Plane Algorithm(平面算法)研究综述
Plane Algorithm 平面算法 - the cutting-plane algorithm, is developed. [1] We combine both techniques in a basic cutting-plane algorithm and test the performance of the resulting algorithm by running it on randomly generated instances. [2] 8786 against an oblivious adversary (here αGW is the approximation achieved by the random hyperplane algorithm of [Goemans-Williamson J. [3] For computational efficiency, our proposed method integrates two cutting-plane algorithms, upper-level cutting-plane algorithm and lower-level one, and each algorithm solves the master problem and the subproblem, respectively. [4] The core of these systems has packet-processing data-plane algorithms that continuously monitor traffic and respond automatically. [5] We develop a new cutting-plane algorithm to strengthen the M-SMIP formulation and facilitate an optimal solution. [6] Nowadays stateful data-plane algorithms are developing in software-defined networks. [7] We use the primal bounds provided by a state-of-the-art cutting-plane algorithm from the literature to evaluate the quality of the solutions obtained by the heuristic. [8] We then present a novel cutting-plane algorithm to solve these problems. [9] This surrogate is then embedded into a design centering problem, formulated as a semi-infinite program and solved using a cutting-plane algorithm. [10] However, optimizing over the semi-metric polytope can be computationally demanding due to the slow convergence of cutting-plane algorithms and the high degeneracy of formulations based on the triangle inequalities. [11] Numerical implementation of the model features an Euler discretization and a cutting-plane algorithm. [12] An exact method using an extension of a cutting-plane algorithm from the literature is proposed and compared with an LP-relaxation heuristic method. [13] In addition, we implement a central cutting-plane algorithm for LSIP to quantify entanglement between three qubits. [14] Under reasonable assumptions, we can derive both a multi- and a single-tree outer-approximation-based cutting-plane algorithm. [15] We develop and analyze an exact solution approach for this problem based on a cutting-plane algorithm. [16] The probabilistic storage planning problem is further decomposed into an upper- level problem and several lower-level problems, and solved via a sub-gradient cutting-plane algorithm. [17] We use a cutting-plane algorithm that relies on the early termination of an interior point method, and we study the performance of SDP and linear programming (LP) relaxations for various values of k and instance types. [18] For the previously known class of facet inequalities of the polytope of the problem, the cutting-plane algorithm is developed. [19] Moreover, an algorithm called modified steepest ascent cutting-plane algorithm is proposed to efficiently compute the IID capacity-achieving distributions. [20] We develop a cutting-plane algorithm to solve the resulting optimization problem. [21] To suppress the search error induced noisy images, we then formulate image selection and classifier learning as a multi-instance learning problem and propose to solve the employed problem by the cutting-plane algorithm. [22] The first-stage decision variables are determined using a cutting-plane algorithm to solve a robust unit commitment; the second stage solves the final dispatch commands using a three-phase optimal power flow. [23] A cutting-plane algorithm is proposed to solve the model under important methods commonly used to deal with a bi-objective model. [24]开发了切割平面算法。 [1] 我们将这两种技术结合在一个基本的切割平面算法中，并通过在随机生成的实例上运行它来测试结果算法的性能。 [2] 8786 对抗不经意的对手（这里 αGW 是 [Goemans-Williamson J. [3] 为了计算效率，我们提出的方法集成了两种切面算法，上层切面算法和下层切面算法，每种算法分别解决主问题和子问题。 [4] 这些系统的核心具有数据包处理数据平面算法，可以持续监控流量并自动响应。 [5] 我们开发了一种新的切割平面算法来加强 M-SMIP 公式并促进最佳解决方案。 [6] 如今，有状态的数据平面算法正在软件定义的网络中发展。 [7] 我们使用文献中最先进的切割平面算法提供的原始边界来评估启发式获得的解决方案的质量。 [8] 然后，我们提出了一种新的切割平面算法来解决这些问题。 [9] 然后将该代理嵌入到设计中心问题中，将其表述为半无限程序并使用切割平面算法进行求解。 [10] 然而，由于切割平面算法的缓慢收敛和基于三角形不等式的公式的高度退化，对半度量多面体进行优化可能在计算上要求很高。 [11] 该模型的数值实现具有欧拉离散化和切割平面算法。 [12] 提出了一种使用文献中切割平面算法扩展的精确方法，并与 LP 松弛启发式方法进行了比较。 [13] 此外，我们为 LSIP 实现了一个中心切割平面算法，以量化三个量子位之间的纠缠。 [14] 在合理的假设下，我们可以推导出基于多树和单树外近似的切割平面算法。 [15] 我们基于切割平面算法开发并分析了该问题的精确解决方法。 [16] 概率存储规划问题进一步分解为一个上层问题和几个下层问题，并通过亚梯度切割平面算法求解。 [17] 我们使用依赖于内点方法提前终止的切割平面算法，并且我们研究了针对各种 k 值和实例类型的 SDP 和线性规划 (LP) 松弛的性能。 [18] 针对该问题的多面体先前已知的一类面不等式，开发了切割平面算法。 [19] 此外，提出了一种称为修正最速上升切割平面算法的算法，以有效地计算 IID 容量实现分布。 [20] 我们开发了一种切割平面算法来解决由此产生的优化问题。 [21] 为了抑制搜索错误导致的噪声图像，我们将图像选择和分类器学习制定为多实例学习问题，并提出通过切割平面算法解决所采用的问题。 [22] 第一阶段决策变量使用切割平面算法确定，以解决鲁棒单元承诺；第二阶段使用三相最优潮流求解最终的调度命令。 [23] 在处理双目标模型常用的重要方法下，提出了一种切割平面算法来求解模型。 [24]
Cutting Plane Algorithm 切割平面算法
Further, to efficiently solve this problem, a novel cutting plane algorithm that makes use of the extremal distributions identified from the second-stage semidefinite programming (SDP) problems is introduced. [1] We propose a cutting plane algorithm which uses the sample average approximation method to model the chance constraints and finds high confidence feasible solutions. [2] This study focuses on an exact cutting plane algorithm for selective coloring in perfect graphs, where the selective coloring problem is known to be NP-hard. [3] We conclude this work with extensive numerical experiments to assess the quality of the mixed-integer linear formulations, as well as the performance of the cutting plane algorithms and the impact of the preprocessing on computation times. [4] The regularized porous crystal plasticity model is implemented as a material model in a finite element code using the cutting plane algorithm. [5] Convergent algorithms are used for the mixed-behavior equilibrium (simplicial decomposition algorithm) and toll determination (cutting plane algorithm). [6] We are able to solve instances upto 50 nodes from AP data-set within 120 and 10 minutes of CPU time for single and multiple allocation settings, respectively, which were unsolved by mixed integer second order cone based reformulation or Kelley’s cutting plane algorithm in the maximum allowed CPU time (3 hours for single allocation and 1 hour for multiple allocation). [7] Moreover, we analyze a linear relaxation strengthened by semidefinite-based constraints, a cutting plane algorithm, and node selection strategies. [8] We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. [9] The pessimistic formulations introduce another level in the optimization problem, for which we propose a cutting plane algorithm. [10] It is solved using a Benders-dual cutting plane algorithm and a column and constraints generation algorithm in a tractable manner. [11] Furthermore, we develop a cutting plane algorithm for constrained bisubmodular minimization based on the poly-bimatroid inequalities. [12] All comparisons demonstrate that the modified cutting plane algorithm with substepping is the most robust and efficient one, followed by the modified Stolle with substepping and the modified Katona with substepping, for an advanced model with multiple hardening parameters. [13] We then solve the model using the sdc cutting plane algorithm for varying risk parameters. [14] To this end, we apply methods from convex optimization (in particular Lagrange duality and the cutting plane algorithm), and propose the novel mixed monotonic programming (MMP) framework to treat the arising nonconvex subproblems. [15] As an application, we propose to design a (k, l)-connected network with minimum cost, by presenting two integer programming formulations and a cutting plane algorithm. [16] Computational results illustrate the effectiveness of our MIQO formulations by comparison with conventional local search algorithms and MIO-based cutting plane algorithms. [17] The resulting bilevel structure is iteratively solved using a cutting plane algorithm. [18] We present a cutting plane algorithm for finding nondominated vertices based on enumerating the vertices of a weight space polyhedron and describe its implementation in PolySCIP, a solver for multicriteria optimisation problems which we developed as a part of this dissertation. [19] The results show that the proposed cutting plane algorithms can solve up to 19% more instances than the classic branch-and-bound algorithms. [20] A novel cutting plane algorithm is developed to deal with the difficulty of solving such model, and exhibits superior computational performance in our numerical experiments over other solution approaches. [21] We find that the analytical reformulation solved using a cutting plane algorithm requires less computational time than the scenario-based method. [22] This paper also develops a strong mixed-integer second-order cone programming based reformulation and a cutting plane algorithm for scalable computation. [23] In this work, we propose a modification on the Extended Cutting Plane algorithm (ECP) that solves convex mixed integer nonlinear programming problems. [24] This problem is NP-hard to be solved, and we propose to relax it and solve it by a cutting plane algorithm. [25] Based on the verification of strong duality of the semidefinite programming (SDP) problems, we propose a cutting plane algorithm for solving the MI-SDPs; we also introduce a SDP relaxation for the feasibility checking problem, which is an intractable biconvex optimization. [26] Combining DC cut with classical cutting planes such as lift-and-project and Gomory’s cut, we establish a DC cutting plane algorithm (DC-CUT algorithm) for globally solving MBLP. [27]此外，为了有效地解决这个问题，引入了一种新颖的切割平面算法，该算法利用了从第二阶段半定规划 (SDP) 问题中识别出的极值分布。 [1] 我们提出了一种切割平面算法，该算法使用样本平均逼近方法对机会约束进行建模，并找到高置信度的可行解。 [2] 本研究侧重于一种精确切割平面算法，用于在完美图中进行选择性着色，其中选择性着色问题已知是 NP-hard。 [3] 我们通过广泛的数值实验来结束这项工作，以评估混合整数线性公式的质量，以及切割平面算法的性能和预处理对计算时间的影响。 [4] 正则化多孔晶体塑性模型使用切割平面算法实现为有限元代码中的材料模型。 [5] 收敛算法用于混合行为平衡（简单分解算法）和收费确定（切割平面算法）。 [6] 对于单个和多个分配设置，我们能够分别在 120 分钟和 10 分钟的 CPU 时间内从 AP 数据集中解决多达 50 个节点的实例，这是通过基于混合整数二阶锥的重构或 Kelley 的切割平面算法最大无法解决的允许的 CPU 时间（单次分配 3 小时，多次分配 1 小时）。 [7] 此外，我们分析了由基于半定的约束、切割平面算法和节点选择策略加强的线性松弛。 [8] 我们提供了一种基于分割切割的多项式时间切割平面算法来求解平面内的整数程序。 [9] 悲观公式在优化问题中引入了另一个层次，为此我们提出了一种切割平面算法。 [10] 它是使用 Benders 双切割平面算法和列和约束生成算法以易于处理的方式解决的。 [11] 此外，我们开发了一种基于多双拟阵不等式的约束双子模最小化切割平面算法。 [12] 所有比较都表明，对于具有多个硬化参数的高级模型，带有子步进的修改切割平面算法是最稳健和最有效的算法，其次是带有子步进的修改 Stolle 和带有子步进的修改 Katona。 [13] 然后，我们使用 sdc 切割平面算法对不同风险参数的模型进行求解。 [14] 为此，我们应用凸优化方法（特别是拉格朗日对偶和切割平面算法），并提出新的混合单调规划（MMP）框架来处理出现的非凸子问题。 [15] 作为一个应用程序，我们建议通过提出两个整数规划公式和一个切割平面算法，以最小的成本设计一个 (k, l) 连接的网络。 [16] 通过与传统的局部搜索算法和基于 MIO 的切割平面算法的比较，计算结果说明了我们的 MIQO 公式的有效性。 [17] 使用切割平面算法迭代求解得到的双层结构。 [18] 我们提出了一种基于枚举权重空间多面体的顶点来寻找非支配顶点的切割平面算法，并描述了它在 PolySCIP 中的实现，PolySCIP 是我们作为本文的一部分开发的多准则优化问题的求解器。 [19] 结果表明，与经典的分支定界算法相比，所提出的切割平面算法可以解决多达 19% 的实例。 [20] 开发了一种新的切割平面算法来解决求解此类模型的困难，并且在我们的数值实验中表现出优于其他求解方法的计算性能。 [21] 我们发现使用切割平面算法求解的解析重构比基于场景的方法需要更少的计算时间。 [22] 本文还开发了一个强大的混合整数二阶锥规划基于重构和可扩展计算的切割平面算法。 [23] 在这项工作中，我们提出了对扩展切割平面算法 (ECP) 的修改，该算法解决了凸混合整数非线性规划问题。 [24] 这个问题是 NP-hard 解决的，我们建议放宽它并通过切割平面算法来解决它。 [25] 在验证了半定规划（SDP）问题的强对偶性的基础上，我们提出了一种求解MI-SDP的切割平面算法；我们还为可行性检查问题引入了 SDP 松弛，这是一种棘手的双凸优化。 [26] 将DC割与lift-and-project、Gomory's cut等经典割平面相结合，建立了一种全局求解MBLP的DC割平面算法（DC-CUT算法）。 [27]