基于种群自适应调整的多目标差分进化算法

为提高已有多目标进化算法在求解复杂多目标优化问题上的收敛性和解集分布性,提出一种基于种群自适应调整的多目标差分进化算法。该算法设计一个种群扩增策略,它在决策空间生成一些新个体帮助搜索更优的非支配解;设计了一个种群收缩策略,它依据对非支配解集的贡献程度淘汰较差的个体以减少计算负荷,并预留一些空间给新的带有种群多样性的扰动个体;引入精英学习策略,防止算法陷入局部收敛。通过典型的多目标优化函数对算法进行测试验证,结果表明所提算法相对于其他算法具有明显的优势,其性能优越,能够在保证良好收敛性的同时,使获得的Pareto最优解集具有更均匀的分布性和更广的覆盖范围,尤其适合于高维复杂多目标优化问题的求解。     

动态种群规模协同进化算法求解多目标投资组合优化问题

为了解决仅含预算约束的投资组合优化模型,提出一种基于种群密度的多目标协同进化算法.算法采用种群竞争的策略自适应的产生不定规模的种群,避免了固定种群规模的缺点.在进化过程中每个种群都会参考自身的最优个体以及竞争种群对自身的影响,超级个体集合存储进化过程中产生的最优解,通过最优个体的引导使算法快速收敛至Pareto前沿.实验结果表明,与NSGA-2算法相比,提出的算法在稳定性和收敛性都有很好的表现,是一种有效的多目标进化算法.     

自适应多种群回溯群居蜘蛛算法求解TSP问题

在群居蜘蛛优化算法中引入自适应决策半径,将蜘蛛种群动态地分成多个种群,种群内适应度不同的个体采取不同的更新方式.在筛选全局极值的基础上,根据进化程度执行回溯迭代更新,提出一种自适应多种群回溯群居蜘蛛优化算法,旨在提高种群样本多样性和算法全局寻优能力.函数寻优结果表明改进算法具有较快的收敛速度和较高的收敛精度.最后将其应用于TSP问题的求解.     

顺序相依拆卸线平衡多目标优化模型及算法研究

拆卸是产品回收过程最关键环节之一,拆卸效率直接影响再制造成本。本文在分析现有模型不足基础上,考虑最小化总拆卸时间,建立多目标顺序相依拆卸线平衡问题优化模型,并提出了一种自适应进化变邻域搜索算法。所提算法引入种群进化机制,并采用一种组合策略构建初始种群,通过锦标赛法选择个体进化;在局部搜索时,设计了邻域结构自适应选择策略,并采用基于交叉的全局学习机制加速跳出局部最优,以提高算法寻优能力。对比实验结果,证实了所提模型的合理性以及算法的高效性。     

改进种群多样性的双变异差分进化算法

差分进化算法(DE)是一种基于种群的启发式随机搜索技术,对于解决连续性优化问题具有较强的鲁棒性.然而传统差分进化算法存在种群多样性和收敛速度之间的矛盾,一种改进种群多样性的双变异差分进化算法(DADE),通过引入BFS-best机制(基于排序的可行解选取递减策略)改进变异算子"DE/current-to-best",将其与DE/rand/1构成双变异策略来改善DE算法中种群多样性减少的问题.同时,每个个体的控制参数基于排序自适应更新.最后,利用多个CEC2013标准测试函数对改进算法进行测试,实验结果表明,改进后的算法能有效改善种群多样性,较好地提高了算法的全局收敛能力和收敛速度.     

约束尺度和算子自适应变化的差分进化算法

由于可行域不连续和函数形式复杂使得许多算法难以有效求解约束优化问题,提出了一种约束尺度和算子自适应变化的差分进化算法.通过统计新个体中可行解和不可行解的数量以自适应调整惩罚系数,使个体能够分布在多个不连续的可行域中,从而找到最优解所在区域.同时,算法还采用了两种不同的差分算子,分别用于局部区域的快速寻优和整个可行域的全局探索.在两种算子的选择上,则根据新个体的存活情况和约束违反情况来自适应调整其选择的概率.最后通过3组标准约束优化问题在10维和30维变量下的测试结果显示:所提算法的性能整体优于对比算法,其平均最优解在10维时至少提升了4.75%.     

基于自适应子种群和动态反向学习的改进鸡群算法

针对鸡群算法(Chicken swarm optimization,CSO)求解复杂高维问题收敛精度低、容易陷入局部极值等问题,提出了一种基于自适应子种群和动态反向学习的改进鸡群(ICSO)算法.根据鸡群算法迭代进化进程,自适应确定公鸡种群规模大小,并据此将母鸡种群和小鸡分成若干个子种群;设计进化停滞判定机制,并引入动态反向学习因子以改进算法个体更新方式,有效保持鸡群样本多样性和算法全局深度搜索能力.典型测试函数仿真实验结果表明,与SFLA算法、PSO等智能优化算法相比,ICSO算法具有更高的收敛精度和更优的复杂函数优化能力.     

融合差分进化与多策略的阿基米德优化算法

鉴于阿基米德优化算法存在易早熟,收敛慢等缺点,提出一种融合差分进化与多策略的阿基米德优化算法.首先,通过位置参数,随机选择两种混沌映射初始化种群来增强种群的多样性;其次,通过余弦控制因子的动态边界策略改进密度因子,来平衡算法的全局探索与局部开发能力;接着,融合差分进化算法,缩小最优位置的范围,以达到快速向最优位置靠拢的目的.最后,选取10个基准测试函数进行仿真实验,并对实验结果进行Wilcoxon秩和检验,结果表明所提算法性能优于对比算法.     

多智能体协调控制的演化博弈方法

提出一种基于演化博弈理论的多智能体系统协调控制方法.在所建立的数学模型框架中智能体根据其自身的利益,通过局部交互,在博弈竞争中学习,自主调整其行为.根据系统整体性能的要求,通过选择合适的博弈类型、设计适宜的收益计算方法、更新进化规则等,实现对多智能体系统的控制.在演化过程中,无需指定某些特定个体的具体动力学行为,只需通过种群的自适应进化即可实现整体目标.以分工合作问题为例,详细解析所提出的控制方法,通过理论分析和仿真验证该方法可以实现多智能体系统的自适应协调控制.     

改进伪并行遗传算法求解作业车间调度问题

针对遗传算法在求解极复杂优化问题中出现的过早收敛、执行效率差的缺点,提出了一种改进的伪并行遗传算法.该算法将并行进化与串行搜索相结合,提高了算法的收敛速度.同时该算法通过种群因子控制伪并行算法中的各子种群的规模,不仅保证了搜索过程中勘探和开采的平衡,克服过早收敛,而且减少了计算的复杂性,特别是在处理复杂优化问题上具有较高的性能.实验结果证明了该算法的有效性.     

多重经济增长路径,多重稳态解和分歧

该文给出一个具有可解内生生育率的Cass-Koopmans（C-K）经济增长模型．证明参数满足时，模型存在多重经济增长路径和多重稳态解；当时，经济增长路径和稳态解唯一，即描述模型的微分动力系统出现分歧．文中讨论了多重经济增长路径的几何形态、位置关系和主要结果的经济意义．     

Least Common Multiple

<正>Work with a partner.Use 9 centimeter cubes to model the first floor of Building 1 and 12 centimeter cubes to model the first floor of Building 2,as shown.1.Add a second floor to each building.Record the total number of cubes used in a table like the one shown below.     

Multiple fractional integrals

Multiple integrals with respect to fractional Brownian motion (with H > 1/2) are constructed for a large class of functions. The first and second moments of the multiple integrals are explicitly identified. Received: 23 February 1998 / Revised version: 31 July 1998     

Loading Multiple Pallets

This paper addresses the problem of loading pallets with non-identical items, i.e. what has been called the ‘Distributor's Pallet Packing Problem’. It concentrates on the situation where the consignment to be loaded cannot be accommodated on a single pallet. A greedy procedure for tackling this problem, which is based on a published approach for loading single pallets, is described and evaluated. Also discussed is a series of possible modifications of the basic method, whereby the pallets involved are packed simultaneously. A detailed performance analysis is undertaken. The paper concludes with suggestions for further work in this area.     

Multiple cover time

Motivated by applications in Markov estimation and distributed computing, we define the blanket time of an undirected graph G to be the expected time for a random walk to hit every vertex of G within a constant factor of the number of times predicted by the stationary distribution. Thus the blanket time is, essentially, the number of steps required of a random walk in order that the observed distribution reflect the stationary distribution. We provide substantial evidence for the following conjecture: that the blanket time of a graph never exceeds the cover time by more than a constant factor. In other words, at the cost of a multiplicative constant one can hit every vertex often instead of merely once. We prove the conjecture in the case where the cover time and maximum hitting time differ by a logarithmic factor. This case includes almost all graphs, as well as most “natural” graphs: the hypercube, k-dimensional lattices for k ≥ 2, balanced k-ary trees, and expanders. We further prove the conjecture for perhaps the most natural graphs not falling in the above case: paths and cycles. Finally, we prove the conjecture in the case of independent stochastic processes. © 1996 John Wiley & Sons, Inc. Random Struct. Alg., 9 , 403–411 (1996)     

Multiple commutator formulas

Let A be a quasi-finite R-algebra (i.e., a direct limit of module finite algebras) with identity. Let I _i , i = 0, …,m, be two-sided ideals of A, GL _n (A, I _i ) be the principal congruence subgroup of level I _i in GL _n (A) and E _n (A, I _i ) be the relative elementary subgroup of level I _i . We prove the multiple commutator formula $$\left[ {{E_n}(A,{I_0}),{\rm{G}}{{\rm{L}}_n}(A,{I_1}),{\rm{G}}{{\rm{L}}_n}(A,{I_2}), \ldots ,{\rm{G}}{{\rm{L}}_n}(A,{I_m})} \right] = \left[ {{E_n}(A,{I_0}),{E_n}(A,{I_1}),{E_n}(A,{I_2}), \ldots ,{E_n}(A,{I_m})} \right],$$ , which is a broad generalization of the standard commutator formulas. This result contains all the published results on commutator formulas over commutative rings and answers a problem posed by A. Stepanov and N. Vavilov.     

Immense Multiple Realization

In his latest book Physicalism, or Something near Enough, Jaegwon Kim argues that his version of functional reductionism is the most promising way for saving mental causation. I argue, on the other hand, that there is an internal tension in his position: Functional reductionism does not save mental causation if Kim’s own supervenience argument is sound. My line of reasoning has the following steps: (1) I discuss the supervenience argument and I explain how it motivates Kim’s functional reductionism; (2) I present what I call immense multiple realization, which says that macro-properties are immensely multiply realized in determinate micro-based properties; (3) on that background I argue that functional reductionism leads to a specified kind of irrealism for mental properties. Assuming that such irrealism is part of Kim’s view, which Kim himself seems to acknowledge, I argue that Kim’s position gets the counterfactual dependencies between macro-causal relata wrong. Consequently, his position does not give a conservative account of mental causation. I end the paper by discussing some alternative moves that Kim seems to find viable in his latest book. I argue on the assumption that the supervenience argument is sound, so the discussion provides further reasons to critically reevaluate that argument because it generalizes in deeply problematic ways.     

Multiple zeta values

The definition of multiple zeta values is extended in the paper. The preservation of the main properties known for multiple zeta values in the sense of their classic definition is proved.     

Multiple ergodic theorems

Given measure preserving transformationsT ₁,T ₂,...,T _s of a probability space (X,B, μ) we are interested in the asymptotic behaviour of ergodic averages of the form $$\frac{1}{N}\sum\limits_{n = 0}^{N - 1} {T_1^n f_1 \cdot T_2^n f_2 } \cdot \cdots \cdot T_s^n f_s $$ wheref ₁,f ₂,...,f _s ?L ^∞(X,B,μ). In the general case we study, mainly for commuting transformations, conditions under which the limit of (1) inL ²-norm is ∫ _x f ₁ dμ·∫ _x f ₂ dμ...∫ _x f _s dμ for anyf ₁,f ₂...,f _s ?L ^∞(X,B,μ). If the transformations are commuting epimorphisms of a compact abelian group, then this limit exists almost everywhere. A few results are also obtained for some classes of non-commuting epimorphisms of compact abelian groups, and for commuting epimorphisms of arbitrary compact groups.