Algorithms for network design and routing problems

In this thesis we study three combinatorial optimization problems belonging to the classes of Network Design and Vehicle Routing problems that are strongly linked in the context of the design and management of transportation networks: the Non-Bifurcated Capacitated Network Design Problem (NBP), the Period Vehicle Routing Problem (PVRP) and the Pickup and Delivery Problem with Time Windows (PDPTW). These problems are NP-hard and contain as special cases some well known difficult problems such as the Traveling Salesman Problem and the Steiner Tree Problem. Moreover, they model the core structure of many practical problems arising in logistics and telecommunications. The NBP is the problem of designing the optimum network to satisfy a given set of traffic demands. Given a set of nodes, a set of potential links and a set of point-to-point demands called commodities, the objective is to select the links to install and dimension their capacities so that all the demands can be routed between their respective endpoints, and the sum of link fixed costs and commodity routing costs is minimized. The problem is called non- bifurcated because the solution network must allow each demand to follow a single path, i.e., the flow of each demand cannot be splitted. Although this is the case in many real applications, the NBP has received significantly less attention in the literature than other capacitated network design problems that allow bifurcation. We describe an exact algorithm for the NBP that is based on solving by an integer programming solver a formulation of the problem strengthened by simple valid inequalities and four new heuristic algorithms. One of these heuristics is an adaptive memory metaheuristic, based on partial enumeration, that could be applied to a wider class of structured combinatorial optimization problems. In the PVRP a fleet of vehicles of identical capacity must be used to service a set of customers over a planning period of several days. Each customer specifies a service frequency, a set of allowable day-combinations and a quantity of product that the customer must receive every time he is visited. For example, a customer may require to be visited twice during a 5-day period imposing that these visits take place on Monday-Thursday or Monday-Friday or Tuesday-Friday. The problem consists in simultaneously assigning a day- combination to each customer and in designing the vehicle routes for each day so that each customer is visited the required number of times, the number of routes on each day does not exceed the number of vehicles available, and the total cost of the routes over the period is minimized. We also consider a tactical variant of this problem, called Tactical Planning Vehicle Routing Problem, where customers require to be visited on a specific day of the period but a penalty cost, called service cost, can be paid to postpone the visit to a later day than that required. At our knowledge all the algorithms proposed in the literature for the PVRP are heuristics. In this thesis we present for the first time an exact algorithm for the PVRP that is based on different relaxations of a set partitioning-like formulation. The effectiveness of the proposed algorithm is tested on a set of instances from the literature and on a new set of instances. Finally, the PDPTW is to service a set of transportation requests using a fleet of identical vehicles of limited capacity located at a central depot. Each request specifies a pickup location and a delivery location and requires that a given quantity of load is transported from the pickup location to the delivery location. Moreover, each location can be visited only within an associated time window. Each vehicle can perform at most one route and the problem is to satisfy all the requests using the available vehicles so that each request is serviced by a single vehicle, the load on each vehicle does not exceed the capacity, and all locations are visited according to their time window. We formulate the PDPTW as a set partitioning-like problem with additional cuts and we propose an exact algorithm based on different relaxations of the mathematical formulation and a branch-and-cut-and-price algorithm. The new algorithm is tested on two classes of problems from the literature and compared with a recent branch-and-cut-and-price algorithm from the literature.

A novel map-matching procedure for low-sampling GPS data with applications to traffic flow analysis

An extensive sample (2%) of private vehicles in Italy are equipped with a GPS device that periodically measures their position and dynamical state for insurance purposes. Having access to this type of data allows to develop theoretical and practical applications of great interest: the real-time reconstruction of traffic state in a certain region, the development of accurate models of vehicle dynamics, the study of the cognitive dynamics of drivers. In order for these applications to be possible, we first need to develop the ability to reconstruct the paths taken by vehicles on the road network from the raw GPS data. In fact, these data are affected by positioning errors and they are often very distanced from each other (~2 Km). For these reasons, the task of path identification is not straightforward. This thesis describes the approach we followed to reliably identify vehicle paths from this kind of low-sampling data. The problem of matching data with roads is solved with a bayesian approach of maximum likelihood. While the identification of the path taken between two consecutive GPS measures is performed with a specifically developed optimal routing algorithm, based on A* algorithm. The procedure was applied on an off-line urban data sample and proved to be robust and accurate. Future developments will extend the procedure to real-time execution and nation-wide coverage.

Decomposition Methods and Network Design Problems

Decomposition based approaches are recalled from primal and dual point of view. The possibility of building partially disaggregated reduced master problems is investigated. This extends the idea of aggregated-versus-disaggregated formulation to a gradual choice of alternative level of aggregation. Partial aggregation is applied to the linear multicommodity minimum cost flow problem. The possibility of having only partially aggregated bundles opens a wide range of alternatives with different trade-offs between the number of iterations and the required computation for solving it. This trade-off is explored for several sets of instances and the results are compared with the ones obtained by directly solving the natural node-arc formulation. An iterative solution process to the route assignment problem is proposed, based on the well-known Frank Wolfe algorithm. In order to provide a first feasible solution to the Frank Wolfe algorithm, a linear multicommodity min-cost flow problem is solved to optimality by using the decomposition techniques mentioned above. Solutions of this problem are useful for network orientation and design, especially in relation with public transportation systems as the Personal Rapid Transit. A single-commodity robust network design problem is addressed. In this, an undirected graph with edge costs is given together with a discrete set of balance matrices, representing different supply/demand scenarios. The goal is to determine the minimum cost installation of capacities on the edges such that the flow exchange is feasible for every scenario. A set of new instances that are computationally hard for the natural flow formulation are solved by means of a new heuristic algorithm. Finally, an efficient decomposition-based heuristic approach for a large scale stochastic unit commitment problem is presented. The addressed real-world stochastic problem employs at its core a deterministic unit commitment planning model developed by the California Independent System Operator (ISO).

Design and Development of Network Monitoring Strategies in P4-enabled Programmable Switches

Network monitoring is of paramount importance for effective network management: it allows to constantly observe the network’s behavior to ensure it is working as intended and can trigger both automated and manual remediation procedures in case of failures and anomalies. The concept of SDN decouples the control logic from legacy network infrastructure to perform centralized control on multiple switches in the network, and in this context, the responsibility of switches is only to forward packets according to the flow control instructions provided by controller. However, as current SDN switches only expose simple per-port and per-flow counters, the controller has to do almost all the processing to determine the network state, which causes significant communication overhead and excessive latency for monitoring purposes. The absence of programmability in the data plane of SDN prompted the advent of programmable switches, which allow developers to customize the data-plane pipeline and implement novel programs operating directly in the switches. This means that we can offload certain monitoring tasks to programmable data planes, to perform fine-grained monitoring even at very high packet processing speeds. Given the central importance of network monitoring exploiting programmable data planes, the goal of this thesis is to enable a wide range of monitoring tasks in programmable switches, with a specific focus on the ones equipped with programmable ASICs. Indeed, most network monitoring solutions available in literature do not take computational and memory constraints of programmable switches into due account, preventing, de facto, their successful implementation in commodity switches. This claims that network monitoring tasks can be executed in programmable switches. Our evaluations show that the contributions in this thesis could be used by network administrators as well as network security engineers, to better understand the network status depending on different monitoring metrics, and thus prevent network infrastructure and service outages.

Characterization of DNA sequence properties through network and statistical approaches

In this thesis we will see that the DNA sequence is constantly shaped by the interactions with its environment at multiple levels, showing footprints of DNA methylation, of its 3D organization and, in the case of bacteria, of the interaction with the host organisms. In the first chapter, we will see that analyzing the distribution of distances between consecutive dinucleotides of the same type along the sequence, we can detect epigenetic and structural footprints. In particular, we will see that CG distance distribution allows to distinguish among organisms of different biological complexity, depending on how much CG sites are involved in DNA methylation. Moreover, we will see that CG and TA can be described by the same fitting function, suggesting a relationship between the two. We will also provide an interpretation of the observed trend, simulating a positioning process guided by the presence and absence of memory. In the end, we will focus on TA distance distribution, characterizing deviations from the trend predicted by the best fitting function, and identifying specific patterns that might be related to peculiar mechanical properties of the DNA and also to epigenetic and structural processes. In the second chapter, we will see how we can map the 3D structure of the DNA onto its sequence. In particular, we devised a network-based algorithm that produces a genome assembly starting from its 3D configuration, using as inputs Hi-C contact maps. Specifically, we will see how we can identify the different chromosomes and reconstruct their sequences by exploiting the spectral properties of the Laplacian operator of a network. In the third chapter, we will see a novel method for source clustering and source attribution, based on a network approach, that allows to identify host-bacteria interaction starting from the detection of Single-Nucleotide Polymorphisms along the sequence of bacterial genomes.

Data-stream driven Fuzzy-granular approaches for system maintenance

Intelligent systems are currently inherent to the society, supporting a synergistic human-machine collaboration. Beyond economical and climate factors, energy consumption is strongly affected by the performance of computing systems. The quality of software functioning may invalidate any improvement attempt. In addition, data-driven machine learning algorithms are the basis for human-centered applications, being their interpretability one of the most important features of computational systems. Software maintenance is a critical discipline to support automatic and life-long system operation. As most software registers its inner events by means of logs, log analysis is an approach to keep system operation. Logs are characterized as Big data assembled in large-flow streams, being unstructured, heterogeneous, imprecise, and uncertain. This thesis addresses fuzzy and neuro-granular methods to provide maintenance solutions applied to anomaly detection (AD) and log parsing (LP), dealing with data uncertainty, identifying ideal time periods for detailed software analyses. LP provides deeper semantics interpretation of the anomalous occurrences. The solutions evolve over time and are general-purpose, being highly applicable, scalable, and maintainable. Granular classification models, namely, Fuzzy set-Based evolving Model (FBeM), evolving Granular Neural Network (eGNN), and evolving Gaussian Fuzzy Classifier (eGFC), are compared considering the AD problem. The evolving Log Parsing (eLP) method is proposed to approach the automatic parsing applied to system logs. All the methods perform recursive mechanisms to create, update, merge, and delete information granules according with the data behavior. For the first time in the evolving intelligent systems literature, the proposed method, eLP, is able to process streams of words and sentences. Essentially, regarding to AD accuracy, FBeM achieved (85.64+-3.69)%; eGNN reached (96.17+-0.78)%; eGFC obtained (92.48+-1.21)%; and eLP reached (96.05+-1.04)%. Besides being competitive, eLP particularly generates a log grammar, and presents a higher level of model interpretability.