共查询到18条相似文献,搜索用时 505 毫秒
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本文主要讨论了二次整数规划问题的线性化方法.在目标函数为二次函数的情况下,我们讨论了带有二次约束的整数规划问题的线性化方法,并将文献中对二次0-1问题的研究拓展为对带有盒约束的二次整数规划问题的研究.最终将带有盒约束的二次整数规划问题转化为线性混合本文主要讨论了二次整数规划问题的线性化方法.在目标函数为二次函数的情况下,我们讨论了带有二次约束的整数规划问题的线性化方法,并将文献中对二次0-1问题的研究拓展为对带有盒约束的二次整数规划问题的研究.最终将带有盒约束的二次整数规划问题转化为线性混合0-1整数规划问题,然后利用Ilog-cplex或Excel软件中的规划求解工具进行求解,从而解决原二次整数规划. 相似文献
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针对考虑协同信息的人员与岗位双边匹配问题,提出一种决策分析方法。首先,给出了考虑协同信息的人员与岗位双边匹配问题描述;其次,依据人员和岗位给出的多指标评价信息,计算了人员对岗位的满意度、岗位对人员的个体技能满意度及人员之间的工作协同度;在此基础上,建立了以人员对岗位满意度最大、岗位对人员个体技能满意度最大和人员之间协同度最大为目标的多目标优化模型,该模型是一个具有多目标的0-1型二次整数规划问题,也是一个NP-hard问题,为了求解该多目标优化模型,设计了一个多目标离散差分进化算法;最后,通过一个实例验证了所提方法的可行性和有效性。 相似文献
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一类特殊二维0-1规划的广义指派模型求解 总被引:2,自引:2,他引:0
二维0-1整数规划模型应用广泛,对广义指派问题的研究,解决了一些二维0-1整数规划问题.但有些实际问题具有特殊上限约束,目前还没有对应的方法.针对该实际情形,本文建立了相应的数学模型,利用对指派模型的推广,求得问题最优解,从理论上解决了这一类特殊约束二维0-1整数规划的最优解求取问题.并通过算例说明了方法的使用. 相似文献
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研究了2011年中国大学生数学建模竞赛B题的突发事件中交巡警对在逃嫌犯的围堵问题。不同于对该问题的以往的研究,本文考虑了交巡警在包围圈中可以占据某些路口,使得嫌犯不能通过这些被交巡警占据的路口,从而为形成包围圈的交巡警赢得更多时间。利用两篇相关文献的关于点截集判断的结论和考虑占位决策的建模方法,以不同的目标函数建立了考虑占位决策的围堵嫌犯问题的三个混合0-1非线性整数规划模型。通过选取部分线性约束和目标函数一起组合成混合0-1线性整数规划模型,设计了基于混合0-1线性整数规划方法的算法,并给出了算例。 相似文献
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本文探讨了一类N车探险问题的近似算法,首先通过建模将N车问题转变为一个等价的非线性0-1混合整数规划问题,进而将该非线性0-1混合整数规划问题转化为一个一般的带约束非线性规划问题,并用罚函数的方法将得到的带约束非线性规划问题化为相应的无约束问题.我们证明了可通过求解该无约束非线性规划问题得到原N车问题的ε-近似度的近似解,并设计了-个收敛速度为二阶的迭代箅法,文章最后给出算法实例. 相似文献
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《应用数学与计算数学学报》2015,(3)
研究一类混合0-1非凸二次约束二次规划问题的近似算法.该问题是在M个非凸二次约束与一个基数约束下,求解一个n维向量的极小范数,变量包含M个0-1变量与一个n维连续向量.该问题是NP-难的.在求解其半正定规划(SDP)松弛问题的基础上,提出了一种随机舍入算法,能够得到原始的问题的一个可行解.数值仿真实验结果表明该方法是十分有效的. 相似文献
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针对突发事件的应急救援人员分组问题,提出了一种考虑人员间协同效应的应急救援人员分组方法。首先,对突发事件应急救援人员分组问题进行了描述。然后,基于系统协同理论的思想,提出了救援小组的协同度模型,定量化的度量救援人员间的协同效应。进一步地,综合考虑救援人员的基础效能与协同效应,基于协同度模型给出了救援人员完成不同任务的实际效能的表达式。在此基础上,以最大化各救援小组的实际效能为目标,构建了突发事件应急救援人员分组的优化模型,并给出了将这一多目标0-1二次规划模型转换为单目标0-1线性规划模型的方法,进而可求解并确定救援人员的最优分组方案。最后,通过一个实例分析说明了本文所提出方法的可行性和有效性。 相似文献
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Parametric global optimisation for bilevel programming 总被引:2,自引:2,他引:0
Nuno P. Faísca Vivek Dua Berç Rustem Pedro M. Saraiva Efstratios N. Pistikopoulos 《Journal of Global Optimization》2007,38(4):609-623
We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based
on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower’s)
problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables
of the outer (leader’s) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem
is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved
to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without
right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global
optimisation strategy. 相似文献
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Lotte Verdonck Patrick Beullens An Caris Katrien Ramaekers Gerrit K Janssens 《The Journal of the Operational Research Society》2016,67(6):853-871
Transport companies may cooperate to increase their efficiency levels by, for example, the exchange of orders or vehicle capacity. In this paper a new approach to horizontal carrier collaboration is presented: the sharing of distribution centres (DCs) with partnering organisations. This problem can be classified as a cooperative facility location problem and formulated as an innovative mixed integer linear programme. To ensure cooperation sustainability, collaborative costs need to be allocated fairly to the different participants. To analyse the benefits of cooperative facility location and the effects of different cost allocation techniques, numerical experiments based on experimental design are carried out on a UK case study. Sharing DCs may lead to significant cost savings up to 21.6%. In contrast to the case of sharing orders or vehicles, there are diseconomies of scale in terms of the number of partners and more collaborative benefit can be expected when partners are unequal in size. Moreover, results indicate that horizontal collaboration at the level of DCs works well with a limited number of partners and can be based on intuitively appealing cost sharing techniques, which may reduce alliance complexity and enforce the strength of mutual partner relationships. 相似文献
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In the case of large-scale surveys, such as a Census, data may contain errors or missing values. An automatic error correction procedure is therefore needed. We focus on the problem of restoring the consistency of agricultural data concerning cultivation areas and number of livestock, and we propose here an approach to this balancing problem based on optimization. Possible alternative models, either linear, quadratic or mixed integer, are presented. The mixed integer linear one has been preferred and used for the treatment of possibly unbalanced data records. Results on real-world Agricultural Census data show the effectiveness of the proposed approach. 相似文献
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求解中大规模复杂凸二次整数规划问题的新型分枝定界算法 总被引:1,自引:0,他引:1
针对现有分枝定界算法在求解高维复杂二次整数规划问题时所存在的诸多不足,本文通过充分挖掘二次整数规划问题的结构特性来设计选择分枝变量与分枝方向的新方法,并将HNF算法与原问题松弛问题的求解相结合来寻求较好的初始整数可行解,由此导出可用于有效求解中大规模复杂二次整数规划问题的改进型分枝定界算法.数值试验结果表明所给算法大大改进了已有相关的分枝定界算法,并具有较好的稳定性与广泛的适用性. 相似文献
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We present a new continuous approach based on the DC (difference of convex functions) programming and DC algorithms (DCA) to the problem of supply chain design at the strategic level when production of a new market opportunity has to be launched among a set of qualified partners. A well known formulation of this problem is the mixed integer linear program. In this paper, we reformulate this problem as a DC program by using an exact penalty technique. The proposed algorithm is a combination of DCA and Branch and Bound scheme. It works in a continuous domain but provides mixed integer solutions. Numerical simulations on many empirical data sets show the efficiency of our approach with respect to the standard Branch and Bound algorithm. 相似文献
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Convex integer quadratic programming involves minimization of a convex quadratic objective function with affine constraints and is a well-known NP-hard problem with a wide range of applications. We proposed a new variable reduction technique for convex integer quadratic programs (IQP). Based on the optimal values to the continuous relaxation of IQP and a feasible solution to IQP, the proposed technique can be applied to fix some decision variables of an IQP simultaneously at zero without sacrificing optimality. Using this technique, computational effort needed to solve IQP can be greatly reduced. Since a general convex bounded IQP (BIQP) can be transformed to a convex IQP, the proposed technique is also applicable for the convex BIQP. We report a computational study to demonstrate the efficacy of the proposed technique in solving quadratic knapsack problems. 相似文献
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Yi‐Fei Pu Patrick Siarry Ji‐Liu Zhou Ni Zhang 《Mathematical Methods in the Applied Sciences》2014,37(12):1784-1806
Traditional integer‐order partial differential equation based image denoising approach can easily lead edge and complex texture detail blur, thus its denoising effect for texture image is always not well. To solve the problem, we propose to implement a fractional partial differential equation (FPDE) based denoising model for texture image by applying a novel mathematical method—fractional calculus to image processing from the view of system evolution. Previous studies show that fractional calculus has some unique properties that it can nonlinearly enhance complex texture detail in digital image processing, which is obvious different with integer‐order differential calculus. The goal of the modeling is to overcome the problems of the existed denoising approaches by utilizing the aforementioned properties of fractional differential calculus. Using classic definition and property of fractional differential calculus, we extend integer‐order steepest descent approach to fractional field to implement fractional steepest descent approach. Then, based on the earlier fractional formulas, a FPDE based multiscale denoising model for texture image is proposed and further analyze optimal parameters value for FPDE based denoising model. The experimental results prove that the ability for preserving high‐frequency edge and complex texture information of the proposed fractional denoising model are obviously superior to traditional integral based algorithms, as for texture detail rich images. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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Osman Y. ?zalt?n Oleg A. Prokopyev Andrew J. Schaefer 《Mathematical Programming》2012,133(1-2):121-158
We consider two-stage quadratic integer programs with stochastic right-hand sides, and present an equivalent reformulation using value functions. We propose a two-phase solution approach. The first phase constructs value functions of quadratic integer programs in both stages. The second phase solves the reformulation using a global branch-and-bound algorithm or a level-set approach. We derive some basic properties of value functions of quadratic integer programs and utilize them in our algorithms. We show that our approach can solve instances whose extensive forms are hundreds of orders of magnitude larger than the largest quadratic integer programming instances solved in the literature. 相似文献