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。     

求解大规模优化问题的可全局收敛蝙蝠算法

为了快速求解大规模优化问题,构造出了可全局收敛的蝙蝠算法。在该算法中,将一个蝙蝠看成是优化问题的一个候选解;采用正交拉丁方原理生成蝙蝠群的初始空间位置,以达到对搜索空间的均衡分散性和整齐可比性覆盖;将蝙蝠的追随、自主、避险和从众行为用于构造每个蝙蝠的空间位置转移策略;利用蝙蝠捕获猎物时的响度和脉冲速率来确保整个蝙蝠群要么保持原状态,要么向好的空间位置转移,但绝不会向差的空间位置转移。在蝙蝠群移动过程中,蝙蝠从一个空间位置转移到另一个空间位置实现了蝙蝠群对优化问题最优解的搜索。结果表明,采用可归约随机矩阵稳定性定理可证明本算法具有全局收敛性。测试案例表明,本算法用于求解大规模优化问题时具有对不同类型优化问题适应性强且收敛速度快的优势。     

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。     

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。     

生态毒理动力学函数优化方法

基于生态毒理动力学模型构造出可全局收敛的函数优化算法。在该算法中,将优化问题的搜索空间看成一个存在污染现象的环境系统,将一个试探解看成一个种群,采用生态毒理动力学模型对种群生长特征的变化规律进行描述。种群在污染作用下不断发生变化,能够抵抗住污染的强壮种群能够获得生长,而无法抵抗住污染的虚弱种群则停止生长。用环境和种群以及种群与种群之间的相互作用关系构造进化算子,这些算子从多种角度实现了种群之间的信息交换。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种群特征参与运算,故提高了算法的收敛速度。测试结果表明本算法的精度和性能优于已有的群智能优化算法。     

记忆原理的元胞自动机优化算法及其收敛性证明

为了求解大规模优化问题,根据记忆原理与元胞自动机的特点构造了求解优化问题的全局收敛算法。在该算法中,将优化问题的理论搜索空间划分为离散搜索空间,该空间定义为元胞空间,其中的每个元胞对应着一个候选解。将记忆原理的记忆、遗忘规律用于控制每个元胞的状态转移;元胞的状态由其空间位置、位置修正量以及记忆残留值构成,该值分为瞬时记忆、短时记忆和长时记忆3种状态类型,并依据元胞接受刺激的强度被加强或衰减;记忆残留值低于某个阈值的元胞时被遗忘,不再被处理。在元胞演化过程中,元胞从一个状态转移到另一个状态实现了元胞空间对理论搜索空间的搜索。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。     

求解非线性方程组的元胞自动机方法及其全局收敛性证明

为了求得非线性方程组所有精确解,根据元胞自动机的特点构造了求解非线性方程组的全局收敛算法。在该算法中,将非线性方程组解的理论搜索空间划分为离散搜索空间,将离散搜索空间定义为元胞空间;离散搜索空间的每个点就是一个元胞,而一个元胞对应着非线性方程组的一个试探解;元胞的状态由其空间位置及位置修正量构成。将元胞空间划分为若干个非空子集,所有元胞的状态从一个非空子集转移到另一个非空子集的状态演化过程实现了元胞空间对理论搜索空间的搜索。在元胞状态演化过程中,元胞从一个状态转移到另一个状态的状态转移概率可以计算出来;元胞演化过程中的每个状态对应于有限Markov链上的一个状态。利用可归约随机矩阵的稳定性条件证明了该算法具有全局收敛性。仿真实例表明该算法是高效的。     

自组织多目标粒子群优化算法

针对多目标粒子群优化算法收敛性和多样性难以平衡的问题,提出一种利用问题的结构信息来解决多目标问题的自组织多目标粒子群算法。通过自组织映射网络发现种群和非支配解集分布的结构,构造出当前粒子的邻域关系,从邻域中选出非支配解,从而引导种群局部和全局的搜索。提出了精英学习策略,通过对精英粒子进行变异,引导算法跳出局部最优。实验结果表明,所提算法可以兼顾收敛性和多样性,有效地解决多目标优化问题。     

基于全局最优位置自适应选取与局部搜索的多目标粒子群优化算法

针对多目标粒子群优化算法全局最优位置〖BP(〗(gbest)〖BP)〗选取存在的缺陷和局部搜索能力弱的缺点,提出一种基于全局最优位置自适应选取与局部搜索的多目标粒子群优化算法MOPSO-GL。首先对Sigma法进行改进,引入拥挤距离机制,不再是粒子从档案中选择全局最优位置,而是档案成员从种群中选择合适的被引导粒子,引导种群均匀快速地向Pareto前沿飞行,提高了Pareto解的收敛性和多样性;其次当种群寻优能力减弱时,引入基于Skew Tent映射的变尺度全面搜索混沌优化策略对外部档案进行局部搜索,以提高算法的收敛性;最后通过与其他多目标优化算法的比较,结果表明MOPSO-GL具有更好的收敛性和分布性。     

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。     

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.     

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.     

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.     

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。     

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.     

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。     

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.     

A New Subdivision Algorithm for the Bernstein Polynomial Approach to Global Optimization

In this paper,an improved algorithm is proposed for unconstrained global optimization to tackle non-convex nonlinear multivariate polynomial programming problems.The proposed algorithm is based on the Bernstein polynomial approach.Novel features of the proposed algorithm are that it uses a new rule for the selection of the subdivision point,modified rules for the selection of the subdivision direction,and a new acceleration device to avoid some unnecessary subdivisions.The performance of the proposed algorithm is numerically tested on a collection of 16 test problems.The results of the tests show the proposed algorithm to be superior to the existing Bernstein algorithm in terms of the chosen performance metrics.