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运筹学学报

运筹学学报

北大核心

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CSTPCD

Operations Research Transactions
本刊是反映运筹学各领域的最新进展、动态、理论、成果等，促进学术交流。是国内唯一的一份全面刊载运筹学各方面的学术性刊物。
  • 发文量：1092
  • 被引量：178
  • H指数：3
  • 开始收录时间：1989,8(1)
  • CNKI综合因子：0.369
  • 维普期刊影响因子： 0.45
  • 万方期刊影响因子：0.25
  • 创刊时间：1997
  • 国内刊号/CN：31-1732/O1
    国际刊号/ISSN：1007-6093
  • 发行周期：季刊
    邮发代号：4-777
  • 主管单位：中国科学技术协会
    主办单位：中国运筹学会
运筹学学报-联系信息
  • 主编：胡旭东
  • 电话：021-66137605
  • 邮箱：ort@mail.shu.edu.cn
  • 地址：上海市上大路99号
  • 邮编：200444
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运筹学学报 >2023年第4期

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  • 摘要：增广Lagrange方法是求解非线性规划的一种有效方法.从一新的角度证明不等式约束非线性非光滑凸优化问题的增广Lagrange方法的收敛性.用常步长梯度法的收敛性定理证明基于增广Lagrange函数的对偶问题的常步长梯度方法的收敛性,由此得到增广Lagrange方法乘子迭代的全局收敛性.%The augmented Lagrange method is an effective method for solving nonlinear optimization problems.This paper,from a new pointview,studies the convergence of the augmented Lagrange method for the nonlinear nonsmooth convex programming problem with inequality constraints.The convergence of the gradient method with constant stepsize for the dual problem,based on the augmented Lagrange function,is demonstrated by using a convergence theorem of a gradient method with constant stepsize,from which the global convergence of the multiplier iteration of augmented Lagrange method is obtained.
  • 摘要：设G是不含孤立点的图,S是G的一个顶点子集,若G的每一个顶点都与S中的某顶点邻接,则称S是G的全控制集.G的最小全控制集所含顶点的个数称为G的全控制数,记为γt(G).Thomassé和Yeo证明了若G是最小度至少为5的n阶连通图,则γt(G)≤17n/44.在5-正则图上改进了Thomassé和Yeo的结论,证明了若G是n阶5-正则图,则γt(G)≤106n/275.%Let G be a graph without isolated vertices.A total dominating set of G is a subset S of V(G) such that every vertex of G is adjacent to a vertex in S.The minimum cardinality of a total dominating set of G is denoted by γt (G).Recently,Thomassé and Yeo showed that γt(G) ≤ 17n/44 for a connected graph G of order n with minimum degree at least five.In this paper we prove that γt(G) ≤ 106n/275 for a 5-regular graph G of order n,which improves sightly the bound of Thomassé and Yeo.
  • 摘要：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.%Differential Evolution (DE) is an efficient population-based heuristic stochastic search technique.It is robust for solving continuous optimization problems.However,the discrepancy of population diversity and convergence rate exists in traditional Differential Evolution.In this paper,differential evolution algorithm based on double mutation strategies for improving population diversity (DADE) was proposed.This algorithm presents a BFS-best mechanism to improve "current-to-best",which cooperates with DE/rand/1 to ensure population diversity.Meanwhile,the control parameters of individuals are updated automatically based on ranking.Finally,several benchmark functions in CEC2013 are used to test the proposed algorithm.The simulation results show that DADE can effectively improve population diversity,achieve better global searching ability and a higher convergence rate.
  • 摘要：设图G是简单连通图.如果任何一个与图G关于拉普拉斯矩阵同谱的图,都与图G同构,称图G可由其拉普拉斯谱确定.定义了树Yn和树F(2,n,1)两类特殊结构的树.利用同谱图线图的特点,证明了树Yn和树F(2,n,1)可由其拉普拉斯谱确定.%Let G be a simple connected graph.A graph G is called to be determined by its Laplacian spectrum if any graph having the same Laplacian spectrum as G is isomorphic to G.In this paper,tree Yn and tree F(2,n,1) which have special structures are defined.It is proved that these two families of trees are determined by their Laplacian spectrum,considering the properties of the line graphs of the cospectral graphs.
  • 摘要：研究了与总误工损失相关的两个代理的单机排序问题.第一个代理以工件的总误工损失为目标函数,第二个代理以工件的总完工时间或总误工工件数为目标函数.目标是寻找一个排序,使得在第二个代理的目标函数不超过给定的上界的条件下,第一个代理的目标函数值最小.对这两个与总误工损失相关的两个代理的单机排序问题,分别给出它们的拟多项式时间的动态规划算法.%We consider two-agent scheduling problem about total late work on a single machine.The first agent has total late work as its objective function,while the second agent considers either the total complete time or the number of tardy jobs as its objective function.The goal is to find a schedule that minimize the objective of the first agent while keeping the objective of the second agent cannot exceed a giving upper bound.We present a pseudo-polynomial time algorithm for these two scheduling problem,respectively.
  • 摘要：精确罚函数方法是求解优化问题的一类经典方法,传统的精确罚函数不可能既是简单的又是光滑的,这里简单的是指罚函数中不包含目标函数和约束函数的梯度信息.针对等式约束问题提出了不同与传统罚函数的一类新的简单光滑罚函数并证明了它是精确的.给出了以新的罚函数为基础的罚函数方法并用数值例子说明算法是可行的.%Exact penalty function method is one of the main approaches for solving constrained nonlinear programming problems.For the traditional exact penalty function,it is not both smooth and simple.It is simple in the sense that the gradient of the objective function and constrained functions is not involved in the penalty function.In this paper,a new class of simple and smooth penalty functions which are different from the tradition penalty functions is proposed for the equality constrained problem.It is proved that the class of exact penalty functions is exact.The algorithm based on the new smoothed penalty functions is proposed.Two numerical examples show that the algorithm is efficient.
  • 摘要：恒定混合策略(CM策略)多期收入保证价格是保本基金发行方采取设置止损的CM策略作为投资策略时收取保本费的理论依据,其中标的资产由复合泊松过程和维纳过程共同驱动,这一定价问题内嵌奇异期权,蒙特卡罗模拟方法擅长处理这种高维数量金融问题.基于风险中性测度推导出多期收入保证价格的现值表达式,用条件蒙特卡罗推导出这一现值表达式的模拟公式.在给定参数下分别用普通蒙特卡罗和条件蒙特卡罗计算CM策略多期收入保证价格的数值解,结果显示两种蒙特卡罗方法均能有效计算其数值解,之后通过给定显著性水平下的置信区间长度评价两种方法的精确度,结果显示条件蒙特卡罗比普通蒙特卡罗有很大改进.接着运用条件蒙特卡罗模拟研究多期收入保证价格对不同参数范围的变化情况.%Value of constant mix strategy (CM strategy) multi-period return guarantee is theoretical basis of charging by the issuers who use CM strategy set stop-loss to manage a principal guaranteed fund.The underlying asset is driven by compound Poisson process and Wiener process.This pricing problem embeds exotic options.Monte Carlo simulation is good at dealing with such a high dimensional quantitative financial problems.We derive the expression of the present value of CM strategy multi-period return guarantee that based on risk-neutral measurement.Then we use conditional Monte Carlo simulation to derive the simulation formula of this present value.Numerical solutions of value of CM strategy multi-period return guarantee were calculated under given parameters by ordinary Monte Carlo and conditional Monte Carlo.Results show two Monte Carlo methods can calculate the numerical solution effectively.Then we appraise the accuracy of the two methods through the length of the confidence interval under a given level of significance.Results show conditional Monte Carlo is better than ordinary Monte Carlo.Then we use conditional Monte Carlo simulation to analyze value of CM strategy multi-period return guarantee on the different parameters range.
  • 摘要：This paper considers a two-echelon supply chain system consisting of one supplier and one retailer under carbon tax regulation.When the time-varying demand rate of retailer is dependent on stock level and selling price,the decentralized and centralized models are constructed and compared.The result shows that cooperation between supplier and retailer lead to higher profit and more carbon emissions.Wholesale price contract and two-part tariff contract are respectively used to coordinate the decentralized supply chain.Several conditions that the supply chain can be coordinated by two-part tariff contract are also obtained.Finally,several numerical examples are provided to verify the theoretical results and impacts of carbon tax price on supply chain coordination under two-part tariff contract are analyzed.%研究由一个供应商和一个零售组成的二级供应链系统在碳税政策下的协调问题.对于市场需求率为时变函数且依赖于当前库存水平和销售价格的情形,建立分散式和集中式供应链决策模型.比较两种模型得出供应商和零售商合作能够提高供应链的整体利润但是也会产生更多的碳排放.分别利用批发价格契约和两部收费契约协调分散式决策模型得出供应链协调的条件.最后通过数值算例验证理论结果并分析碳税单价对供应链在两部收费契约下实现协调的影响.
  • 摘要：In this paper,we consider the two-machine flow-shop scheduling with deterioration and rejection,in which each job's processing time is simple linear increasing function of its starting time.A job is either accepted and processed on the two machines in a flow-shop system,or rejected with a certain penalty having to be paid.The objective is to minimize the sum of the makespan of the accepted jobs plus the total penalty of the rejected jobs.We show that the problem is NP-hard and present a dynamic programming algorithm.Furthermore,we propose an optimal schedule for one special case.%考虑了工件具有退化效应的两台机器流水作业可拒绝排序问题,其中工件的加工时间是其开工时间的简单线性增加函数.每个工件或者被接收,依次在两台流水作业机器上被加工,或者被拒绝但需要支付一个确定的费用.考虑的目标是被接收工件的最大完工时间加上被拒绝工件的总拒绝费用之和.证明了问题是NP-难的,并提出了一个动态规划算法.最后对一种特殊情况设计了多项式时间最优算法.
  • 摘要：研究一类储存时间有上限的两阶段供应链排序问题.两阶段是指工件先加工,后运输:加工阶段是一台加工机器逐个加工工件;运输阶段是无限台车辆分批运输完工的工件.工件的运输完成时刻与完工时刻之差定义为工件的储存时间,且有相应的储存费用,且任意工件的储存时间都不超过某一常数.若工件的运输完成时刻早于(晚于)交货期窗口的开始(结束)时刻,则有相应的提前(延误)惩罚费用.目标是极小化总提前惩罚费用、总延误惩罚费用、总储存费用、总运输费用以及与交货期窗口有关的费用之和.先证明该问题是NP-难的,后对单位时间的储存费用不超过单位时间的延误惩罚费用的情形给出了伪多项式时间算法.%We investigate a two-stage supply chain scheduling problem in which jobs have the holding time which is limited by a constant.A job which is processed completely by the machine needs to dispatch with batch to customer by many vehicles,and a job will incur a holding cost if its completion time is earlier than its dispatch date.Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule.The objective is to find the optimal size and location of the window,the optimal dispatch date for each job,as well as an optimal job sequence to minimize a cost function based on earliness,tardiness,holding time,window location,window size,and batch delivery.We provide the proof of NP-hard for the problem.Then,we consider the case where the unit cost of holding time is not more than the unit cost of tardiness and give a pseudo-polynomial time algorithm for this case.
  • 摘要：In this paper,we propose a nonlinear dynamical system of batch fermentation with the continuous piecewise linear functions as parameters,and investigate the existence of solution about the nonlinear dynamical system.Based on a smooth curve which is fitted to the experimental data,a new identifiable model was established by using the continuous piecewise linear function as optimization parameters.According to the relationship between the state variables and identification function,an efficient algorithm is developed to solve the identification system,and the convergence of optimization algorithm is also analysed.Finally,numerical results are discussed to illustrate the validity of the present model.%建立以连续分段线性函数为参量的间歇发酵非线性动力系统,证明该动力系统的主要性质及解的存在性.以实验数据拟合得到的光滑曲线为依据,提出了连续分段线性函数为优化变量的辨识模型,论述可辨识性.依状态变量与辨识函数的相关性,构造求解辨识模型的优化算法,并给出优化算法的收敛性分析及数值结果.
  • 摘要：对一类在压缩感知、图像处理等相关领域有广泛应用的特殊非光滑优化问题进行了研究,给出了求解此类问题的光滑梯度法及算法的全局收敛性证明,相关的数值实验表明算法的有效性.%In this paper,we study a kind of special nonsmooth optimization problem,which is widely used in the field of compressed sensing and image processing.A smoothing gradient method is proposed and the global convergence is also given.Finally,the related numerical results indicate the efficiency of the given method.
  • 摘要：问题的复杂性概念起源于离散的图灵计算机理论的研究,在离散优化问题的研究中被广泛的接受.近期连续优化领域的很多文章中提及NP难这个概念.从而来对比介绍离散优化和连续优化研究中这两个概念的差异.%Complexity concepts oriented from the theoretical Turing machine are widely accepted in study of combinatorial optimization problems.The polynomially computable and NP-hard concepts are frequently used in recent papers on continuous optimization problems.This paper presents a very brief introduction to show their relationship and difference used in the two fields.
  • 摘要：单值中智集不仅能描述现实决策系统中不完整信息而且能描述不确定性和不一致信息,已有关于单值中智集的决策方法只能用来解决属性间相互独立的多属性决策问题.考虑到Choquet积分算子的特点,将Choquet积分算子应用到单值中智集中,用以解决属性间有关联关系的多属性群决策问题.首先应用单值中智集余弦相似度比较方法,提出了单值中智集Choquet积分算子,研究了其性质.然后建立了基于单值中智集Choquet积分算子的多属性群决策方法.最后通过实例分析说明了算法的可行性和有效性.%Single valued neutrosophic set (SVNS) depicts not only the incomplete information,but also the indeterminate information and inconsistent information which exist commonly in belief systems.The existing decision making methods for SVNS consider the case that the attributes are independent,and cannot handle the correlation among attributes.Based on the Choquet integral and the cosine similarity degree of single valued neutrosophic number,we propose an operator to aggregate single valued neutrosophic numbers (SVNNs),which can deal with the single valued neutrosophic information with connective attributes.By using the proposed single valued neutrosophic Choquet integral operator,an approach is given for the multi-attribute group decision making problems with SVNNs.An example is showed to illustrate the validity and applicability of the proposed method.
  • 摘要：1978年，科学的春天到来了!小平同志在多灾、多难又多事的科教战线挂帅出征；叶剑英元帅亲自赋诗，急令攻关：世上无难事，只要肯登攀，科学有险阻，苦战能过关!孔子的家乡——曲阜、山东的一个小县城，那里有个大学——曲阜师范学院，大学生、研究生，莘莘学子，荟萃于此，青春勃发，春意盎然，为中华崛起而读书。那时候，数学系的学生哪个不知道，在全国学术界有名气的专业和老师：数论，首屈代表邵品琮教授；微分方程，赵素霞；运筹学，王长钰——都是学子们向往的专业、崇拜的老师。
  • 摘要：In this paper,we focus on the optimality conditions for a class of stochastic optimization problem with probabilistic complementarity constraints.By using a kind of nonlinear complementarity (NCP) function,we transform the probabilistic complementary constraint into a chance constraint.By using the theories in chance constraint,we obtain an optimization problem with inequality constraint and then,optimality conditions for weak stationary points and the optimal solutions are given.%主要讨论了一类带概率互补约束的随机优化问题的最优性条件.首先利用一类非线性互补(NCP)函数将概率互补约束转化成为一个通常的概率约束.然后,利用概率约束的相关理论结果,将其等价地转化成一个带不等式约束的优化问题.最后给出了这类问题的弱驻点和最优解的最优性条件.
  • 摘要：High-dimensional constrained matrix regression refers to non-convex constrained statistical regression with the multivariate responses and multivariate predictors in the high-dimensional setting.Its mathematical model is a matrix optimization,which is generally NP-hard and has a wide range of applications in a lot of areas such as machine learning and artificial intelligence,medical imaging and diagnosis,gene expression analysis,neural networks,risk management.This paper briefly reviews the new results on optimization theory and algorithm of high-dimensional constrained matrix regression.Moreover,we list the corresponding important references.%高维约束矩阵回归是指高维情况下带非凸约束的多响应多预测统计回归问题,其数学模型是一个NP-难的矩阵优化,它在机器学习与人工智能、医学影像疾病诊疗、基因表达分析、脑神经网络、风险管理等领域有广泛应用.从高维约束矩阵回归的优化理论和算法两方面总结和评述这些新成果,同时,列出了相应的重要文献.
  • 摘要：The κ-means is one of the most classical problems in both computer science and combinatorial optimization.The κ-means clustering is popular as one of the most significant and easiest methods of cluster analysis in data mining.The κ-means problem can be described as:Given a set of observations with n elements,where each element is a d-dimensional real vector.The objective is to partition the n observations into κ sets,so as to minimize within-cluster sum of squares,where we call the center of the cluster the mean of the observations in it.The κ-means is NP-hard in theory however,there are efficient heuristic algorithms employed widely in market segmentation,machine vision,geostatistics,astronomy,agriculture and so on.With more and more complicated the problem we meet in practical,and larger and larger the data grows,further research is needed.This article aims at listing the classical algorithms for solving κ-means as well as the variety of the variants and generalization of it,and summarize some problems in κ-means which have not been solved for readers.%κ-平均问题是计算机科学和组合优化领域的经典问题之一.κ-平均聚类作为最受重视而且最简单易懂的一种聚类分析方法流行于数据挖掘领域.κ-平均问题可描述为:给定n个元素的观测集,其中每个观测点都是d维实向量,目标是把这n个观测点划分到κ(≤n)个集合中,使得所有集合中的点到对应的聚类中心的距离的平方和最小,其中一个集合的聚类中心指的是该集合中所有观测点的均值.κ-平均问题在理论上是NP-难的,但有高效的启发式算法,广泛应用在市场划分、机器视觉、地质统计学、天文学和农业等实际背景中.随着实际问题中遇到的κ-平均问题更加复杂,数据量更加庞大,还需学者进行更深一步的研究.罗列出k-平均问题及其诸多变形及推广问题的经典算法,并总结κ-平均中尚待研究的若干问题.
  • 摘要：The difficulties in optimizing the steady-state gas network are the complex structure and big scale of the network,high nonlinearities of the objective and the constraints.In this paper,we formulate the steady-state gas network optimization as a mixed integer nonlinear programming model.Then based on the techniques of network reduction and linearization,we develop a new algorithm for the problem.Numerical results on an instance of the western natural gas network of China show that the proposed algorithm is promising.%天然气稳态运行优化问题的难点在于网络结构复杂、规模大、目标函数及约束高度非线性.针对其混合整数非线性规划模型,基于网络约简和线性化技术,建立了线性近似模型,并提出一种新的求解算法.将新算法用于优化我国西部天然气管网系统,结果表明所提算法是有效的.
  • 摘要：考虑线性方程组l1范数间题的求解,在分别将其转化为一个分裂可行问题和凸可行问题的基础上,设计了几种松弛投影算法,然后将所设计的求解方法用于信号处理问题的求解上.%This paper discusses of the methods for solving the l1-norm problem of linear equations.First,the problem is translated into a split feasibility problem and a convex feasibility problem,respectively.Then,some relaxed projection algorithms are presented.Finally,the new algorithms are applied to solve some signal processing problems.
  • 摘要：图论、最优化理论显然在蛋白质结构的研究中大有用场.首先,调查/回顾了研究蛋白质结构的所有图论模型.其后,建立了一个图论模型:让蛋白质的侧链来作为图的顶点,应用图论的诸如团、κ-团、社群、枢纽、聚类等概念来建立图的边.然后,应用数学最优化的现代摩登数据挖掘算法/方法来分析水牛普里昂蛋白结构的大数据.成功与令人耳目一新的数值结果将展示给朋友们.%Graph theory and optimization theory are clearly very useful in the study of protein structures.Firstly,this paper is to research/review graph theory models in studies of protein structures.Secondly,we build a graph theory model to let the sidechain of a protein as a node,in the use of graph theory concepts such as clique,κ-clique,community,hub,and cluster to build the edges.Thirdly,we solve the graph theory model built,using optimization theory/modern data mining algorithms/methods.Successful and fresh numerical results of data mining the large scale buffalo prion protein database will be illuminated.
  • 摘要：A successive linearization method with flexible penalty is presented to solve a nonlinear semidefinite programming with nonlinear inequality constraints.The new method does not require the penalty function to be reduced and does not use filter technique.The storage of the filter set is avoided.The updating of the penalty parameter is flexible,which is only dependent on the message of the current iterate.The penalty parameter sequence corresponding to the successful iterate point does not need to increase monotonically.To decide whether the trial step can be accepted or not,the new method requires the measure of constraint violation to be improved or the value of the objective function to be improved within the measure of feasibility control.Under the usual assumptions,we prove that the algorithm is well defined and globally convergent.Finally,preliminary numerical results are reported.%针对非线性不等式约束半定规划问题提出一种新的逐次线性化方法,新算法既不要求罚函数单调下降,也不使用过滤技巧,尝试步的接受准则仅仅依赖于目标函数和约束违反度,罚函数中对应于成功迭代点的罚因子不需要单调增加.新算法或者要求违反约束度量有足够改善,或者在约束违反度的一个合理范围内要求目标函数值充分下降,在通常假设条件下,分析了新算法的适定性及全局收敛性.最后,给出了非线性半定规划问题的数值试验结果,结果表明了新算法的有效性.
  • 摘要：传统的求解0-1规划问题方法大多属于直接离散的解法.现提出一个包含严格转换和近似逼近三个步骤的连续化解法:(1)借助阶跃函数把0-1离散变量转化为[0,1]区间上的连续变量;(2)对目标函数采用逼近折中阶跃函数近光滑打磨函数,约束条件采用线性打磨函数逼近折中阶跃函数,把0-1规划问题由离散问题转化为连续优化模型;(3)利用高阶光滑的解法求解优化模型.该方法打破了特定求解方法仅适用于特定类型0-1规划问题惯例,使求解0-1规划问题的方法更加一般化.在具体求解时,采用正弦型光滑打磨函数来逼近折中阶跃函数,计算效果很好.%Traditional solutions of 0-1 programming problems belong mostly to direct discrete solving methods.A strict conversion for the problem and approximate continuous solution are proposed in this paper which have three steps:(1) 0-1 discrete variables were expressed as continuous variables on the interval [0,1] by means of a step function;(2) Objective function is approximated to take more near smooth polish function to approach tradeoff step function,and every constraint function is approximated to take linear polish function to approach tradeoff step function,then 0-1 programming problem is transformed to continuous optimization model from discrete problem;(3) The model is solved by using the method with high smoothness solution.This method breaks certain solving method applies only to certain types of 0-1 programming,so it can solve more general problems.During the solving process,a sinusoidal polish function is taken to obtain very good computational results.
  • 摘要：以往关于广义博弈Nash平衡的稳定性的研究,均利用可行策略映射之间的一致度量.现考虑在更弱的度量下,利用可行策略映射图像之间的Hausdorff距离定义度量.在此弱图像拓扑下,证明了广义博弈空间的完备性,以及Nash平衡映射的上半连续性和紧性,进而得到广义博弈Nash平衡的通有稳定性.即在Baire分类的意义下,大多数的广义博弈都是本质的.%For the stability of generalized games' Nash equilibria,current researches are investigated by uniform metric topology of feasible strategy correspondence.However,this paper presents a weaker metric and uses Hausdorff distance of graph of feasible strategy correspondence to study the stability of Nash equilibria.Under weaker graph topology,we prove that the space of generalized games is complete,and Nash equilibrium correspondence is upper semi-continuous and compact-valued.These lead to generic stability of generalized games' Nash equilibria,i.e.,in the sense of Baire category,most of generalized games are essential.
  • 摘要：非线性整数规划问题是一类复杂的优化问题,填充函数算法是求解整数规划问题的一类有效方法.构造一个新的单参数填充函数,分析并证明了其填充性质;然后,基于该填充函数并结合离散最速下降法提出了一种新的填充函数算法;最后,采用新算法对6个测试函数进行数值实验,结果表明该算法具有良好的计算效果,是有效可行的.%Nonlinear integer programming problem is a kind of complex optimization problem.The filled function algorithm is an effective method for solving integer programming problems.It involves an auxiliary function to move successively from one local minimum to another better one.At the same time,the method for using only the local minimization algorithm of mature and popular.However,most of the existing filled functions contain one or two interdependent parameters,which makes it difficult to select and adjust the parameters.And the filled function is a composite function of the objective function,and the objective function itself is more complex.Therefore,it is important to construct a filled function which is simple in form,with fewer parameters and good properties.To solve such problems,in this paper,firstly,we construct a new filled function with one parameter,analyze and prove its filling properties;then,the filled function combined with discrete steepest descent method and proposes a new filled function algorithm;finally,the implementation of the algorithms on six test problems show that the algorithm has good effect and is effective and feasible.
  • 摘要：The semistrong product of simple graphs G and H is the simple graph G·H with vertex set V(G) ×V(H),in which (u,v) is adjacent to (u',v') if and only if either u =u'and vv'∈ E(H) or uu'∈ E(G) and vv'∈ E(H).An adjacent vertex distinguishing edge (total) coloring of a graph is a proper edge (total) coloring of the graph such that no pair of adjacent vertices meets the same set of colors.The adjacent vertex distinguishing edge coloring and adjacent vertex distinguishing total coloring of a graph are collectively called the adjacent vertex distinguishing coloring of the graph.The minimum number of colors required for an adjacent vertex distinguishing coloring of G is called the adjacent vertex distinguishing chromatic number of G,and denoted by x(τ)a(G),where T =1,2,x(1)a(G) and x(2)a(G) denote the adjacent vertex distinguishing edge chromatic number and adjacent vertex distinguishing total chromatic number,respectively.An upper bound for these parameters of the semistrong product of two simple graphs G and H is given in this paper,and it is proved that the upper bound is attained precisely.Then the necessary and sufficient conditions is discussed which the two different semistrong product of two trees have the same the value of these parameters.Furthermore,the exact value of these parameters for the semistrong product of a class graphs and complete graphs are determined.%两个简单图G与H的半强积G·H是具有顶点集V(G)×V(H)的简单图,其中两个顶点(u,v)与(u',v')相邻当且仅当u=u'且vv'∈E(H),或uu'∈E(G)且vv'∈E(H).图的邻点可区别边(全)染色是指相邻点具有不同色集的正常边(全)染色.统称图的邻点可区别边染色与邻点可区别全染色为图的邻点可区别染色.图G的邻点可区别染色所需的最少的颜色数称为邻点可区别染色数,并记为x(τ)a(G),其中τ=1,2,且x(1)a(G)与x(2)a(G)分别表示G的邻点可区别的边色数与全色数.给出了两个简单图的半强积的邻点可区别染色数的一个上界,并证明了该上界是可达的.然后,讨论了两个树的不同半强积具有相同邻点可区别染色数的充分必要条件.另外,确定了一类图与完全图的半强积的邻点可区别染色数的精确值.
  • 摘要：引进了一种新的切锥,讨论它与相依切锥的关系.借助这种新的切锥引进了一类新的二阶组合切导数,并讨论了它与其他二阶切导数的关系.利用这类新的二阶组合切导数,建立了集值优化分别取得Henig有效元和全局有效元的最优性必要条件.%A new kind of tangent cones is introduced,whose relationship to the contingent cone is discussed.With the introduced cones,a new kind of second-order tangent derivatives,termed second-order composed tangent derivatives,is developed,and its relationship to other second-order composed tangent derivatives is discussed.Then,with the help of second-order composed tangent derivatives,optimality necessary conditions are established respectively for a Henig efficient solution and a globally proper efficient solution of set-valued optimization.
  • 摘要：Bilevel programming has been widely applied to economics,transportation,ecology,engineering and other fields.At present,the research of bilevel programming is mainly based on the strong bilevel programming and the weak bilevel programming.However,there are few studies on the solution methods to the weak bilevel programming.In this paper,we present a global optimization method for solving the weak linear bilevel programming problems (WLBPP).We first give the relations between the WLBPP and its relaxation problem with respect to their optimal solutions.Using the dual theory of linear programming and penalty function method,we then discuss the relations between the relaxation problem and its penalized problem.Furthermore,we develop a global optimization method,whose advantage is that it only requires solving several linear programming problems to obtain a globally optimal solution of the original problem,for solving the WLBPP.Finally,a simple example illustrates that the proposed method is feasible.%双层规划在经济、交通、生态、工程等领域有着广泛而重要的应用.目前对双层规划的研究主要是基于强双层规划和弱双层规划.然而,针对弱双层规划的求解方法却鲜有研究.研究求解弱线性双层规划问题的一种全局优化方法,首先给出弱线性双层规划问题与其松弛问题在最优解上的关系,然后利用线性规划的对偶理论和罚函数方法,讨论该松弛问题和它的罚问题之间的关系.进一步设计了一种求解弱线性双层规划问题的全局优化方法,该方法的优势在于它仅仅需要求解若干个线性规划问题就可以获得原问题的全局最优解.最后,用一个简单算例说明了所提出的方法是可行的.
  • 摘要：Calculating the genus distributions of double-path graphs is a concerned topic in topological graph theory.In this paper,by using transfer matrix method and a vectorized production matrix,the calculation formulas for the genus distributions of two types of graphs formed by double-path connect in series are derived.%计算双路图的亏格分布是拓扑图论关注的一个问题,利用传递矩阵与向量积矩阵,给出了两类由双路图串联构建而成的两类闭链图的亏格分布.
  • 摘要：In this paper,we derive the convergence problem of an intrinsic steepest descent algorithm for semi-supervised metric learning problem on symmetric positive definite matrices groups.We first rewrite semi-supervised metric learning problem into an unconstrained optimization problem on symmetric positive definite matrices groups.Then we present an intrinsic steepest descent algorithm with an adaptive iteration step-size.Moreover,we prove that the algorithm converges linearly by using a Taylor's expansion of smooth function at any point in Lie groups.Finally,we show a few numerical experiments on classification problem to demonstrate the effectiveness of the proposed algorithm.%主要研究对称正定矩阵群上的内蕴最速下降算法的收敛性问题.首先针对一个可转化为对称正定矩阵群上无约束优化问题的半监督度量学习模型,提出对称正定矩阵群上一种自适应变步长的内蕴最速下降算法.然后利用李群上的光滑函数在任意一点处带积分余项的泰勒展开式,证明所提算法在对称正定矩阵群上是线性收敛的.最后通过在分类问题中的数值实验说明算法的有效性.

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