occupancy time. Computer programs, covering all steps of evaluating prototype nozzle performance, model sting nozzle design, model test evaluation and interpretation have been developed. The modeling methodology is supported by experimental results obtained in an induction wind tunnel at the FFA, Bromma, Sweden and in the 16 T and VKF-A altitude tunnels at AEDC, Tullahoma, Tenn.     

考虑低空运行环境求解无人机任务分配问题的研究

在低空救援中如何合理的分配无人机的搜救任务长期以来都是研究的重点。本文在分层级分布式分配方法的基础上建立多目标多无人机任务分配模型,在模型中以搜救费用、无人机使用数量、完成任务的均衡性为目标函数,并且采用改进的NSGA-Ⅱ算法进行求解。结果表明：本文建立的模型有效,能在不同搜救环境下给出合理有效的分配方案;在搜救中考虑以搜救效率最高为导向时,带来无人机成本和数量的增加;当实际搜救的无人机非常有限时,则需要时间成本的投入;以经济利益为导向时,则会导致搜救时间的增加。     

遗传算法在雷达吸波涂层多目标优化设计中的应用

本文利用遗传算法实现了雷达吸波涂层的多目标优化设计.首先对目标函数进行合理设计,同时基于Pareto最优概念,采用非劣分层遗传算法(NSGA)进行多目标优化.对具体实例的优化结果表明,该方法利用共享函数和小生境技术,可以使优化结果均匀的收敛于Pareto域附近.同传统优化方法相比,该方法物理意义明确,对决策者来说更具科学性、针对性和实用价值.     

基于多目标帝国竞争算法的进场排序与调度

为兼顾空管、机场、航司以及民众的不同诉求,提出了基于多目标帝国竞争算法的进场排序与调度方法,达到平衡交通需求与进场管理的目的。首先,借鉴机器调度领域研究成果,梳理与精简进场排序与调度的评价指标,并结合运行约束构建多目标进场排序与调度模型。接着,引入非支配排序,设计多目标帝国竞争算法,给出衡量帕累托解集优劣的评价指标。最后,采用通用数据集与长沙黄花机场实际运行数据实施案例进行仿真与验证。结果表明：提出的多目标帝国竞争算法,相对于带精英策略的非支配排序遗传算法以及多目标模拟退火算法而言,解集更占支配地位、分布更均匀、收敛性更好,求解的效率也更高;提出的算法能有效实现进场排序与调度,即便以标准间隔的1.8倍实施仿真,总延误时间、总飞行时间和最大飞行时间,相对于实际运行分别降低了41.2%、11.4%和8.6%。     

Aircraft maneuverability improvement by direct lift control system application

The handling qualities of an aircraft will be improved if the Direct Lift Control (DLC) system is applied. In this paper, an attempt has been made to evaluate the influence of DLC-type system parameters on the aircraft's maneuverability and to determine the desired values of these parameters for the purpose of obtaining required values of the handling maneuverability criteria. Published papers which deal with direct lift control do not list requirements for evaluating handling qualities and maneuverability of aircraft equipped with DLC system. In this paper, three new criteria permitting the evaluation of results of employing DLC have been defined. Analysis of influence of DLC system parameters on selected known handling qualities criteria (for example CAP, C^*), as well as new DLC efficiency coefficients, have been illustrated with a numeric example of A4D “Skyhawk” fighter aircraft and PZL M-18 “Dromader” agricultural airplane control system modification.     

用INSGA-Ⅱ进化NPCs的复杂行为

目前游戏中NPCs多目标行为进化是一个非常复杂的问题。对此建立了NPCs多目标优化的数学模型,并提出了一种NSGA-Ⅱ的改进算法——INSGA-Ⅱ。该算法在进行精英选择时,采用了基于K-均值聚类的方法联合了不同等级之间的个体进行集合划分,然后从不同的集合中选择下一代个体,从而更好地保持了种群的多样性。通过实例比较证明,在玩家和NPCs作战的游戏场景下,INSGA-Ⅱ能够得到NPCs复杂多目标控制问题的Pareto最优解,而且比NSGA-Ⅱ表现出更好的收敛性和多样性。     

飞机地面压力加油系统的优化性能分析

针对传统遗传算法和退火单纯形法 ,提出了一种基于邻域函数的尺度参数自寻优和多操作的基于概率接受思想的变异操作及竞争生存的种群数量控制策略的高级遗传退火算法。基于飞机地面压力加油系统节流孔优化配置的数值仿真研究验证了本文的算法对高维复杂函数最优化的高效性 ,其性能明显优于传统遗传算法、退火单纯形法 ,极大提高了加油管路节流孔优化配置的效率。     

基于Nash-Pareto策略的两种改进算法及其应用

针对多目标、多设计变量的优化问题,提出了两种优化的新算法:一种是将多目标问题转化为单目标时,对目标权重的确定提出了新的途径;另一种是直接对多目标问题进行优化,并对Pareto遗传优化技术作了改进,以得到均匀分布的Pareto最优解集.两种新算法都是建立在Nash的系统分解与Pareto遗传算法的基础上,因此称这类算法为Nash-Pareto策略.借助于这类算法,文中以跨声速压气机双圆弧类叶型的气动优化为例,给出了气动优化的全过程.数值优化的实验表明所给出的改进算法是可行的、有效的.     

基于粒子群和人工蜂群混合算法的气动优化设计

现代启发式智能算法存在全局与局部搜索能力的平衡问题,针对此问题,采用双种群进化策略和信息交流机制,提出一种基于粒子群算法和人工蜂群算法相结合的新型混合优化算法——MABCPSO,并分别进行函数测试和翼型的气动优化设计验证。结果表明:MABCPSO新型混合优化算法具有更好的寻优能力,相比粒子群算法和人工蜂群算法,该算法能以更少的进化代数分别提高1.7%和2.2%的减阻效果。     

自适应差分进化算法在气动优化设计中的应用

以实数编码的差分进化（DE）算法为基础,引入种群熵估计方法分析种群个体的分散程度,自适应地调整设计变量的搜索范围。采用Navier-Stokes方程作为主控方程计算翼型气动性能,分别采用标准遗传算法（SGA）、基本DE算法和自适应差分进化（ARDE）算法作为气动性能优化算法进行了针对翼型的气动优化设计。函数测试实例表明,ARDE算法具有更好的收敛稳定性和收敛速度。并针对翼型气动优化问题的特点,分析了参数设置对ARDE算法优化结果的影响。实验结果对比表明,ARDE算法得到了更好的优化结果。     

Topology optimization of support structure of telescope skin based on bit-matrix representation NSGA-II

Non-dominated sorting genetic algorithm II（NSGA-II）with multiple constraints handling is employed for multi-objective optimization of the topological structure of telescope skin,in which a bit-matrix is used as the representation of a chromosome,and genetic algorithm（GA）operators are introduced based on the matrix.Objectives including mass,in-plane performance,and out-of-plane load-bearing ability of the individuals are obtained by fnite element analysis（FEA）using ANSYS,and the matrix-based optimization algorithm is realized in MATLAB by handling multiple constraints such as structural connectivity and in-plane strain requirements.Feasible confgurations of the support structure are achieved.The results confrm that the matrix-based NSGA-II with multiple constraints handling provides an effective method for two-dimensional multi-objective topology optimization.     

基于NSGA-Ⅱ复杂系统航空备件需求研究与应用

目前航空公司对航空备件的需求计算主要针对单个备件进行,这产生一定的误差.因此,本文利用NSGA-Ⅱ多目标遗传优化算法来解决在一定成本约束条件下可用度、可靠度等性能指标均能得到满足.为了便于算法的应用,论文对罚函数进行了改进并进行实例分析.结果表明本方法适于处理航空公司复杂的备件需求决策,并起到一定的作用.     

基于 Kriging模型机翼平面外形气动优化设计

使用基于Kriging模型的优化设计方法,进行了非常规布局机翼的平面外形多目标优化设计。利用CFD技术进行机翼升力系数和阻力系数的气动计算,通过拉丁超立方试验设计生成样本点,建立了Kriging代理模型,结合多目标遗传算法对机翼平面外形进行多点多目标优化设计,最终得到了Pareto最优解集。根据设计需求,从Pa-ret0前沿选取一个非劣解作为优化结果。结果表明：陆ging模型与cFD计算误差很小,可信度高;在不问设计状态下,机翼气动性能都得到了提高,表明优化设计方法具有可行性和高效性。     

Aerodynamic multi-objective integrated optimization based on principal component analysis

Based on improved multi-objective particle swarm optimization (MOPSO) algorithm with principal component analysis (PCA) methodology,an efficient high-dimension multiobjective optimization method is proposed,which,as the purpose of this paper,aims to improve the convergence of Pareto front in multi-objective optimization design.The mathematical efficiency,the physical reasonableness and the reliability in dealing with redundant objectives of PCA are verified by typical DTLZ5 test function and multi-objective correlation analysis of supercritical airfoil,and the proposed method is integrated into aircraft multi-disciplinary design (AMDEsign) platform,which contains aerodynamics,stealth and structure weight analysis and optimization module.Then the proposed method is used for the multi-point integrated aerodynamic optimization of a wide-body passenger aircraft,in which the redundant objectives identified by PCA are transformed to optimization constraints,and several design methods are compared.The design results illustrate that the strategy used in this paper is sufficient and multi-point design requirements of the passenger aircraft are reached.The visualization level of non-dominant Pareto set is improved by effectively reducing the dimension without losing the primary feature of the problem.     

考虑性能及成本的固体火箭发动机多学科设计优化

为综合考虑固体火箭发动机的燃烧室、药柱、内弹道、喷管及成本等学科影响,梳理学科间耦合关系,并建立了以总冲最大、成本最小为优化目标的固体火箭发动机多学科设计优化（MDO）模型。为降低MDO问题的计算成本,提出一种基于Kriging代理模型的多目标自适应优化方法（KRG-MAOM）。优化过程中,分别对目标与约束构建Kriging模型,并采用多目标优化算法求解,在伪Pareto解中综合考虑支配关系与分布特性选取新增样本点,引导优化快速收敛。算例结果表明,KRG-MAOM算法在全局收敛性与优化效率方面具有显著优势。最后,采用KRG-MAOM算法求解该MDO问题,得到可行的Pareto解集方案,与初始方案相比,同性能情况下成本节省约3.36%;同成本情况下性能提升约10.93%,从而验证MDO模型合理性与KRG-MAOM算法有效性。