1,721,067 research outputs found
A subexponential algorithm for the coloured tree partition problem
No full textAbstractGiven a tree of n vertices and a list of feasible colours for each vertex, the coloured tree partition problem (CTPP) consists in partitioning the tree into p vertex-disjoint subtrees of minimum total cost, and assigning to each subtree a different colour, which must be feasible for all of its vertices. The problem is strongly NP-hard on general graphs, as well as on grid and bipartite graphs. This paper deals with the previously open case of tree graphs, showing that it is strongly NP-complete to determine whether a feasible solution exists. It presents reduction, decomposition and bounding procedures to simplify the problem and an exact algorithm of O(nplog2(ap-2)) complexity (with a>32) for the special case in which a vertex of each subtree is given
A very large neighbourhood search approach to the swath segment selection problem
Full text linkThe Swath Segment Selection Problem (SSSP) arises from the planning
of Earth observations performed by satellites in quasi-polar orbits
The multicommodity multilevel bottleneck assignment problem
Full text linkThe Multilevel Bottleneck Assignment Problem is defined on a weighted graph of L levels and consists in finding Formula Not Shown complete matchings between contiguous levels, such that the heaviest path formed by the arcs in the matchings has a minimum weight. The problem, introduced by Carraresi and Gallo (1984) to model the rostering of bus drivers in order to achieve an even balance of the workload among the workers, though frequently cited, seems to have never been applied or extended to more general cases. In this paper, we discuss one possible extension, that is the introduction of multicommodity aspects to model different classes of workers
An Exact Algorithm for the Node Weighted Steiner Tree Problem
No full textThe Node Weighted Steiner Tree Problem (NW-STP) is a generalization of the Steiner Tree Problem. A lagrangean heuristic presented in EngevallS: StrLBN: 98, and based on the work in Lucena: 92, solves the problem by relaxing an exponential family of generalized subtour elimination constraints and taking into account only the violated ones as the computation proceeds. In EngevallS: StrLBN: 98 the computational results refer to complete graphs up to one hundred vertices. In this paper, we present a branch-and-bound algorithm based on this formulation. Its performance on the instances from the literature confirms the effectiveness of the approach. The experimentation on a newly generated set of benchmark problems, more similar to the real-world applications, shows that the approach is still valid, provided that suitable refinements on the bounding procedures and a preprocessing phase are introduced. The algorithm solves to optimality all of the considered instances up to one thousand vertices, with the exception of 11 hard instances, derived from the literature of a similar problem, the Prize Collecting Steiner Tree Problem
Better and faster solutions for the maximum diversity problem
Full text linkThe aim of the Maximum Diversity Problem (MDP) is to extract a subset M of given cardinality from a set of elements N, in such a way that the sum of the pairwise distances between the elements of M is maximum. This problem, introduced by Glover [7], has been deeply studied using GRASP methodologies [6, 1, 17, 2, 16]. Usually, effective algorithms owe their success more to the careful exploitation of problem-specific features than to the application of general-purpose methods. A solution for MDP has a very simple structure which can not be exploited for sophisticated neighborhood search. This paper explores the performance of three alternative solution approaches, that is Tabu Search, Variable Neighborhood Search and Scatter Search, comparing them with those of best GRASP algorithms in literature. We also focus our attention on the comparison of these three methods applied in their pure form
Solving the quadratic minimum spanning tree problem
No full textGiven an undirected graph with costs associated to its edges and pairs of
edges, the \emph{Quadratic Minimum Spanning Tree Problem} (\emph{QMSTP})
requires to determine a spanning tree of minimum total cost. This is a proper model for network problems in which both routing and interference costs need to be considered. It is -hard in the strong sense and not approximable unless . This paper describes a Tabu Search algorithm, with two independent and adaptively tuned tabu lists, and a Variable Neighbourhood Search algorithm. Both metaheuristics are based on the same neighbourhood, but the Tabu Search proves more effective and robust than the Variable Neighbourhood Search. To assess the quality of these results, we provide a comparison with the heuristic algorithms proposed in the recent literature and we reimplement, with minor improvements, an exact algorithm
drawn from the literature, which confirms the optimality of the results obtained
on small instances
Comparing local search metaheuristics for the maximum diversity problem
No full textThe Maximum Diversity Problem (MDP) requires to extract a subset M of given cardinality from a set N, maximising the sum of the pair-wise diversities between the extracted elements. The MDP has recently been the subject of much research, and several sophisticated heuristics have been proposed to solve it. The present work compares four local search metaheuristics for the MDP, all based on the same Tabu Search procedure, with the aim to identify what additional elements provide the strongest improvement. The four metaheuristics are an Exploring Tabu Search, a Scatter Search, a Variable Neighbourhood Search and a simple Random Restart algorithm. All of them prove competitive with the best algorithms proposed in the literature. Quite surprisingly, the best ones are the simple Random Restart algorithm and a Variable Neighbourhood Search algorithm with an unusual parameter setting, which makes it quite close to random restart. Although this is probably related to the elementary structure of the MDP, it also suggests that, more often than expected, simpler algorithms might be better
A relax-and-cut algorithm for the knapsack node weighted Steiner tree problem
No full textThe Knapsack Node Weighted Steiner Tree Problem (KNWSTP) is a generalization of the Steiner Tree Problem on graphs, which takes into account the classical cost function defined on the edges, as well as a prize function defined on the vertices and a limit on the size of the solution. It has several applications to network design. We propose an exact branch-and-bound algorithm for this problem, based on a relax-and-cut approach: the algorithm relaxes an exponential family of generalized subtour elimination constraints and takes into account only the violated ones as the computation proceeds. The performance of the algorithm has been tested on a wide set of benchmark problems, up to three hundred vertices, whose structure reflects the features of the most likely applications (sparse graphs with Euclidean costs) and covers different cases with respect to the prize function (only positive, or both positive and negative prizes) and the weight threshold
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