具有脉冲毒素输入的生态毒理动力学的函数优化方法

为了解决某些函数优化问题,基于具有脉冲毒素输入的生态毒理动力学模型提出了可全局收敛的函数优化算法。在该算法中,令环境系统与优化问题的搜索空间相对应,该环境系统存在污染现象,污染源定期地向环境系统注入有毒污染物。有多种不同类型的种群生活在该环境系统中,不同类型的种群之间存在竞争关系和捕食-被捕食关系,每个种群对应着优化问题的一个试探解。将生态毒理动力学模型映射成对种群的特征的变化规律的描述,利用环境和种群以及种群与种群之间的相互作用构造种群的进化算子,这些算子从多种角度实现了种群与环境以及种群与种群之间的信息交换。结果表明:因环境污染影响的是种群的很少部分特征,当种群演化时,只涉及到很少一部分特征参与运算,故收敛速度可得到提升;环境系统脉冲式注入毒素,可以导致种群的特征状态值发生突然改变,这种特点有利于使搜索跳出局部最优解陷阱;使能够抵抗污染的强壮种群获得生长,而无法抵抗污染的虚弱种群则停止生长,此特点确保了该算法具有全局收敛性。测试结果表明:对某些函数优化问题的求解,本算法与已有的群智能优化算法相比,均具有较高的精度和性能。     

微生物动力学优化算法

为了解决一类函数优化问题,利用带时滞影响的混杂食物链微生物培养动力学理论提出一种微生物动力学优化(MDO)算法。在该算法中,假设有多个微生物种群在一个培养系统中培养,微生物种群的生长不但受注入到培养系统中的培养液流量、营养物质和有害物质的浓度影响,而且受种群之间相互作用的影响;定期注入的培养液会突然增加营养物质和有毒物质的浓度,从而会突然加大对种群的影响。利用上述特点构造出了吸收算子、攫取算子、混杂算子和毒素算子;利用这些算子和种群的生长变化,能够快速求解优化问题的全局最优解。仿真实验结果表明,MDO算法对求解维数较高的优化问题具有一定的优势。     

基于3种群Lotka-Volterra模型的种群动力学函数优化算法

基于3种群Lotka-Volterra模型构造出了可全局收敛的种群动力学优化算法。在该算法中,每个种群对应着优化问题的一个试探解;基于3种群间的每种相互作用关系,提出了相应的图形表示方法以及对应的Lotka-Volterra模型构建方法,种群间的相互作用关系包括竞争关系、互惠共存关系、捕食-被食关系或者它们间的任意组合;3种群间的每种相互作用关系均对应着一种种群进化算子,该算子的数学表达式就是其对应的Lotka-Volterra模型的离散化表达式;另外,为了求解更复杂的优化问题求解,将种群融合、突变和选择等行为也构造成操作算子。所有算子的特性可以确保整个种群的适应度指数要么保持原状不变,要么向好的方向转移,从而确保了算法的全局收敛性;在种群演变过程中,种群从一种状态转移到另一种状态实现了种群对优化问题最优解的搜索。应用可归约随机矩阵的稳定性条件证明了本算法具有全局收敛性。测试结果表明本算法是高效的。     

种群动力学优化算法

为了快速求解大规模复杂优化问题,基于种群动力学理论构造出了可全局收敛的种群动力学优化算法。在该算法中,每个种群对应着优化问题的一个试探解,种群的一个特征对应于试探解的一个变量;采用正交拉丁方原理构造出了种群初始值确定方法,以达到对搜索空间的均衡分散性和整齐可比性覆盖;将任意两种群间的竞争、互利、捕食-被食、融合、突变和选择等行为用于构造种群的进化策略,以使种群的适应度指数要么保持原状不变,要么向好的方向转移,从而确保整个算法的全局收敛性;在种群演变过程中,种群从一种状态转移到另一种状态,实现了种群对优化问题全局最优解的搜索。应用可归约随机矩阵的稳定性条件证明了本算法具有全局收敛性。测试结果表明本算法是高效的。     

具脉冲出生和季节性捕杀的种群系统优化算法

为了求解一些非线性优化问题,采用具有脉冲出生和季节性捕杀的种群动力学模型提出了一种新的群智能优化算法(PSO-IBSK).在该算法中,假设某种群由具有幼年和成年两种阶段状态的若干个体组成,幼体是由成体脉冲产生的,经过一段时间后会变成为成体.为了提升种群的整体质量,需要季节性地对一些生长状况不良的成体进行捕杀.该算法中的出生算子和成长算子可分别实现成体向幼体瞬时和延迟传递信息,有助于搜索跳出局部最优解陷阱;捕杀算子可周期性地将不良成体清除,死亡算子可将虚弱个体随机清除,该两个算子有利于提升算法的求精能力;强势算子可实现强壮个体向虚弱个体扩散强壮信息,竞争算子可实现幼年和成体之间的有效信息交换,该两个算子有利于提升算法的探索能力;进化算子可确保算法具有全局收敛性.该算法的大部分参数采用该种群动力学模型确定,具有很好的科学性;该算法每次只处理个体特征数的6‰～8％,从而使时间复杂度大幅降低.测试结果表明,该算法具有较优越的性能,适于求解维数较高的优化问题.     

生态平衡动力学优化算法

为了解决复杂函数优化问题,提出了一种Lotka-Volterra生态平衡动力学优化算法。该算法假设在某个生态系统中有自养者、消费者和分解者3个种群。自养者主要是植物;消费者主要是以自养者为食的动物;分解者主要分解消费者的死有机体,并给自养者提供营养物质。根据上述生态系统中种群的关系构造出了消费者-自养者算子、自养者-分解者算子、分解者-消费者算子和生长算子。自养者、消费者和分解者种群的生长变化相当于搜索空间的试探解从一个位置转移到另外一个位置。该算法具有搜索能力强和全局收敛性的特点,为复杂优化问题的求解提供了一种解决方案。     

保护区种群迁移动力学优化算法

为了求解一些复杂优化问题的全局最优解,基于保护区种群迁移动力学模型,提出了一种新的群智能优化算法,简称PZPMDO算法。在该算法中,假设有很多生物种群生活在某生态系统中,该生态系统被分成两个区域,即非保护区和保护区,对生活在保护区内的生物种群实施各种保护。在非保护区与保护区之间存在种群迁移通道,若某区域内的某生物种群的密度过高,该生物种群就会自发地迁移到低密度区域,从而导致低密度区域内的生物种群受到迁移过来的生物种群的影响;若某生物种群的占比越大,该生物种群的影响也就越大;若某生物种群越强壮,该生物种群就越会将其优势传播给其他生物种群。不同区域内的各生物种群因生存竞争而相互影响,这种影响会体现在种群部分特征间的相互作用上,且该影响是随时间变化的。文中采用ZGI指数描述一个生物种群的强弱程度,利用保护区种群迁移动力学模型、种群迁移和相互影响关系构造算子。PZPMDO算法拥有8个算子,且演化时每次仅处理总变量数的1/1000~1/100,具有搜索速度快和全局收敛性的特点,适用于求解维数较高的全局优化问题。     

一种有效的解无约束全局优化的进化算法

为了解决进化算法在求解全局优化时易陷入局部最优和收敛速度慢的问题,设计了一个杂交算子,利用种群中最好点与其他点间的关系确定搜索方向,从而快速地找到实值函数的下降方向,一旦算法找到优于种群中最好点的点,利用所构造的两条直线交点的投影对其进行进一步优化,使函数值更迅速地下降.提出了适合杂交算子的初始种群生成方法.设计了一个既能提高收敛速度又能摆脱局部最优的变异算子以增强算法的效果.在此基础上,提出了一个求解全局优化问题的高效进化算法,并从理论上证明了全局收敛性,从数值上验证了有效性.     

一种变增长率的多种群竞争协同进化

为提高遗传算法的收敛性能,借鉴生态学对个体生存环境和种群竞争的认识,并根据原有的生态种群竞争模型的协同进化模式,对种群增长与环境间的动力学特征的方程进行了优化,提出了一种变增长率的多种群竞争协同进化.利用信息熵的概念,构造出含有熵的多目标优化模型,利用该模型可以直接显式地给出作为拉格朗日乘子的种群最优解存在概率,从而得出种群的增长率.采用该模式的遗传算法在改善未成熟收敛和收敛速度两方面具有较好的性能.     

垂直结构群落系统优化算法

为了求解一类复杂非线性优化问题的全局最优解,基于采用垂直结构群落动力学理论,提出了一种新的垂直结构群落系统优化算法,简称为VS-CSO算法。该算法将优化问题的搜索空间视为一个生态系统,该生态系统具有若干个垂直结构分叉营养水平,在各个营养水平中生活着不同种类的生物种群;在每个种群内,有若干生物个体在活动;生物个体不能跨种群迁移,但在同类种群中会相互影响。各种群以循环捕食-被食或资源-消耗连接在一起。运用垂直结构群落动力学模型开发出了通吃算子、择食算子、干扰算子、侵染算子、新生算子、死亡算子。其中,通吃算子和择食算子可实现个体跨种群的信息交换,而干扰算子和侵染算子可实现种群内部个体之间的信息交换,从而确保个体间信息的充分交换;新生算子可适时补充新个体到种群中,而死亡算子可将种群中的虚弱个体适时清除掉,从而大幅提升算法跳出局部陷阱的能力。在求解过程中,VS-CSO算法每次只对极少变量进行处理,因此可求解高维优化问题。测试结果表明,VS-CSO算法能求解一类非常复杂的单峰函数、多峰函数和复合函数优化问题,其求精能力、探索能力及两者的协调性均优良,且具有全局收敛性的特点。该算法为求解一些较高维复杂函数优化问题的全局最优解提供了可行方案。     

Web前端性能优化方案与实践

针对Web前端性能低下的问题,通过分析归纳Web中从后端到前端的B/S架构原理、浏览器缓存、浏览器的加载方式、服务器关于HTTP相关的配置等过程中一些影响前端性能优化的因素,系统地提出一个旨在提高网页加载速度、呈现速度和用户体验,整体性、通用性强的完整Web前端性能优化解决方案。该解决方案包括服务器端优化、HTML优化、Java Script优化、CSS优化、图片优化等内容。并在HTTP代理工具Fiddler搭建的512 KB慢网速下通过Speed Tracer监测UI Thread,寻找基于HTML5技术的Web移动电子商务项目"指尖点餐系统"的点餐页面前端性能中的瓶颈,根据所提出的Web前端性能优化解决方案对其进行优化实践。优化前后的Timeline以及UI Thread对比分析表明,优化后加载时间降低了82%,页面渲染降低了32%,脚本执行减少了79%。     

Seeker optimisation (human group optimisation) algorithm with chaos

Seeker optimisation algorithm (SOA), also referred to as human group metaheuristic optimisation algorithms form a very hot area of research, is an emerging population-based and gradient-free optimisation tool. It is inspired by searching behaviour of human beings in finding an optimal solution. The principal shortcoming of SOA is that it is easily trapped in local optima and consequently fails to achieve near-global solutions in complex optimisation problems. In an attempt to relieve this problem, in this article, chaos-based strategies are embedded into SOA. Five various chaotic-based SOA strategies with four different chaotic map functions are examined and the best strategy is chosen as the suitable chaotic scheme for SOA. The results of applying the proposed chaotic SOA to miscellaneous benchmark functions confirm that it provides accurate solutions. It surpasses basic SOA, genetic algorithm, gravitational search algorithm variant, cuckoo search optimisation algorithm, firefly swarm optimisation and harmony search the proposed chaos-based SOA is expected successfully solve complex engineering optimisation problems.     

The multi-disciplinary design of a large-scale civil aircraft wing taking account of manufacturing costs

This paper presents results from a major research programme funded by the European Union and involving 14 partners from across the Union. It shows how a complex tool set was assembled which was able to optimise a large civil airliner wing for weight, drag and cost. A multi-level MDO process was constructed and implemented through a hierarchical system in which cost comprised the top level. Conventional structural sizing parameters were employed to optimise structural weight but the upper-level optimisation used 6 overall design variables representing major design parameters. The paper concludes by presenting results from a case study which included all the components of the total design system.     

Dynamic Ant Colony Optimisation

Ant Colony optimisation has proved suitable to solve static optimisation problems, that is problems that do not change with time. However in the real world changing circumstances may mean that a previously optimum solution becomes suboptimal. This paper explores the ability of the ant colony optimisation algorithm to adapt from the optimum solution for one set of circumstances to the optimal solution for another set of circumstances. Results are given for a preliminary investigation based on the classical travelling salesman problem. It is concluded that, for this problem at least, the time taken for the solution adaption process is far shorter than the time taken to find the second optimum solution if the whole process is started over from scratch.     

Enhanced leader PSO (ELPSO): A new PSO variant for solving global optimisation problems

Particle swarm optimisation (PSO) is a well-established optimisation algorithm inspired from flocking behaviour of birds. The big problem in PSO is that it suffers from premature convergence, that is, in complex optimisation problems, it may easily get trapped in local optima. In this paper, a new PSO variant, named as enhanced leader PSO (ELPSO), is proposed for mitigating premature convergence problem. ELPSO is mainly based on a five-staged successive mutation strategy which is applied to swarm leader at each iteration. The experimental results confirm that in all terms of accuracy, scalability and convergence rate, ELPSO performs well.     

A new effective operator for the hybrid algorithm for solving global optimisation problems

Hybrid algorithms have been recently used to solve complex single-objective optimisation problems. The ultimate goal is to find an optimised global solution by using these algorithms. Based on the existing algorithms (HP_CRO, PSO, RCCRO), this study proposes a new hybrid algorithm called MPC (Mean-PSO-CRO), which utilises a new Mean-Search Operator. By employing this new operator, the proposed algorithm improves the search ability on areas of the solution space that the other operators of previous algorithms do not explore. Specifically, the Mean-Search Operator helps find the better solutions in comparison with other algorithms. Moreover, the authors have proposed two parameters for balancing local and global search and between various types of local search, as well. In addition, three versions of this operator, which use different constraints, are introduced. The experimental results on 23 benchmark functions, which are used in previous works, show that our framework can find better optimal or close-to-optimal solutions with faster convergence speed for most of the benchmark functions, especially the high-dimensional functions. Thus, the proposed algorithm is more effective in solving single-objective optimisation problems than the other existing algorithms.     

A genetic algorithm for combined topology and shape optimisations

A method to find optimal topology and shape of structures is presented. With the first the optimal distribution of an assigned mass is found using an approach based on homogenisation theory, that seeks in which elements of a meshed domain it is present mass; with the second the discontinuous boundaries are smoothed. The problem of the optimal topology search has an ON/OFF nature and has suggested the employment of genetic algorithms. Thus in this paper a genetic algorithm has been developed, which uses as design variables, in the topology optimisation, the relative densities (with respect to effective material density) 0 or 1 of each element of the structure and, in the shape one, the coordinates of the keypoints of changeable boundaries constituted by curves. In both the steps the aim is that to find the variable sets producing the maximum stiffness of the structure, respecting an upper limit on the employed mass. The structural evaluations are carried out with a FEM commercial code, linked to the algorithm. Some applications have been performed and results compared with solutions reported in literature.     

一种解决复合形局部最优及加速计算的方法

对求解非线性约束优化问题的复合形法陷入局部最优的问题进行探讨,给出了一种改进的方法.改进后的方法不仅可以有效地寻找全局最优解,而且计算速度较传统复合形算法快.     

Finding the maximal membership in a fuzzy set of an element from another fuzzy set

The problem of finding the maximal membership grade in a fuzzy set of an element from another fuzzy set is an important class of optimisation problems manifested in the real world by situations in which we try to find what is the optimal financial satisfaction we can get from a socially responsible investment. Here, we provide a solution to this problem. We then look at the proposed solution for fuzzy sets with various types of membership grades, ordinal, interval value and intuitionistic.     

Hindrances for robust multi-objective test problems

Despite the significant number of benchmark problems for evolutionary multi-objective optimisation algorithms, there are few in the field of robust multi-objective optimisation. This paper investigates the characteristics of the existing robust multi-objective test problems and identifies the current gaps in the literature. It is observed that the majority of the current test problems suffer from simplicity, so five hindrances are introduced to resolve this issue: bias towards non-robust regions, deceptive global non-robust fronts, multiple non-robust fronts (multi-modal search space), non-improving (flat) search spaces, and different shapes for both robust and non-robust Pareto optimal fronts. A set of 12 test functions are proposed by the combination of hindrances as challenging test beds for robust multi-objective algorithms. The paper also considers the comparison of five robust multi-objective algorithms on the proposed test problems. The results show that the proposed test functions are able to provide very challenging test beds for effectively comparing robust multi-objective optimisation algorithms. Note that the source codes of the proposed test functions are publicly available at www.alimirjalili.com/RO.html.