1,223 research outputs found
Solving Medium to Large Sized Euclidean Generalized Minimum Spanning Tree Problems
The generalized minimum spanning tree problem is a generalization of the minimum spanning tree problem. This network design problems ďŹnds several practical applications, especially when one considers the design of a large-capacity backbone network connecting several individual networks. In this paper we study the performance of six neighborhood search heuristics based on tabu search and variable neighborhood search on this problem domain. Our principal ďŹnding is that a tabu search heuristic almost always provides the best quality solution for small to medium sized instances within short execution times while variable neighborhood decomposition search provides the best quality solutions for most large instances.
An oil pipeline design problem
Copyright @ 2003 INFORMSWe consider a given set of offshore platforms and onshore wells producing known (or estimated) amounts of oil to be connected to a port. Connections may take place directly between platforms, well sites, and the port, or may go through connection points at given locations. The configuration of the network and sizes of pipes used must be chosen to minimize construction costs. This problem is expressed as a mixed-integer program, and solved both heuristically by Tabu Search and Variable Neighborhood Search methods and exactly by a branch-and-bound method. Two new types of valid inequalities are introduced. Tests are made with data from the South Gabon oil field and randomly generated problems.The work of the first author was supported by NSERC grant #OGP205041. The work of the second author was supported by FCAR (Fonds pour la Formation des Chercheurs et lâAide Ă la Recherche) grant #95-ER-1048, and NSERC grant #GP0105574
Automatically Produced Algorithms for the Generalized Minimum Spanning Tree Problem
The generalized minimum spanning tree problem consists of finding a minimum cost spanning tree in an undirected graph for which the vertices are divided into clusters. Such spanning tree includes only one vertex from each cluster. Despite the diverse practical applications for this problem, the NP-hardness continues to be a computational challenge. Good quality solutions for some instances of the problem have been found by combining specific heuristics or by including them within a metaheuristic. However studied combinations correspond to a subset of all possible combinations. In this study a technique based on a genotype-phenotype genetic algorithm to automatically construct new algorithms for the problem, which contain combinations of heuristics, is presented. The produced algorithms are competitive in terms of the quality of the solution obtained. This emerges from the comparison of the performance with problem-specific heuristics and with metaheuristic approaches
The minimum spanning tree problem with conflict constraints and its variations
AbstractWe consider the minimum spanning tree problem with conflict constraints (MSTC). The problem is known to be strongly NP-hard and computing even a feasible solution is NP-hard. When the underlying graph is a cactus, we show that the feasibility problem is polynomially bounded whereas the optimization version is still NP-hard. When the conflict graph is a collection of disjoint cliques, (equivalently, when the conflict relation is transitive) we observe that MSTC can be solved in polynomial time. We also identify other special cases of MSTC that can be solved in polynomial time. Exploiting these polynomially solvable special cases we derive strong lower bounds. Also, various heuristic algorithms and feasibility tests are discussed along with preliminary experimental results. As a byproduct of this investigation, we show that if an Ďľ-optimal solution to the maximum clique problem can be obtained in polynomial time, then a (3Ďľâ1)-optimal solution to the maximum edge clique partitioning (Max-ECP) problem can be obtained in polynomial time. As a consequence, we have a polynomial time approximation algorithm for the Max-ECP with performance ratio O(n(loglogn)2log3n), improving the best previously known bound of O(n)
Approximation Algorithms for Generalized MST and TSP in Grid Clusters
We consider a special case of the generalized minimum spanning tree problem
(GMST) and the generalized travelling salesman problem (GTSP) where we are
given a set of points inside the integer grid (in Euclidean plane) where each
grid cell is . In the MST version of the problem, the goal is to
find a minimum tree that contains exactly one point from each non-empty grid
cell (cluster). Similarly, in the TSP version of the problem, the goal is to
find a minimum weight cycle containing one point from each non-empty grid cell.
We give a and -approximation
algorithm for these two problems in the described setting, respectively.
Our motivation is based on the problem posed in [7] for a constant
approximation algorithm. The authors designed a PTAS for the more special case
of the GMST where non-empty cells are connected end dense enough. However,
their algorithm heavily relies on this connectivity restriction and is
unpractical. Our results develop the topic further
Insertion Heuristics for Central Cycle Problems
A central cycle problem requires a cycle that is
reasonably short and keeps a the maximum distance
from any node not on the cycle to its nearest
node on the cycle reasonably low. The objective
may be to minimise maximumdistance or cycle
length and the solution may have further constraints.
Most classes of central cycle problems
are NP-hard. This paper investigates insertion
heuristics for central cycle problems, drawing on
insertion heuristics for p-centres [7] and travelling
salesman tours [21]. It shows that a modified
farthest insertion heuristic has reasonable worstcase
bounds for a particular class of problem.
It then compares the performance of two farthest
insertion heuristics against each other and
against bounds (where available) obtained by integer
programming on a range of problems from
TSPLIB [20]. It shows that a simple farthest insertion
heuristic is fast, performs well in practice
and so is likely to be useful for a general problems
or as the basis for more complex heuristics
for specific problems
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