2017 Vol.21

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CVaR robust mean-CVaR portfolio optimization  model and the solving methods KANG Zhilin, LI Zhongfei Operations Research Transactions    2017, 21 (1): 1-12.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.001 Abstract （1606）      PDF（pc） （649KB）（739）       Knowledge map    Save When calculating the optimal portfolios,  the traditional mean-risk (including variance, value-at-risk (VaR), conditional value at risk (CVaR)) optimization model often assumes that mean returns are known constant values. In actual asset allocation, however, estimation of mean return will have deviation, namely there exists risk of estimation. On the basis of estimating the risk measured by CVaR, this paper further studies CVaR robust mean-CVaR portfolio optimization model and presents two different optimization algorithms, namely, the dual method and the smoothing method. Moreover, we explore some properties and characteristics of the two methods. Finally, we give some numerical experiments to show the feasibility and effectiveness of these two methods. Reference | Related Articles | Metrics | Comments（0）

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Two-agent scheduling problem about total late  work on a single machine MA Lu, ZHANG Xingong Operations Research Transactions    2017, 21 (1): 13-22.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.002 Abstract （881）      PDF（pc） （509KB）（382）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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The epsilon-weak proper efficiency of multiobjective  semidefinite programming with set-valued maps YUAN Chunhong Operations Research Transactions    2017, 21 (1): 23-32.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.003 Abstract （908）      PDF（pc） （557KB）（346）       Knowledge map    Save epsilon-weak efficient solutions of multiobjective semidefinite programming with set-valued maps are discussed. Under the condition of nearly cone-subconvexlikeness, the alternative theorem which contained matrix and vector is established, then the epsilon-Lagrange multiplier theorem, the scalarization theorem and epsilon-weak saddle point theorem of the primal programming are obtained. Reference | Related Articles | Metrics | Comments（0）

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A new class of simple smooth exact penalty functions  for equality constrained optimization problems LIAN Shujun, DU Aihua, TANG Jiahui Operations Research Transactions    2017, 21 (1): 33-43.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.004 Abstract （1143）      PDF（pc） （538KB）（564）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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Differential evolution algorithm with double  mutation strategies for improving population diversity LI Rongyu, CHEN Qingqian, CHEN Feier Operations Research Transactions    2017, 21 (1): 44-54.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.005 Abstract （1108）      PDF（pc） （1395KB）（560）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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A filled-filter function algorithm for solving  unconstrained nonlinear optimization SHI Litang, CHEN Wei Operations Research Transactions    2017, 21 (1): 55-64.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.006 Abstract （963）      PDF（pc） （554KB）（409）       Knowledge map    Save In this article, we proposed a filled function with parameter free for solving  unconstrained nonlinear programming problems, and analysed its properties.  With the help of the introduced filter method,  we constructed a parameter free filled-filter function algorithm. Numerical experiments showed that the algorithm is effective. Reference | Related Articles | Metrics | Comments（0）

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A generalized trapezoidal approximation operator and  its application to fuzzy transportation problems XIE Haibin, CHEN Disan, LIANG Yanyan Operations Research Transactions    2017, 21 (1): 65-77.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.007 Abstract （1235）      PDF（pc） （1036KB）（437）       Knowledge map    Save This paper studies fuzzy transportation problems with general fuzzy transportation costs. Firstly, by preserving the core of a generalized fuzzy number, the minimal optimization model is structured based on the distance between general fuzzy numbers and general trapezoidal fuzzy numbers. By solving the optimization model, a generalized trapezoidal approximation operator is obtained and some properties of the operator are studied such as scale invariance, translation invariance, continuity. Secondly, the approximation operator is used to convert generalized fuzzy transportation table to generalized trapezoidal fuzzy transportation table. Moreover, the existing GFLCM and GFMDM algorithms are used to get the nearest optimal solution of fuzzy transportation problems. Finally, a numerical example is presented to illustrate the feasibility and validity of the proposed method. Reference | Related Articles | Metrics | Comments（0）

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Maintenance strategy of restricted working time for single-unit repairable system CHENG Xiaoxuan, YUE Dequan, ZHAO Bing Operations Research Transactions    2017, 21 (1): 78-86.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.008 Abstract （895）      PDF（pc） （1021KB）（283）       Knowledge map    Save By applying the geometric process theory, the optimal repair replacement policy for a single-unit system with limited working time is studied in this paper. Assuming that the maintenance time and working time obey the general distribution, when the working time is lower than the settled threshold phi, or if the system is repaired N times, the system will be replaced. By using the theory of renewal process, some reliability indices including the average occurrence of failure and average availability for the system are obtained. The function expression for long-run expected benefit is also obtained. Finally, by numerical simulation, the effects of the lower threshold and the working times on optimal strategy are discussed. Reference | Related Articles | Metrics | Comments（0）

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Simulation of value of CM strategy multi-period  return guarantee under asset jump HE Zhiquan Operations Research Transactions    2017, 21 (1): 87-102.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.009 Abstract （1088）      PDF（pc） （1691KB）（352）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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Two families of trees determined by  their Laplacian spectrum ZHANG Tao, BAI Yanqin Operations Research Transactions    2017, 21 (1): 103-110.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.010 Abstract （958）      PDF（pc） （3190KB）（339）       Knowledge map    Save 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 Y_n 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. Reference | Related Articles | Metrics | Comments（0）

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A look at the convergence of the augmented  Lagrange method for nondifferentiable convex programming from  the view of a gradient method with constant stepsize TIAN Zhaowei, ZHANG Liwei Operations Research Transactions    2017, 21 (1): 111-117.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.011 Abstract （1203）      PDF（pc） （500KB）（485）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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Spectral sufficient conditions on traceable graphs YU Guidong, ZHOU Fu, LIU Qi Operations Research Transactions    2017, 21 (1): 118-124.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.012 Abstract （1209）      PDF（pc） （471KB）（437）       Knowledge map    Save Let G be a simple graph, A(G), Q(G) and Q(G) are the adjacency matrix, the signless Laplacian matrix, and the distance signless Laplacian matrix of G, respectively. The largest eigenvalues of A(G), Q(G) and Q(G) are called the spectral radius, the signless Laplacian spectral radius and the distance signless Laplacian spectral radius of G, respectively. A path is called a Hamilton path if it contains all vertices of G. A graph is traceable if it contains a Hamilton path. A graph is traceable from every vertex if it contains a Hamilton path from every vertex. The main research of this paper is to give some sufficient conditions for a graph to be traceable from every vertex in terms of spectral radius, signless Laplacian spectral radius and distance signless Laplacian spectral radius of the graph, respectively. Reference | Related Articles | Metrics | Comments（0）

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A note on total domination in 5-regular graphs LI Shan, SHAN Erfang, ZHANG Lin Operations Research Transactions    2017, 21 (1): 125-128.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.013 Abstract （977）      PDF（pc） （434KB）（396）       Knowledge map    Save 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 \gamma_t(G). Recently, Thomass\'e and Yeo showed that \gamma_t(G)\le 17n/44 for a connected graph G of order n with minimum degree at least five. In this paper we prove that \gamma_t(G)\le 106n/275 for a 5-regular graph G of order n, which improves sightly the bound of Thomass\'e and Yeo. Reference | Related Articles | Metrics | Comments（0） Cited: Baidu(4)

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Supply chain coordination model with  time-varying demand depending on stock and selling price under carbon tax regulation ZHANG Yuzhong, BAI Qingguo Operations Research Transactions    2017, 21 (2): 1-12.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.001 Abstract （1071）      PDF（pc） （1263KB）（706）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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A mixed integer model and an algorithm for steady-state gas network optimization HUANG Yakui, LI Bo, KANG Yang, DAI Yuhong, LIU Jianjun Operations Research Transactions    2017, 21 (2): 13-23.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.002 Abstract （1195）      PDF（pc） （616KB）（594）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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Optimality conditions for a class of stochastic optimization problems with probabilistic complementarity constraints CHEN Lin, YANG Xinmin Operations Research Transactions    2017, 21 (2): 24-30.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.003 Abstract （835）      PDF（pc） （469KB）（445）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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High-dimensional constrained matrix regression problems KONG Lingchen, CHEN Bingzhen, XIU Naihua, QI Houduo Operations Research Transactions    2017, 21 (2): 31-38.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.004 Abstract （949）      PDF（pc） （573KB）（568）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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Complexity concepts for combinatorial and continuous optimization problems XING Wenxun Operations Research Transactions    2017, 21 (2): 39-45.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.005 Abstract （1770）      PDF（pc） （502KB）（560）       Knowledge map    Save  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. Reference | Related Articles | Metrics | Comments（0）

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Nonlinear dynamic system of batch fermentation with the function as parameters and identification YANG Qi, JIANG Zhigang, FENG Enmin, YIN Hongchao, XIU Zhilong Operations Research Transactions    2017, 21 (2): 46-56.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.006 Abstract （759）      PDF（pc） （782KB）（340）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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The relaxed projection methods for solving the  l_1-norm problem of linear equations and their applications QU Biao, ZHANG Wenwei, YU Lichao Operations Research Transactions    2017, 21 (2): 57-65.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.007 Abstract （1011）      PDF（pc） （1101KB）（511）       Knowledge map    Save This paper discusses of the methods for solving the l_1-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. Reference | Related Articles | Metrics | Comments（0）

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Two-machine flow-shop scheduling with deterioration and rejection MIAO Cuixia, MENG Fanxiao Operations Research Transactions    2017, 21 (2): 66-72.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.008 Abstract （998）      PDF（pc） （470KB）（336）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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Using graph theory and optimization theory to do data mining the large scale buffalo prion protein structure database ZHANG Jiapu, CHATTERJEE Subhojyoti, WANG Feng Operations Research Transactions    2017, 21 (2): 73-83.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.009 Abstract （1095）      PDF（pc） （3468KB）（612）       Knowledge map    Save  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 side-chain of a protein as a node, in the use of graph theory concepts such as clique, k-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. Reference | Related Articles | Metrics | Comments（0）

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A successive linearization method with flexible penalty for nonlinear semidefinite programming CHEN Zhongwen, ZHAO Qi, BIAN Kai Operations Research Transactions    2017, 21 (2): 84-100.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.010 Abstract （1034）      PDF（pc） （545KB）（571）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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A survey on algorithms for k-means problem and its variants XU Dachuan, XU Yicheng, ZHANG Dongmei Operations Research Transactions    2017, 21 (2): 101-109.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.011 Abstract （1041）      PDF（pc） （525KB）（584）       Knowledge map    Save The k-means is one of the most classical problems in both computer science and combinatorial optimization. The k-means clustering is popular as one of the most significant and easiest methods of cluster analysis in data mining. The k-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 k 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 k-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 k-means as well as the variety of the variants and generalization of it, and summarize some problems in k-means which have not been solved for readers. Reference | Related Articles | Metrics | Comments（0）

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Group decision making method based on single valued neutrosophic Choquet integral operator HAN Lili, WEI Cuiping Operations Research Transactions    2017, 21 (2): 110-118.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.012 Abstract （945）      PDF（pc） （535KB）（337）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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The smoothing gradient method for a kind of special optimization problem CHEN Yuanyuan, GAO Yan, LIU Zhimin, DU Shouqiang Operations Research Transactions    2017, 21 (2): 119-125.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.013 Abstract （726）      PDF（pc） （1895KB）（580）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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Two-stage supply chain scheduling with a limited holding time ZHANG Long Operations Research Transactions    2017, 21 (2): 126-134.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.014 Abstract （864）      PDF（pc） （516KB）（494）       Knowledge map    Save 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. Reference | Related Articles | Metrics | Comments（0）

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Convergence analysis of an intrinsic steepest descent method on semi-supervised metric learning LI Xin, BAI Yanqin Operations Research Transactions    2017, 21 (3): 1-13.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.03.001 Abstract （1132）      PDF（pc） （1389KB）（486）       Knowledge map    Save 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. Related Articles | Metrics | Comments（0）

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Single machine scheduling with dynamic delivery cost and fixed delivery dates WANG Lei, ZHANG Yuzhong, XING Wei, REN Jianfeng Operations Research Transactions    2017, 21 (3): 14-22.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.03.002 Abstract （1198）      PDF（pc） （530KB）（339）       Knowledge map    Save This paper considers a coordination scheduling of production and delivery on a single machine. A customer places some jobs to a manufacturer at the planning horizon. Processed jobs are delivered in batches to their customer. Each batch can dispatch to its customer at some fixed delivery dates, and different delivery dates corresponding to different delivery cost. The objective is to find a coordinated production-and-delivery schedule to minimize the weighted sum of the scheduling cost and delivery cost. We consider four main objective functions in scheduling theory, construct the models in single machine environment, analyze the problem complexity and give optimal algorithms to solve the problems under the constraint that the delivery cost are non-increasing with respect to time. Related Articles | Metrics | Comments（0）

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The crossing number of the join product of C_6+3K_2 with P_n and C_n SU Zhenhua Operations Research Transactions    2017, 21 (3): 23-34.   Abstract （756）      PDF（pc） （656KB）（272）       Knowledge map    Save Let P_n be the path on n vertices, C_n be the cycle with n edges, C_6+3K_2 be the graph which is obtained from the cycle C_6 by adding three adjacent edges. In the paper, for special graph C_6+3K_2, we give the crossing numbers of its join product with the path P_n as well as the cycle C_n are Z(6,n)+3\lfloor \frac{n}{2} \rfloor+2 and Z(6,n)+3\lfloor \frac{n}{2} \rfloor+4. Our proof depends on Kleitman's results for the complete bipartite graph cr(K_{6,n})=Z(6,n). Related Articles | Metrics | Comments（0）

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Continuous solution method for 0-1 programming based on the sinusoidal smooth polish function SUI Yunkang, LI Zhenzhen, LI Hong, CHEN Guoqing Operations Research Transactions    2017, 21 (3): 35-44.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.03.004 Abstract （1282）      PDF（pc） （902KB）（210）       Knowledge map    Save 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. Related Articles | Metrics | Comments（0）

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A new kind of second-order composed tangent derivatives and its applications ZHOU Lixia, XU Yihong, L\"{U} Qiang Operations Research Transactions    2017, 21 (3): 45-54.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.03.005 Abstract （1003）      PDF（pc） （496KB）（204）       Knowledge map    Save 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. Related Articles | Metrics | Comments（0）

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Genus distributions of double-path in series graphs ZHANG Xianglin, HUANG Yuanqiu, GUO Ting Operations Research Transactions    2017, 21 (3): 55-64.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.03.006 Abstract （974）      PDF（pc） （1111KB）（230）       Knowledge map    Save 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. Related Articles | Metrics | Comments（0）

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Analysis and optimal control policy N* for Geo^{lambda_1, lambda_2}/Geo/1(MWV) queueing system with negative customers and N-policy PAN Quyu, TANG Yinghui, LAN Shaojun Operations Research Transactions    2017, 21 (3): 65-76.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.03.007 Abstract （1045）      PDF（pc） （1191KB）（255）       Knowledge map    Save This paper deals with a discrete-time Geo/Geo/1 working vacations queue with negative customers and N-policy control in which the positive customers arrive at the system in different input rates during the working vacation period and the normal busy period.  Employing the quasi birth-death process and the matrix-geometric solution method, we derive the steady-state queue length distribution and the expected queue length, as well as the steady-state probabilities that the system is in working vacation state and busy state. Meanwhile, the busy period and the application for the steady state queue length distribution in system capacity optimum design are discussed. Finally, through numerical calculation, it is determined the optimal control policy N* such that the long-run expected cost rate is minimum under a given cost structure. Related Articles | Metrics | Comments（0）

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The stability of Nash equilibria for generalized games under graph topology of feasible strategy correspondence CHEN Pinbo, WANG Nengfa, QIU Xiaoling, WANG Chun Operations Research Transactions    2017, 21 (3): 77-85.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.03.008 Abstract （966）      PDF（pc） （570KB）（239）       Knowledge map    Save 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. Related Articles | Metrics | Comments（0）

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A global optimization method for solving the weak linear bilevel programming problems ZHENG Yue, ZHUANG Daoyuan, WAN Zhongping Operations Research Transactions    2017, 21 (3): 86-94.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.03.009 Abstract （1195）      PDF（pc） （525KB）（300）       Knowledge map    Save 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. Related Articles | Metrics | Comments（0）

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Nonsmooth Newton method for solving symmetrical tensor absolute value equations LIANG Na, DU Shouqiang Operations Research Transactions    2017, 21 (3): 95-102.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.03.010 Abstract （1063）      PDF（pc） （541KB）（263）       Knowledge map    Save In this paper, we propose a kind of  symmetrical tensor absolute value equations. And a kind of nonsmooth Newton method is also proposed. Under mild assumption, the local convergence of the method is given. Finally, numerical results indicate the efficiency of the method. Related Articles | Metrics | Comments（0）

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Bounds of the general Randi\'{c} Estrada index of a graph GAO Nan, LI Meili, SHE Yanhong Operations Research Transactions    2017, 21 (3): 103-110.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.03.011 Abstract （956）      PDF（pc） （494KB）（239）       Knowledge map    Save Motivated by the Randi\'{c} Estrada index and the general Randi\'{c} energy of a graph, we define the concept of general Randi\'{c} Estrada index of a graph. By using the algebraic and elementary analysis method, we obtain lower and upper bounds for the general Randi\'{c} Estrada index of a simple connected graph of order n and an r-regular graph, which generalize the results of Bozkurt et. al. on the Randi\'{c} Estrada of a graph. Related Articles | Metrics | Comments（0）

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A new single parameter filled function method for nonlinear integer programming WU Peipei, GAO Yuelin Operations Research Transactions    2017, 21 (3): 111-118.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.03.012 Abstract （1038）      PDF（pc） （518KB）（255）       Knowledge map    Save 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. Related Articles | Metrics | Comments（0）

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Adjacent vertex-distinguishing colorings of the semistrong product of graphs TIAN Shuangliang, DONG Xinfang, LIU Ruilin Operations Research Transactions    2017, 21 (3): 119-125.   DOI: 10.15960/j.cnki.issn.1007-6093.2017.03.013 Abstract （1015）      PDF（pc） （554KB）（227）       Knowledge map    Save The semistrong product of simple graphs G and H is the simple graph G\bullet H with vertex set V(G)\times V(H), in which (u,v) is adjacent to (u',v') if and only if either u=u' and vv'\in E(H) or uu'\in E(G) and vv'\in 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 \chi^{(\tau)}_{a}(G), where \tau=1,2, \chi^{(1)}_{a}(G) and \chi^{(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. Related Articles | Metrics | Comments（0）

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