One of the most promising solutions to deal with huge data traffic demands in large communication networks is given by flexible optical networking, in particular the flexible grid (flexgrid) technology specified in th...
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One of the most promising solutions to deal with huge data traffic demands in large communication networks is given by flexible optical networking, in particular the flexible grid (flexgrid) technology specified in the ITU-T standard G.694.1. In this specification, the frequency spectrum of an optical fiber link is divided into narrow frequency slots. Any sequence of consecutive slots can be used as a simple channel, and such a channel can be switched in the network nodes to create a lightpath. In this kind of networks, the problem of establishing lightpaths for a set of end-to-end demands that compete for spectrum resources is called the routing and spectrum allocation problem (RSA). Due to its relevance, RSA has been intensively studied in the last years. It has been shown to be NP-hard and different solution approaches have been proposed for this problem. In this paper we present several families of valid inequalities, valid equations, and optimality cuts for a natural integer programming formulation of RSA and, based on these results, we develop a branch-and-cut algorithm for this problem. Our computational experiments suggest that such an approach is effective at tackling this problem.
Three formulations for the Minimum 2-Connected Dominating Set Problem, valid inequalities, a primal heuristic and branch-and-cut algorithms are introduced in this paper. As shown here, the preliminary computational re...
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Optimization has been a central topic in most scientific disciplines for centuries. Continu- ous optimization has long benefited from well-established techniques of calculus. Discrete optimization, on the other hand, ...
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Optimization has been a central topic in most scientific disciplines for centuries. Continu- ous optimization has long benefited from well-established techniques of calculus. Discrete optimization, on the other hand, has risen to prominence quite recently. Advances in combinatorial optimization and integer programming in the past few decades, together with the improvement of computer hardware have enabled computer scientists to approach the problems in this area both theoretically and computationally. However, obtaining the exact solution for many discrete optimization problems remains is still a challenging task, mainly because most of these problems are NP -hard. Under the widespread assumption that P 6= NP, these problems are intractable from a computational complexity standpoint. Therefore, we should settle for near-optimal solutions. In this thesis, we develop techniques to obtain solutions that are provably close to the optimal for different indivisible resource allocation problems. Indivisible resource allocation encompasses a large class of problems in discrete optimization which can appear in disguise in various theoretical or applied settings. Specifically, we consider two indivisible resource allocation problems. The first one is a variant of the vehicle routing problem known as Skill Vehicle Routing problem, in which the aim is to obtain optimal tours for a fleet of vehicles that provides service to a set of customers. Each of the vehicles possesses a particular set of skills suitable for a subset of the tasks. Each customer, based on the type of service he requires, can only be served by a subset of vehicles. We study this problem computationally and find either the optimal solution or a relatively tight bound on the optimal solution on fairly large problem instances. The second problem involves approximation algorithms for two versions of the classic scheduling problem, the restricted R | | C max and the restricted Santa Claus problem. The objective is
A formulation, a heuristic, and branch-and-cut algorithms are investigated for the chordless cycle problem. This is the problem of finding a largest simple cycle for a given graph so that no edge between nonimmediatel...
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A formulation, a heuristic, and branch-and-cut algorithms are investigated for the chordless cycle problem. This is the problem of finding a largest simple cycle for a given graph so that no edge between nonimmediately subsequent cycle vertices is contained in the graph. Leaving aside procedures based on complete enumeration, no previous exact solution algorithm appears to exist for the problem, which is relevant both in theoretical and practical terms. Extensive computational results are reported here for randomly generated graphs and for graphs originating from the literature. Under acceptable CPU times, certified optimal solutions are presented for graphs with as many as 100 vertices.
Assume one is given an angle alpha is an element of(0, 2 pi] and a complete undirected graph G = (V, E). The vertices in V represent points in the Euclidean plane. The edges in E represent the line segments between th...
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Assume one is given an angle alpha is an element of(0, 2 pi] and a complete undirected graph G = (V, E). The vertices in V represent points in the Euclidean plane. The edges in E represent the line segments between these points, with edge weights equal to segment lengths. Spanning trees of G are called alpha-spanning trees (alpha-STs) if, for any i is an element of V, the smallest angle that encloses all line segments corresponding to its i-incident edges does not exceed alpha. The Angular Constrained Minimum Spanning Tree Problem (alpha-MSTP) seeks an alpha-ST with the least weight. The problem arises in the design of wireless communication networks operating under directional antennas. We propose two alpha-MSTP formulations. One, F-x requiring, in principle, O(2(vertical bar V vertical bar)) inequalities to model the angular constraints (alpha-AC). For alpha is an element of(0, pi), however, we show that just O(vertical bar V vertical bar(3)) of them suffice to attain not only a formulation but also the same Linear Programming relaxation (LPR) bound as the full blown model. The other formulation, F-xy, enlarges the set of F-x variables but manages to model alpha-AC, compactly. Furthermore, F-xy LPR bounds are proven to dominate their F-x counterparts. That dominance, however, is empirically shown to reduce as alpha increases. Finally, exact branch-and-cut algorithms implemented for the two formulations are shown, empirically, to exchange roles as top performer, throughout the [0, 2 pi) range of alpha values. (C) 2019 Elsevier Ltd. All rights reserved.
This paper surveys the most effective mathematical models and exact algorithms proposed for finding the optimal solution of the well-known Asymmetric Traveling Salesman Problem (ATSP). The fundamental Integer Linear P...
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This paper surveys the most effective mathematical models and exact algorithms proposed for finding the optimal solution of the well-known Asymmetric Traveling Salesman Problem (ATSP). The fundamental Integer Linear Programming (ILP) model proposed by Dantzig, Fulkerson and Johnson is first presented, its classical (assignment, shortest spanning r-arborescence, linear programming) relaxations are derived, and the most effective branch-and-bound and branch-andcutalgorithms are described. The polynomial ILP formulations proposed for the ATSP are then presented and analyzed. The considered algorithms and formulations are finally experimentally compared on a set of benchmark instances.
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