共查询到20条相似文献,搜索用时 750 毫秒
1.
无容量限制设施选址问题是经典的组合优化问题, 具有广泛的应用价值,然而该问题已被证明是NP难问题, 并且传统的分支定界方法求解速度较慢.研究以最大化总收益费用与总投建费用之差为目标的无容量限制设施选址问题,将其转化为节点包装问题,并根据模型的图形特点提出了新的合法不等式族------轴不等式族,经过严格的数学证明后得出轴不等式要强于原有的奇洞不等式. 同时,设计出切割不等式快速搜索算法嵌入到分支割平面方法中. 最后,通过实验验证了轴不等式族的强有效性,
以及分支割平面方法比分支定界方法求解速度快、节点数量少的优点. 相似文献
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Géraldine Heilporn Martine Labbé Patrice Marcotte Gilles Savard 《Discrete Optimization》2011,8(3):393-410
Motivated by an application in highway pricing, we consider the problem that consists in setting profit-maximizing tolls on a clique subset of a multicommodity transportation network. We formulate the problem as a linear mixed integer program and propose strong valid inequalities, some of which define facets of the two-commodity polyhedron. The numerical efficiency of these inequalities is assessed by embedding them within a branch-and-cut framework. 相似文献
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This is the first of a series of two papers dedicated to efficient separation heuristics for violated inequalities in the
context of solving to optimality instances of the Traveling Salesman Problem via branch-and-cut. In this paper we give the
basic ideas behind these heuristics and design heuristics for comb separation. The second paper will deal with more complex
inequalities such as Clique Tree, Star or Path and Ladder inequalities and give computational results.
Received: September 1999 / Accepted: August 2001?Published online February 14, 2002 相似文献
6.
The Cardinality Constrained Circuit Problem (CCCP) is the problem of finding a minimum cost circuit in a graph where the circuit
is constrained to have at most k edges. The CCCP is NP-Hard. We present classes of facet-inducing inequalities for the convex hull of feasible circuits, and
a branch-and-cut solution approach using these inequalities.
Received: April 1998 / Accepted: October 2000?Published online October 26, 2001 相似文献
7.
Stefan Gollowitzer Bernard Gendron Ivana Ljubić 《Computational Optimization and Applications》2013,55(3):647-674
We consider a network design problem that arises in the cost-optimal design of last mile telecommunication networks. It extends the Connected Facility Location problem by introducing capacities on the facilities and links of the networks. It combines aspects of the capacitated network design problem and the single-source capacitated facility location problem. We refer to it as the Capacitated Connected Facility Location Problem. We develop a basic integer programming model based on single-commodity flows. Based on valid inequalities for the capacitated network design problem and the single-source capacitated facility location problem we derive several (new) classes of valid inequalities for the Capacitated Connected Facility Location Problem including cut set inequalities, cover inequalities and combinations thereof. We use them in a branch-and-cut framework and show their applicability and efficacy on a set of real-world instances. 相似文献
8.
The Delay Constrained Relay Node Placement Problem (DCRNPP) frequently arises in the Wireless Sensor Network (WSN) design. In WSN, Sensor Nodes are placed across a target geographical region to detect relevant signals. These signals are communicated to a central location, known as the Base Station, for further processing. The DCRNPP aims to place the minimum number of additional Relay Nodes at a subset of Candidate Relay Node locations in such a manner that signals from various Sensor Nodes can be communicated to the Base Station within a pre-specified delay bound. In this paper, we study the structure of the projection polyhedron of the problem and develop valid inequalities in form of the node-cut inequalities. We also derive conditions under which these inequalities are facet defining for the projection polyhedron. We formulate a branch-and-cut algorithm, based upon the projection formulation, to solve DCRNPP optimally. A Lagrangian relaxation based heuristic is used to generate a good initial solution for the problem that is used as an initial incumbent solution in the branch-and-cut approach. Computational results are reported on several randomly generated instances to demonstrate the efficacy of the proposed algorithm. 相似文献
9.
A cardinality constrained knapsack problem is a continuous knapsack problem in which no more than a specified number of nonnegative
variables are allowed to be positive. This structure occurs, for example, in areas such as finance, location, and scheduling.
Traditionally, cardinality constraints are modeled by introducing auxiliary 0-1 variables and additional constraints that
relate the continuous and the 0-1 variables. We use an alternative approach, in which we keep in the model only the continuous
variables, and we enforce the cardinality constraint through a specialized branching scheme and the use of strong inequalities
valid for the convex hull of the feasible set in the space of the continuous variables. To derive the valid inequalities,
we extend the concepts of cover and cover inequality, commonly used in 0-1 programming, to this class of problems, and we
show how cover inequalities can be lifted to derive facet-defining inequalities. We present three families of non-trivial
facet-defining inequalities that are lifted cover inequalities. Finally, we report computational results that demonstrate
the effectiveness of lifted cover inequalities and the superiority of the approach of not introducing auxiliary 0-1 variables
over the traditional MIP approach for this class of problems.
Received: March 13, 2003
Published online: April 10, 2003
Key Words. mixed-integer programming – knapsack problem – cardinality constrained programming – branch-and-cut 相似文献
10.
By reformulating quadratic programs using necessary optimality conditions, we obtain a linear program with complementarity constraints. For the case where the only constraints are bounds on the variables, we study a relaxation based on a subset of the optimality conditions. By characterizing its convex hull, we obtain a large class of valid inequalities. These inequalities are used in a branch-and-cut scheme, see [13].Mathematics Subject Classification (2000): 90C26, 90C27, 90C20 相似文献
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Lifting is a procedure for deriving valid inequalities for mixed-integer sets from valid inequalities for suitable restrictions
of those sets. Lifting has been shown to be very effective in developing strong valid inequalities for linear integer programming
and it has been successfully used to solve such problems with branch-and-cut algorithms. Here we generalize the theory of
lifting to conic integer programming, i.e., integer programs with conic constraints. We show how to derive conic valid inequalities
for a conic integer program from conic inequalities valid for its lower-dimensional restrictions. In order to simplify the
computations, we also discuss sequence-independent lifting for conic integer programs. When the cones are restricted to nonnegative
orthants, conic lifting reduces to the lifting for linear integer programming as one may expect. 相似文献
12.
Oktay Günlük 《Mathematical Programming》1999,86(1):17-39
We present a branch-and-cut algorithm to solve capacitated network design problems. Given a capacitated network and point-to-point
traffic demands, the objective is to install more capacity on the edges of the network and route traffic simultaneously, so
that the overall cost is minimized. We study a mixed-integer programming formulation of the problem and identify some new
facet defining inequalities. These inequalities, together with other known combinatorial and mixed-integer rounding inequalities,
are used as cutting planes. To choose the branching variable, we use a new rule called “knapsack branching”. We also report
on our computational experience using real-life data.
Received April 29, 1997 / Revised version received January 9, 1999? Published online June 28, 1999 相似文献
13.
We present a new branch-and-cut algorithm for the capacitated vehicle routing problem (CVRP). The algorithm uses a variety of cutting planes, including capacity, framed capacity, generalized capacity, strengthened comb, multistar, partial multistar, extended hypotour inequalities, and classical Gomory mixed-integer cuts. For each of these classes of inequalities we describe our separation algorithms in detail. Also we describe the other important ingredients of our branch-and-cut algorithm, such as the branching rules, the node selection strategy, and the cut pool management. Computational results, for a large number of instances, show that the new algorithm is competitive. In particular, we solve three instances (B-n50-k8, B-n66-k9 and B-n78-k10) of Augerat to optimality for the first time. 相似文献
14.
Classical cuts for mixed-integer programming and branch-and-cut 总被引:1,自引:0,他引:1
Manfred Padberg 《Mathematical Methods of Operations Research》2001,53(2):173-203
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We present the implementation of a branch-and-cut algorithm for bound constrained nonconvex quadratic programs. We use a class of inequalities developed in [12] as cutting planes. We present various branching strategies and compare the algorithm to several other methods to demonstrate its effectiveness.Mathematics Subject Classification (2000): 90C26, 90C27, 90C20 相似文献
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A branch-and-cut algorithm for solving linear problems with continuous separable piecewise linear cost functions was developed in 2005 by Keha et al. This algorithm is based on valid inequalities for an SOS2 based formulation of the problem. In this paper we study the extension of the algorithm to the case where the cost function is only lower semicontinuous. We extend the SOS2 based formulation to the lower semicontinuous case and show how the inequalities introduced by Keha et al. can also be used for this new formulation. We also introduce a simple generalization of one of the inequalities introduced by Keha et al. Furthermore, we study the discontinuities caused by fixed charge jumps and introduce two new valid inequalities by extending classical results for fixed charge linear problems. Finally, we report computational results showing how the addition of the developed inequalities can significantly improve the performance of CPLEX when solving these kinds of problems. 相似文献
17.
《European Journal of Operational Research》1999,118(1):127-138
Given a graph and costs of assigning to each vertex one of k different colors, we want to find a minimum cost assignment such that no color q induces a subgraph with more than a given number (γq) of connected components. This problem arose in the context of contiguity-constrained clustering, but also has a number of other possible applications. We show the problem to be NP-hard. Nevertheless, we derive a dynamic programming algorithm that proves the case where the underlying graph is a tree to be solvable in polynomial time. Next, we propose mixed-integer programming formulations for this problem that lead to branch-and-cut and branch-and-price algorithms. Finally, we introduce a new class of valid inequalities to obtain an enhanced branch-and-cut. Extensive computational experiments are reported. 相似文献
18.
In this paper, we consider the Capacitated Network Design (CND) problem. We investigate the relationship between CND and the Bin-Packing problem. This is exploited for identifying new classes of valid inequalities for the CND problem and developing a branch-and-cut algorithm to solve it efficiently. 相似文献
19.
Recent work has demonstrated the potential for globally optimizing nonconvex quadratic programs using a reformulation based
on the first order optimality conditions. We show how this reformulation may be generalized to account for fixed cost variables.
We then extend some of the polyhedral work that has been done for bound constrained QPs to handle such fixed cost variables.
We show how to lift known classes of inequalities for the case without fixed cost variables and propose several new classes.
These inequalities are incorporated in a branch-and-cut algorithm. 相似文献
20.
A branch-and-cut algorithm for a generalization of the Uncapacitated Facility Location Problem 总被引:1,自引:0,他引:1
Summary We introduce a generalization of the well-know Uncapacitated Facility Location Problem, in which clients can be served not
only by single facilities but also by sets of facilitities. The problem, calledGaneralized Uncapacitated Facility Lacition Problem (GUFLP), was inspired by the Index Selection Problem in physical database design. We for mulate GUFLP as a Set Packing Problem,
showing that our model contains all the clique inequalities (in polynomial number). Moreover, we describe and exact separation
procedure for odd-hole inequalities, based on the particular structure of the problem. These results are used within a branch-and-cut
algorithm for the exact solution of GUFLP. Computational results on two different classes of test problems are given. 相似文献