共查询到20条相似文献,搜索用时 15 毫秒
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Audet C. Hansen P. Jaumard B. Savard G. 《Journal of Optimization Theory and Applications》1997,93(2):273-300
We study links between the linear bilevel and linear mixed 0–1 programming problems. A new reformulation of the linear mixed 0–1 programming problem into a linear bilevel programming one, which does not require the introduction of a large finite constant, is presented. We show that solving a linear mixed 0–1 problem by a classical branch-and-bound algorithm is equivalent in a strong sense to solving its bilevel reformulation by a bilevel branch-and-bound algorithm. The mixed 0–1 algorithm is embedded in the bilevel algorithm through the aforementioned reformulation; i.e., when applied to any mixed 0–1 instance and its bilevel reformulation, they generate sequences of subproblems which are identical via the reformulation. 相似文献
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Mixed-integer rounding (MIR) inequalities play a central role in the development of strong cutting planes for mixed-integer
programs. In this paper, we investigate how known MIR inequalities can be combined in order to generate new strong valid inequalities.?Given
a mixed-integer region S and a collection of valid “base” mixed-integer inequalities, we develop a procedure for generating new valid inequalities
for S. The starting point of our procedure is to consider the MIR inequalities related with the base inequalities. For any subset
of these MIR inequalities, we generate two new inequalities by combining or “mixing” them. We show that the new inequalities
are strong in the sense that they fully describe the convex hull of a special mixed-integer region associated with the base
inequalities.?We discuss how the mixing procedure can be used to obtain new classes of strong valid inequalities for various
mixed-integer programming problems. In particular, we present examples for production planning, capacitated facility location,
capacitated network design, and multiple knapsack problems. We also present preliminary computational results using the mixing
procedure to tighten the formulation of some difficult integer programs. Finally we study some extensions of this mixing procedure.
Received: April 1998 / Accepted: January 2001?Published online April 12, 2001 相似文献
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Classical Cuts for Mixed-Integer Programming and Branch-and-Cut 总被引:2,自引:0,他引:2
We review classical valid linear inequalities for mixed-integer programming, i.e., Gomory's fractional and mixed-integer cuts,
and discuss their use in branch-and-cut. In particular, a generalization of the recent mixed-integer rounding (MIR) inequality
and a sufficient condition for the global validity of classical cuts after branching has occurred are derived.
Work supported in part by a grant from the Office of Naval Research (N00014-96-0327). Reprinted from Math. Meth. Oper. Res. (2001) 53, 173–203. 相似文献
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本文针对线性双层规划问题提出一个由KMY算法演变而来的原对偶内点算法.与现在很多线性双层规划单纯型算法不同,作者提出的算法从一可行初始点穿过约束多面体内部直接得到近似最优解,当约束条件和变量数目增加时,本算法的迭代次数和计算时间变化很小.所以大大提高实际可操作性能和运算效率. 相似文献
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J. Glackin J. G. Ecker M. Kupferschmid 《Journal of Optimization Theory and Applications》2009,140(2):197-212
We present an algorithm for solving bilevel linear programs that uses simplex pivots on an expanded tableau. The algorithm
uses the relationship between multiple objective linear programs and bilevel linear programs along with results for minimizing
a linear objective over the efficient set for a multiple objective problem. Results in multiple objective programming needed
are presented. We report computational experience demonstrating that this approach is more effective than a standard branch-and-bound
algorithm when the number of leader variables is small. 相似文献
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多表旋转算法是一种基于旋转算法来求解线性二层规划问题的方法,通过表格组合还可以求解线性多层规划、以及线性一主多从有关联的stackelberg-nash均衡等问题,求解的思想是使用旋转算法,在多个主体间通过约束传递达到均衡。通过算例显示该方法可以迅速地算出局部最优解,如果问题的诱导域是连通的,还可以计算出全局最优解。 相似文献
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Global Optimization of Nonlinear Bilevel Programming Problems 总被引:5,自引:0,他引:5
A novel technique that addresses the solution of the general nonlinear bilevel programming problem to global optimality is presented. Global optimality is guaranteed for problems that involve twice differentiable nonlinear functions as long as the linear independence constraint qualification condition holds for the inner problem constraints. The approach is based on the relaxation of the feasible region by convex underestimation, embedded in a branch and bound framework utilizing the basic principles of the deterministic global optimization algorithm, BB [2, 4, 5, 11]. Epsilon global optimality in a finite number of iterations is theoretically guaranteed. Computational studies on several literature problems are reported. 相似文献
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The bilevel programming problem (BLPP) is equivalent to a two-person Stackelberg game in which the leader and follower pursue individual objectives. Play is sequential and the choices of one affect the choices and attainable payoffs of the other. The purpose of this paper is to investigate an extension of the linear BLPP where the objective functions of both players are bilinear. To overcome certain discontinuities in the master problem, a regularized term is added to the follower objective function. Using ideas from parametric programming, the generalized Jacobian and the pseudodifferential of the regularized follower solution function are computed. This allows us to develop a bundle trust-region algorithm. Convergence analysis of the proposed methodology is given. 相似文献
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本文利用重新排列下标的技巧,提出了一个新的criss-cross算法.并证明了其有限性,理论分析及初步的计算实验表明,新算法比最小下标criss-cross算法效率更高. 相似文献
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A novel approach to Bilevel nonlinear programming 总被引:3,自引:3,他引:0
Recently developed methods of monotonic optimization have been applied successfully for studying a wide class of nonconvex
optimization problems, that includes, among others, generalized polynomial programming, generalized multiplicative and fractional
programming, discrete programming, optimization over the efficient set, complementarity problems. In the present paper the
monotonic approach is extended to the General Bilevel Programming GBP Problem. It is shown that (GBP) can be transformed into
a monotonic optimization problem which can then be solved by “polyblock” approximation or, more efficiently, by a branch-reduce-and-bound
method using monotonicity cuts. The method is particularly suitable for Bilevel Convex Programming and Bilevel Linear Programming.
相似文献
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双层线性规划的一个全局优化方法 总被引:7,自引:0,他引:7
用线性规划对偶理论分析了双层线性规划的最优解与下层问题的对偶问题可行域上极点之间的关系,通过求得下层问题的对偶问题可行域上的极点,将双层线性规划转化为有限个线性规划问题,从而用线性规划方法求得问题的全局最优解.由于下层对偶问题可行域上只有有限个极点,所以方法具有全局收敛性. 相似文献
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通过分析双层线性规划可行域的结构特征和全局最优解在约束域的极点上达到这一特性,对单纯形方法中进基变量的选取法则进行适当修改后,给出了一个求解双层线性规划局部最优解方法,然后引进上层目标函数对应的一种割平面约束来修正当前局部最优解,直到求得双层线性规划的全局最优解.提出的算法具有全局收敛性,并通过算例说明了算法的求解过程. 相似文献
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基于双层线性分式规划的性质,讨论了上层不带约束的双层线性分式规划模型,给出了求其所有顶点的算法.此算法为进一步进行双层线性分式规划的灵敏度分析打下了坚实的基础,通过例子对算法进行了检验,并利用结果进行了灵敏度分析. 相似文献
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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