Topological Design of Survivable Networks

In the field of telecommunications there are several ways of establishing links between different physical places that must be connected according to the characteristics and the type of service they should provide. Two main considerations to be taken into account and which require the attention of the network planners are, in one hand the economic effort necessary to build the network, and in the other hand the resilience of the network to remain operative in the event of failure of any of its components. A third consideration, which is very important when quality of services required, such as video streaming or communications between real-time systems, is the diameter constrained reliability. In this thesis we study a set of problems that involve such considerations. Firstly, we model a new combinatorial optimization problem called Capacitated m-Two Node Survivable Star Problem (CmTNSSP). In such problem we optimize the costs of constructing a network composed of 2-node-connected components that converge in a central node and whose terminals can belong to these connected 2-node structures or be connected to them by simple edges. The CmTNSSP is a relaxation of the Capacitated Ring Star Problem (CmRSP), where the cycles of the latter can be replaced by arbitrary 2-node-connected graphs. According to previous studies, some of the structural properties of 2-node-connected graphs can be used to show a potential improvement in construction costs, over solutions that exclusively use cycles. Considering that the CmTNSSP belongs to the class of NP-Hard computational problems, a GRASP-VND metaheuristic was proposed and implemented for its approximate resolution, and a comparison of results was made between both problems (CmRSP and CmTNSSP) for a series of instances. Some local searches are based on exact Integer Linear Programming formulations. The results obtained show that the proposed metaheuristic reaches satisfactory levels of accuracy, attaining the global optimum in several instances. Next, we introduce the Capacitated m Ring Star Problem under Diameter Constrained Reliability (CmRSP-DCR) wherein DCR is considered as an additional restriction, limiting the number of hops between nodes of the CmRSP problem and establishing a minimum level of network reliability. This is especially useful in networks that should guarantee minimum delays and quality of service. The solutions found in this problem can be improved by applying some of the results obtained in the study of the CmTNSSP. Finally, we introduce a variant of the CmTNSSP named Capacitated Two-Node Survivable Tree Problem, motivated by another combinatorial optimization problem most recently treated in the literature, called Capacitated Ring Tree Problem (CRTP). In the CRTP, an additional restriction is added with respect to CmRSP, where the terminal nodes are of two different types and tree structures are also allowed. Each node in the CRTP may be connected exclusively in one cycle, or may be part of a cycle or a tree indistinctly, depending on the type of node. In the variant we introduced, the cycles are replaced by 2-node-connected structures. This study proposes and implements a GRASP-VND metaheuristic with specific local searches for this type of structures and adapts some of the exact local searches used in the resolution CmTNSSP. A comparison of the results between the optimal solutions obtained for the CRTP and the CTNSTP is made. The results achieved show the robustness and efficiency of the metaheuristi

Spatial coverage in routing and path planning problems

Routing and path planning problems that involve spatial coverage have received increasing attention in recent years in different application areas. Spatial coverage refers to the possibility of considering nodes that are not directly served by a vehicle as visited for the purpose of the objective function or constraints. Despite similarities between the underlying problems, solution approaches have been developed in different disciplines independently, leading to different terminologies and solution techniques. This paper proposes a unified view of the approaches: Based on a formal introduction of the concept of spatial coverage in vehicle routing, it presents a classification scheme for core problem features and summarizes problem variants and solution concepts developed in the domains of operations research and robotics. The connections between these related problem classes offer insights into common underlying structures and open possibilities for developing new applications and algorithms

Metaheuristics and cooperative approaches for the Bi-objective Ring Star Problem

International audienceThis paper presents and investigates different approaches to solve a new bi-objective routing problem called the ring star problem. It consists of locating a simple cycle through a subset of nodes of a graph while optimizing two kinds of cost. The first objective is the minimization of a ring cost that is related to the length of the cycle. The second one is the minimization of an assignment cost from non-visited nodes to visited ones. In spite of its obvious bi-objective formulation, this problem has always been investigated in a single-objective way. To tackle the bi-objective ring star problem, we first investigate different stand-alone search methods. Then, we propose two cooperative strategies that combine two multi-objective metaheuristics: an elitist evolutionary algorithm and a population-based local search. We apply these new hybrid approaches to well-known benchmark test instances and demonstrate their effectiveness in comparison to non-hybrid algorithms and to state-of-the-art methods

Kiertovaihtoalgoritmi ja muunnoksia yleistetylle ajoneuvoreititysongelmalle

Vehicle routing problems have numerous applications in fields such as transportation, supply logistics and network design. The optimal design of these routes fall in the category of NP-hard optimization problems, meaning that the computational complexity increases extremely fast with increasing problem size. The Generalized Vehicle Routing Problem (GVRP) is a general problem type that includes a broad variety of other problems as special cases. The main special feature of the GVRP is that the customers are grouped in clusters. For each cluster, only one customer is visited. In this thesis, we implement a heuristic algorithm to solve GVRP instances in reasonable time. Especially, we include a cyclic exchange method that considers a very large search neighborhood. In addition, we study the related Capacitated m-Ring-Star Problem (CmRSP). We present the Distance-Constrained Capacitated m-Ring-Star Problem (DCmRSP) and show that it contains the Multivehicle Covering Tour Problem (MCTP) as a special case. We show that DCmRSP instances can be transformed to (distance-constrained) GVRP with minor adaptations and solved with the same heuristic algorithm. Our algorithm is able to find best known solutions to all GVRP test instances; for two of them, our method shows strict improvement. The transformed CmRSP and MCTP instances are solved successfully by the same algorithm with adequate performance.Ajoneuvoreititysongelmilla on lukuisia sovelluksia muun muassa logistiikan ja verkostosuunnittelun aloilla. Tällaisten reittien optimaalinen ratkaiseminen kuuluu NP-vaikeiden optimointiongelmien kategoriaan, eli ratkaisuun vaadittava laskentateho kasvaa erittäin nopeasti ongelman koon suhteen. Yleistetty ajoneuvoreititysongelma (Generalized Vehicle Routing Problem, GVRP) on ongelmatyyppi, joka kattaa joukon muita reititysongelmia erikoistapauksina. GVRP:n selkein erityispiirre on asiakkaiden jako ryppäisiin: kussakin ryppäässä on käytävä tasan yhden asiakkaan luona. Tässä diplomityössä esitellään ja toteutetaan heuristinen algoritmi, joka etsii kohtalaisessa ajassa ratkaisuja GVRP-ongelmiin. Menetelmä sisältää kiertovaihtoalgoritmin, joka kykenee etsimään ratkaisuja hyvin laajasta ympäristöstä. Tutkimuksen kohteena on lisäksi m-rengastähtiongelma (Capacitated m-Ring-Star Problem, CmRSP). Esittelemme ongelman etäisyysrajoitetun version (DCmRSP), ja näytämme, että kyseiseen ongelmaan sisältyy usean ajoneuvon peittävän reitin ongelma (Multivehicle Covering Tour Problem). Näytämme, että DCmRSP-ongelman pystyy pienin muutoksin muuntamaan GVRP-ongelmaksi ja ratkaisemaan samalla heuristisella algoritmilla. Algoritmi löytää parhaat tunnetut ratkaisut kaikkiin GVRP-testitehtäviin. Kahdessa tapauksessa ratkaisu on parempi aiemmin löydettyihin nähden. Algoritmi kykenee ratkaisemaan muunnetut CmRSP- ja MCTP-testitehtävät kohtalaisella ratkaisulaadulla

Metaheuristics and Their Hybridization to Solve the Bi-objective Ring Star Problem: a Comparative Study

This paper presents and experiments approaches to solve a new bi-objective routing problem called the ring star problem. It consists of locating a simple cycle through a subset of nodes of a graph while optimizing two kinds of cost. The first objective is the minimization of a ring cost that is related to the length of the cycle. The second one is the minimization of an assignment cost from non-visited nodes to visited ones. In spite of its obvious bi-objective formulation, this problem has always been investigated in a single-objective way. To tackle the bi-objective ring star problem, we first investigate different stand-alone search methods. Then, we propose two cooperative strategies that combines two multiple objective metaheuristics: an elitist evolutionary algorithm and a population-based local search. We apply this new hybrid approaches to well-known benchmark test instances and demonstrate their effectiveness in comparison to non-hybrid algorithms and to state-of-the-art methods

Felix Alexandrovich Berezin and his work

This is a survey of Berezin's work focused on three topics: representation theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page

Singularity structure of the pi N scattering amplitude in a meson-exchange model up to energies W < 2.0 GeV

Within the previously developed Dubna-Mainz-Taipei meson-exchange model, the singularity structure of the pi N scattering amplitudes has been investigated. For all partial waves up to F waves and c.m. energies up to W = 2 GeV, the T-matrix poles have been calculated by three different techniques: analytic continuation into the complex energy plane, speed-plot and the regularization method. For all 4-star resonances, we find a perfect agreement between the analytic continuation and the regularization method. We also find resonance poles for resonances that are not so well established, but in these cases the pole positions and residues obtained by analytic continuation can substantially differ from the results predicted by the speed-plot and regularization methods.Comment: 21 pages, 4 figures, 4 table