Mathematical Optimization Applied to Thermal and Electrical Energy Systems

This Thesis aims at building and discussing mathematical models applications focused on Energy problems, both on the thermal and electrical side. The objective is to show how mathematical programming techniques developed within Operational Research can give useful answers in the Energy Sector, how they can provide tools to support decision making processes of Companies operating in the Energy production and distribution and how they can be successfully used to make simulations and sensitivity analyses to better understand the state of the art and convenience of a particular technology by comparing it with the available alternatives. The first part discusses the fundamental mathematical background followed by a comprehensive literature review about mathematical modelling in the Energy Sector. The second part presents mathematical models for the District Heating strategic network design and incremental network design. The objective is the selection of an optimal set of new users to be connected to an existing thermal network, maximizing revenues, minimizing infrastructure and operational costs and taking into account the main technical requirements of the real world application. Results on real and randomly generated benchmark networks are discussed with particular attention to instances characterized by big networks dimensions. The third part is devoted to the development of linear programming models for optimal battery operation in off-grid solar power schemes, with consideration of battery degradation. The key contribution of this work is the inclusion of battery degradation costs in the optimisation models. As available data on relating degradation costs to the nature of charge/discharge cycles are limited, we concentrate on investigating the sensitivity of operational patterns to the degradation cost structure. The objective is to investigate the combination of battery costs and performance at which such systems become economic. We also investigate how the system design should change when battery degradation is taken into account.

An architecture for network acceleration as a service in the cloud continuum

The pervasive availability of connected devices in any industrial and societal sector is pushing for an evolution of the well-established cloud computing model. The emerging paradigm of the cloud continuum embraces this decentralization trend and envisions virtualized computing resources physically located between traditional datacenters and data sources. By totally or partially executing closer to the network edge, applications can have quicker reactions to events, thus enabling advanced forms of automation and intelligence. However, these applications also induce new data-intensive workloads with low-latency constraints that require the adoption of specialized resources, such as high-performance communication options (e.g., RDMA, DPDK, XDP, etc.). Unfortunately, cloud providers still struggle to integrate these options into their infrastructures. That risks undermining the principle of generality that underlies the cloud computing scale economy by forcing developers to tailor their code to low-level APIs, non-standard programming models, and static execution environments. This thesis proposes a novel system architecture to empower cloud platforms across the whole cloud continuum with Network Acceleration as a Service (NAaaS). To provide commodity yet efficient access to acceleration, this architecture defines a layer of agnostic high-performance I/O APIs, exposed to applications and clearly separated from the heterogeneous protocols, interfaces, and hardware devices that implement it. A novel system component embodies this decoupling by offering a set of agnostic OS features to applications: memory management for zero-copy transfers, asynchronous I/O processing, and efficient packet scheduling. This thesis also explores the design space of the possible implementations of this architecture by proposing two reference middleware systems and by adopting them to support interactive use cases in the cloud continuum: a serverless platform and an Industry 4.0 scenario. A detailed discussion and a thorough performance evaluation demonstrate that the proposed architecture is suitable to enable the easy-to-use, flexible integration of modern network acceleration into next-generation cloud platforms.

Portfolio Approaches in Constraint Programming

Recent research has shown that the performance of a single, arbitrarily efficient algorithm can be significantly outperformed by using a portfolio of —possibly on-average slower— algorithms. Within the Constraint Programming (CP) context, a portfolio solver can be seen as a particular constraint solver that exploits the synergy between the constituent solvers of its portfolio for predicting which is (or which are) the best solver(s) to run for solving a new, unseen instance. In this thesis we examine the benefits of portfolio solvers in CP. Despite portfolio approaches have been extensively studied for Boolean Satisfiability (SAT) problems, in the more general CP field these techniques have been only marginally studied and used. We conducted this work through the investigation, the analysis and the construction of several portfolio approaches for solving both satisfaction and optimization problems. We focused in particular on sequential approaches, i.e., single-threaded portfolio solvers always running on the same core. We started from a first empirical evaluation on portfolio approaches for solving Constraint Satisfaction Problems (CSPs), and then we improved on it by introducing new data, solvers, features, algorithms, and tools. Afterwards, we addressed the more general Constraint Optimization Problems (COPs) by implementing and testing a number of models for dealing with COP portfolio solvers. Finally, we have come full circle by developing sunny-cp: a sequential CP portfolio solver that turned out to be competitive also in the MiniZinc Challenge, the reference competition for CP solvers.

On Reasonable Space and Time Cost Models for the λ-Calculus

Slot and van Emde Boas Invariance Thesis states that a time (respectively, space) cost model is reasonable for a computational model C if there are mutual simulations between Turing machines and C such that the overhead is polynomial in time (respectively, linear in space). The rationale is that under the Invariance Thesis, complexity classes such as LOGSPACE, P, PSPACE, become robust, i.e. machine independent. In this dissertation, we want to find out if it possible to define a reasonable space cost model for the lambda-calculus, the paradigmatic model for functional programming languages. We start by considering an unusual evaluation mechanism for the lambda-calculus, based on Girard's Geometry of Interaction, that was conjectured to be the key ingredient to obtain a space reasonable cost model. By a fine complexity analysis of this schema, based on new variants of non-idempotent intersection types, we disprove this conjecture. Then, we change the target of our analysis. We consider a variant over Krivine's abstract machine, a standard evaluation mechanism for the call-by-name lambda-calculus, optimized for space complexity, and implemented without any pointer. A fine analysis of the execution of (a refined version of) the encoding of Turing machines into the lambda-calculus allows us to conclude that the space consumed by this machine is indeed a reasonable space cost model. In particular, for the first time we are able to measure also sub-linear space complexities. Moreover, we transfer this result to the call-by-value case. Finally, we provide also an intersection type system that characterizes compositionally this new reasonable space measure. This is done through a minimal, yet non trivial, modification of the original de Carvalho type system.

Vehicle routing and location routing problems with minimum latency: algorithms and models

Latency can be defined as the sum of the arrival times at the customers. Minimum latency problems are specially relevant in applications related to humanitarian logistics. This thesis presents algorithms for solving a family of vehicle routing problems with minimum latency. First the latency location routing problem (LLRP) is considered. It consists of determining the subset of depots to be opened, and the routes that a set of homogeneous capacitated vehicles must perform in order to visit a set of customers such that the sum of the demands of the customers assigned to each vehicle does not exceed the capacity of the vehicle. For solving this problem three metaheuristic algorithms combining simulated annealing and variable neighborhood descent, and an iterated local search (ILS) algorithm, are proposed. Furthermore, the multi-depot cumulative capacitated vehicle routing problem (MDCCVRP) and the multi-depot k-traveling repairman problem (MDk-TRP) are solved with the proposed ILS algorithm. The MDCCVRP is a special case of the LLRP in which all the depots can be opened, and the MDk-TRP is a special case of the MDCCVRP in which the capacity constraints are relaxed. Finally, a LLRP with stochastic travel times is studied. A two-stage stochastic programming model and a variable neighborhood search algorithm are proposed for solving the problem. Furthermore a sampling method is developed for tackling instances with an infinite number of scenarios. Extensive computational experiments show that the proposed methods are effective for solving the problems under study.