Dorabella Santos

Fourier analysis of symbolic data: A brief review

We overview and discuss several methods for the Fourier analysis of symbolic data, such as DNA sequences, emphasizing their mutual connections. We consider the indicator sequence approach, the vector and the symbolic autocorrelation methods, and methods such as the spectral envelope, that for each frequency optimize the symbolic-no-numeric mapping to emphasize any periodic data features. We discuss the equivalence or connections between these methods. We show that it is possible to define the autocorrelation function of symbolic data, assuming only that we can compare any two symbols and decide if they are equal or distinct. The autocorrelation is a numeric sequence, and its Fourier transform can also be obtained by summing the squares of the Fourier transform of indicator sequences (zero/one sequences indicating the position of the symbols). Another interpretation of the spectrum is given, borrowing from the spectral envelope concept: among all symbolic-to-numeric mappings there is one that maximizes the spectral energy at each frequency, and leads to the spectrum.

Traffic Engineering of Multiple Spanning Tree Routing Networks: the Load Balancing Case

This paper deals with optimal load balancing in telecommunication networks based on multiple spanning tree routing. This is the case in switched Ethernet networks where the operator configures different routing spanning trees and assigns each demand VLAN to one of the spanning trees. We consider modeling and solving three load balancing objectives: (i) minimization of the average link load with a guaranteed optimal worst case link load, (ii) minimization of the worst case link load with a guaranteed optimal average link load and (iii) the min-max optimization of link loads. We also propose heuristic techniques to compute both feasible solutions and lower bounds for the addressed optimization problems. Finally, we assess both the efficiency and the efficacy of the different solution techniques and compare the quality of each problem solution taking into account the optimization criteria of the other problems.

Combining column generation and metaheuristics

In this Chapter, we consider the hybridization of column generation (CG) with metaheuristics (MHs) for solving integer programming and combinatorial optimization problems. We describe a general framework entitled ”metaheuristic search by column generation” (for short, SearchCol). CG is a decomposition approach in which one linear programming master problem interacts with subproblems to obtain an optimal solution to a relaxed version of a problem. The subproblems may be solved by problem-specific algorithms. After CG is applied, a set of subproblem’s solutions, optimal primal and dual values of the master problem variables and a lower bound to the optimal value of the problem are available. In contrast with enumerative approaches (e.g, branch-and-price), in SearchCol the information provided by CG is used in a MH search. The search is based on representing a solution (to the overall problem) as being composed by one solution from each subproblem. After a search is conducted, a perturbation for CG is defined and a new iteration begins. The perturbation consists in forcing or forbidding attributes of the subproblem’s solutions and, in general, leads to the generation of new subproblem’s solutions and different optimal primal and dual values of the master problem variables. In this Chapter, we discuss (i) which models are suitable for decomposition approaches as SearchCol, (ii) different alternatives for generating initial solutions for the search (with different degrees of randomization, greediness and influence of CG) (iii) different search approaches based on local search, (iv) different alternatives for perturbing CG (influenced by CG, based on the incumbent, and based on the memory of the search).

A hybrid column generation with GRASP and path relinking for the network load balancing problem

In this paper, a hybrid meta-heuristic is proposed which combines the GRASP with path relinking method and Column Generation. The key idea of this method is to run a GRASP with path relinking search on a restricted search space, defined by Column Generation, instead of running the search on the complete search space of the problem. Moreover, column generation is used not only to compute the initial restricted search space but also to modify it during the whole algorithm. The proposed heuristic is used to solve the network load balancing problem: given a capacitated telecommunications network with single path routing and an estimated traffic demand matrix, the network load balancing problem is the determination of a routing path for each traffic commodity such that the network load balancing is optimized, i.e., the worst link load is minimized, among all such solutions, the second worst link load is minimized, and continuing in this way until all link loads are minimized. The computational results presented in this paper show that, for the network load balancing problem, the proposed heuristic is effective in obtaining better quality solutions in shorter running times.

Optimizing network load balancing: an hybridization approach of metaheuristics with column generation

Given a capacitated telecommunications network with single path routing and an estimated traffic demand matrix, we aim to determine the routing path of each traffic commodity such that the whole set of paths provide an optimal network load balancing. In a recent paper, we have proposed a column generation based heuristic where, in the first step, we use column generation to solve a linear programming relaxation of the original problem (obtaining, in this way, a lower bound and a set of paths for each commodity) and, in the second step, we apply a multi-start local search with path relinking heuristic on the solution space defined by the paths of the first step. Here, we propose a hybridization approach of the metaheuristic with column generation that can be seen as an enhanced version of the previous approach: we run column generation not only at the beginning (to define the initial search space) but also during the search. These additional column generation steps consist in solving a perturbed problem defined by the incumbent solution. In the previous paper, we have shown that the first approach is efficient in obtaining near optimal routing solutions within short running times. With the enhanced version, we show through computational results that the additional paths, introduced by the additional column generation steps, either improve the efficiency of the algorithm or show similar efficiency in the cases where the original algorithm is already very efficient.

Link load balancing optimization of telecommunication networks: A column generation based heuristic approach

This paper deals with optimal load balancing in telecommunication networks. For a capacitated telecommunications network with single path routing and an estimated traffic demand matrix, we wish to determine the routing paths aiming at min-max optimization of link loads. To solve this problem, we propose a column (path) generation based heuristic. In the first step, we use column generation to solve a linear programming relaxation of the basic problem (obtaining a lower bound and a set of paths). In the second step, we apply a multi-start local search heuristic with path-relinking to the search space defined by the paths found in the first step. In order to assess the merits of this approach, we also implemented a search heuristic which is equivalent to the second step of the proposed one but with no constraints on the set of paths that can be used. Through a set of computational results, we show that the proposed heuristic is efficient in obtaining near optimal routing solutions within short running times. Moreover, the comparison of the two heuristics show that constraining the search space to the columns given by column generation gives better results since this solution space contains good quality solutions and, due to its size, enables to find them in short running times.

Load Balancing Optimization of Capacitated Networks with Path Protection

Abstract This article deals with the routing of a given set of traffic flows over a telecommunications network with given link capacities. The aim is to optimize the network load balancing. We address the case where each traffic flow is supported by two edge disjoint routing paths, a mechanism known as path protection, which guarantees full traffic protection of single link failures. We describe an exact solving method based on mathematical programming and propose a meta-heuristic algorithm. Then, we define a set of case studies arising in the context of metropolitan Ethernet networks. Finally, we present the computational results of both methods and compare them in terms of solutions optimality versus runtime.

Traffic Engineering of Telecommunication Networks Based on Multiple Spanning Tree Routing

This paper focuses on traffic engineering of telecommunication networks, which arises in the context of switched Ethernet networks. It addresses the minimization of the maximum network link load. With the IEEE 802.1s Multiple Spanning Tree Protocol, it is possible to define multiple routing spanning trees to provide multiple alternatives to route VLAN traffic demands. Two compact mixed integer linear programming models defining the optimization problem and several models based on the Dantzig-Wolfe decomposition principle, which are solved by branch-and-price, are proposed and compared. The different decompositions result from defining as subproblems either the supporting spanning trees and/or the demand routing paths, which can be solved by well known efficient algorithms.

The Dynamics of Chung-Freese Braneworld

It is shown that the ansatz of Chung-Freese models a new braneworld, and while superluminal, this braneworld does not suffer from the pathologies of other FTL methods. It is also shown that our universe is a trapped surface inside a universe with large extra dimensions, and in order to preserve compatibility with the Standard Model (SM), we present two trapping mechanisms that keeps SM fields inside our brane. For the Chung-Freese braneworld we develop a similar formalism to Morris domain walls, and we present our universe as a low level state in a potential well with the bulk in the highest levels of potential. Finally, we show that the Israel condition can also act as a trapping mechanism for SM fields inside the brane. Our model uses the idea that fermions are allowed to escape to the bulk inspired by the work of Havoudiasl-Hewett-Rizzo [2].

Compact Models for Critical Node Detection in Telecommunication Networks

Abstract Given a network defined by a graph, a weight associated to each node pair and a positive parameter p, the CND problem addressed here is to identify a set of at most p critical nodes minimizing the total weight of the node pairs that remain connected when all critical nodes are removed. We improve previously known compact models and present computational results, based on telecommunication backbone networks, showing that the proposed models are much more efficiently solved and enable us to obtain optimal solutions for networks up to 200 nodes and p values up to 20 critical nodes within a few minutes in the worst cases.