VNF placement optimization at the edge and cloud

Network Function Virtualization (NFV) has revolutionized the way network services are offered to end users. Individual network functions are decoupled from expensive and dedicated middleboxes and are now provided as software-based virtualized entities called Virtualized Network Functions (VNFs). NFV is often complemented with the Cloud Computing paradigm to provide networking functions t

Routing and scheduling optimisation under uncertainty for engineering applications

The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits.The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits

Study, evaluation and contributions to new algorithms for the embedding problem in a network virtualization environment

Network virtualization is recognized as an enabling technology for the future Internet. It aims to overcome the resistance of the current Internet to architectural change and to enable a new business model decoupling the network services from the underlying infrastructure. The problem of embedding virtual networks in a substrate network is the main resource allocation challenge in network virtualization and is usually referred to as the Virtual Network Embedding (VNE) problem. VNE deals with the allocation of virtual resources both in nodes and links. Therefore, it can be divided into two sub-problems: Virtual Node Mapping where virtual nodes have to be allocated in physical nodes and Virtual Link Mapping where virtual links connecting these virtual nodes have to be mapped to paths connecting the corresponding nodes in the substrate network. Application of network virtualization relies on algorithms that can instantiate virtualized networks on a substrate infrastructure, optimizing the layout for service-relevant metrics. This class of algorithms is commonly known as VNE algorithms. This thesis proposes a set of contributions to solve the research challenges of the VNE that have not been tackled by the research community. To do that, it performs a deep and comprehensive survey of virtual network embedding. The first research challenge identified is the lack of proposals to solve the virtual link mapping stage of VNE using single path in the physical network. As this problem is NP-hard, existing proposals solve it using well known shortest path algorithms that limit the mapping considering just one constraint. This thesis proposes the use of a mathematical multi-constraint routing framework called paths algebra to solve the virtual link mapping stage. Besides, the thesis introduces a new demand caused by virtual link demands into physical nodes acting as intermediate (hidden) hops in a path of the physical network. Most of the current VNE approaches are centralized. They suffer of scalability issues and provide a single point of failure. In addition, they are not able to embed virtual network requests arriving at the same time in parallel. To solve this challenge, this thesis proposes a distributed, parallel and universal virtual network embedding framework. The proposed framework can be used to run any existing embedding algorithm in a distributed way. Thereby, computational load for embedding multiple virtual networks is spread across the substrate network Energy efficiency is one of the main challenges in future networking environments. Network virtualization can be used to tackle this problem by sharing hardware, instead of requiring dedicated hardware for each instance. Until now, VNE algorithms do not consider energy as a factor for the mapping. This thesis introduces the energy aware VNE where the main objective is to switch off as many network nodes and interfaces as possible by allocating the virtual demands to a consolidated subset of active physical networking equipment. To evaluate and validate the aforementioned VNE proposals, this thesis helped in the development of a software framework called ALgorithms for Embedding VIrtual Networks (ALEVIN). ALEVIN allows to easily implement, evaluate and compare different VNE algorithms according to a set of metrics, which evaluate the algorithms and compute their results on a given scenario for arbitrary parameters

Adaptive and Restorative Capacity Planning for Complex Infrastructure Networks: Optimization Algorithms and Applications

This research focuses on planning and scheduling of adaptive and restorative capacity enhancement efforts provided by complex infrastructure network in the aftermath of disruptive events. To maximize the adaptive capacity, we propose a framework to optimize the performance level to which a network can quickly adapt to post-disruption conditions by temporary means. Optimal resource allocation is determined with respect to the spatial dimensions of network components and available resources, the effectiveness of the resources, the importance of each element, and the system-wide impact to potential flows within the network. Optimal resource allocation is determined with respect to the spatial dimensions of network components and available resources, the effectiveness of the resources, the importance of each element, and the system-wide impact to potential flows within the network. To optimize the restorative capacity enhancement, we present two mathematical formulations to assign restoration crews to disrupted components and maximize network resilience progress in any given time horizon. In the first formulation, the number of assigned restoration crews to each component can vary to increase the flexibility of models in the presence of different disruption scenarios. Along with considering the assumptions of the first formulation, the second formulation models the condition where the disrupted components can be partially active during the restoration process. We test the efficacy of proposed formulation, for adaptive and restorative capacity enhancement, on the realistic data set of 400-kV French electric transmission Network. The results indicate that the proposed formulations can be used for a wide variety of infrastructure networks and real-time restoration process planning. Approaching the proposed formulations to reality introduces a synchronized routing problem for planning and scheduling restorative efforts for infrastructure networks in the aftermath of a disruptive event. In this problem, a set of restoration crews are dispatched from depots to a road network to restore the disrupted infrastructure network. Considering Binary and Proportional Active formulation, we propose two mathematical formulation in which the number of restoration crews assigned to each disrupted component, the arrival time of each assigned crew to each disrupted component and consequently the restoration rate associated with each disrupted component are considered as variables to increase the flexibility of the model in the presence of different disruptive events. To find the coordinated routes, we propose a relaxed mixed integer program as well as a set of valid inequalities which relates the planning and scheduling efforts to decision makers policies. The integration of the relaxed formulation and valid inequalities results in a lower bound for the original formulations. Furthermore, we propose a constructive heuristic algorithm based on the strong initial solution obtained from feasibility algorithm and a local search algorithm. Computational results on gas, water, and electric power infrastructure network instances from Shelby County, TN data, demonstrates both the effectiveness of the proposed model formulation, in solving small to medium scale problems, the strength of the initial solution procedure, especially for large-scale problems. We also prove that the heuristic algorithm to obtain the near optimal or near-optimal solutions

Electric vehicle routing problem with backhauls considering the location of charging stations and the operation of the electric power distribution system

Las compañías logísticas están altamente motivadas en hacer que sus operaciones sean menos contaminantes a través de una solución eficiente con vehículos eléctricos (VEs). Sin embargo, el rango de conducción es uno de los aspectos limitantes en la inserción de los vehículos eléctricos en las flotas logísticas, debido a la baja capacidad proporcionada por las baterías para completar las rutas. En este sentido, es necesario desarrollar un marco de trabajo para incrementar de forma virtual la capacidad de la batería, por medio de la ubicación de estaciones de recarga a lo largo de la red de transporte, y completar las rutas satisfactoriamente. Por otro lado, los operadores de redes de distribución expresan su preocupación asociada a la inclusión de nuevas cargas eléctricas (estaciones de recarga de VEs), sin desmejorar la gestión óptima de suministro de energía a los usuarios finales. Bajo estas circunstancias, en este artículo se introduce el problema de ruteamiento de vehículos eléctricos con recogidas, formulado como un modelo de programación lineal entera mixta y considerando la operación del sistema de distribución en condiciones de máxima demanda. Se consideran diferentes puntos candidatos a estaciones de recarga de VEs para recargar la batería al final de una ruta linehaul o durante la ruta backhaul. El problema se formula con un enfoque multiobjetivo, donde se modela la operación de las redes de transporte y de distribución de energía eléctrica. El modelo propuesto es evaluado en instancias del VRPB (Vehicle Routing Problem with Backhauls) junto con sistemas de prueba de distribución de la literatura especializada. Para cada prueba, se presentan los correspondientes frentes de Pareto usando el método ε-constraint. Logistics companies are largely encouraged to make greener their operations through an efficient solution with electric vehicles (EVs). However, the driving range is one of the limiting aspects for the introduction of EVs in logistics fleet, due to the low capacity provided by the batteries to perform the routes. In this regards, it is necessary to set up a framework to virtually increase this battery capacity by locating EV charging stations (EVCSs) along the transportation network for the completion of their routes. By the other side, the Distribution Network Operators (DNOs) express the concern associated with the inclusion of new power demands to be attended (installation of EVCSs) in the Distribution Network (DN), without reducing the optimal power supply management for the end-users. Under these circumstances, in this paper the Electric Vehicle Routing Problem with Backhauls and optimal operation of the Distribution Network (EVRPB-DN) is introduced and formulated as a mixed-integer linear programming model, considering the operation of the DN in conditions of maximum power demand. Different candidate points for the EVs charging are considered to recharge the battery at the end of the linehaul route or during the backhaul route. The problem is formulated as a multi-objective approach where the transportation and power distribution networks operation are modeled. The performance and effectiveness of the proposed formulation is tested in VRPB instance datasets and DN test systems from the literature. Pareto fronts for each instance are presented, using the ε-constraint methodology

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set