Enhanced Mixed Integer Programming Techniques and Routing Problems

Mixed integer programming is up today one of the most widely used techniques for dealing with hard optimization problems. On the one side, many practical optimization problems arising from real-world applications (such as, e.g., scheduling, project planning, transportation, telecommunications, economics and finance, timetabling, etc) can be easily and effectively formulated as Mixed Integer linear Programs (MIPs). On the other hand, 50 and more years of intensive research has dramatically improved on the capability of the current generation of MIP solvers to tackle hard problems in practice. However, many questions are still open and not fully understood, and the mixed integer programming community is still more than active in trying to answer some of these questions. As a consequence, a huge number of papers are continuously developed and new intriguing questions arise every year. When dealing with MIPs, we have to distinguish between two different scenarios. The first one happens when we are asked to handle a general MIP and we cannot assume any special structure for the given problem. In this case, a Linear Programming (LP) relaxation and some integrality requirements are all we have for tackling the problem, and we are ``forced" to use some general purpose techniques. The second one happens when mixed integer programming is used to address a somehow structured problem. In this context, polyhedral analysis and other theoretical and practical considerations are typically exploited to devise some special purpose techniques. This thesis tries to give some insights in both the above mentioned situations. The first part of the work is focused on general purpose cutting planes, which are probably the key ingredient behind the success of the current generation of MIP solvers. Chapter 1 presents a quick overview of the main ingredients of a branch-and-cut algorithm, while Chapter 2 recalls some results from the literature in the context of disjunctive cuts and their connections with Gomory mixed integer cuts. Chapter 3 presents a theoretical and computational investigation of disjunctive cuts. In particular, we analyze the connections between different normalization conditions (i.e., conditions to truncate the cone associated with disjunctive cutting planes) and other crucial aspects as cut rank, cut density and cut strength. We give a theoretical characterization of weak rays of the disjunctive cone that lead to dominated cuts, and propose a practical method to possibly strengthen those cuts arising from such weak extremal solution. Further, we point out how redundant constraints can affect the quality of the generated disjunctive cuts, and discuss possible ways to cope with them. Finally, Chapter 4 presents some preliminary ideas in the context of multiple-row cuts. Very recently, a series of papers have brought the attention to the possibility of generating cuts using more than one row of the simplex tableau at a time. Several interesting theoretical results have been presented in this direction, often revisiting and recalling other important results discovered more than 40 years ago. However, is not clear at all how these results can be exploited in practice. As stated, the chapter is a still work-in-progress and simply presents a possible way for generating two-row cuts from the simplex tableau arising from lattice-free triangles and some preliminary computational results. The second part of the thesis is instead focused on the heuristic and exact exploitation of integer programming techniques for hard combinatorial optimization problems in the context of routing applications. Chapters 5 and 6 present an integer linear programming local search algorithm for Vehicle Routing Problems (VRPs). The overall procedure follows a general destroy-and-repair paradigm (i.e., the current solution is first randomly destroyed and then repaired in the attempt of finding a new improved solution) where a class of exponential neighborhoods are iteratively explored by heuristically solving an integer programming formulation through a general purpose MIP solver. Chapters 7 and 8 deal with exact branch-and-cut methods. Chapter 7 presents an extended formulation for the Traveling Salesman Problem with Time Windows (TSPTW), a generalization of the well known TSP where each node must be visited within a given time window. The polyhedral approaches proposed for this problem in the literature typically follow the one which has been proven to be extremely effective in the classical TSP context. Here we present an overall (quite) general idea which is based on a relaxed discretization of time windows. Such an idea leads to a stronger formulation and to stronger valid inequalities which are then separated within the classical branch-and-cut framework. Finally, Chapter 8 addresses the branch-and-cut in the context of Generalized Minimum Spanning Tree Problems (GMSTPs) (i.e., a class of NP-hard generalizations of the classical minimum spanning tree problem). In this chapter, we show how some basic ideas (and, in particular, the usage of general purpose cutting planes) can be useful to improve on branch-and-cut methods proposed in the literature.

A study on set variable representations in constraint programming

Il lavoro presentato in questa tesi si colloca nel contesto della programmazione con vincoli, un paradigma per modellare e risolvere problemi di ricerca combinatoria che richiedono di trovare soluzioni in presenza di vincoli. Una vasta parte di questi problemi trova naturale formulazione attraverso il linguaggio delle variabili insiemistiche. Dal momento che il dominio di tali variabili può essere esponenziale nel numero di elementi, una rappresentazione esplicita è spesso non praticabile. Recenti studi si sono quindi focalizzati nel trovare modi efficienti per rappresentare tali variabili. Pertanto si è soliti rappresentare questi domini mediante l'uso di approssimazioni definite tramite intervalli (d'ora in poi rappresentazioni), specificati da un limite inferiore e un limite superiore secondo un'appropriata relazione d'ordine. La recente evoluzione della ricerca sulla programmazione con vincoli sugli insiemi ha chiaramente indicato che la combinazione di diverse rappresentazioni permette di raggiungere prestazioni di ordini di grandezza superiori rispetto alle tradizionali tecniche di codifica. Numerose proposte sono state fatte volgendosi in questa direzione. Questi lavori si differenziano su come è mantenuta la coerenza tra le diverse rappresentazioni e su come i vincoli vengono propagati al fine di ridurre lo spazio di ricerca. Sfortunatamente non esiste alcun strumento formale per paragonare queste combinazioni. Il principale obiettivo di questo lavoro è quello di fornire tale strumento, nel quale definiamo precisamente la nozione di combinazione di rappresentazioni facendo emergere gli aspetti comuni che hanno caratterizzato i lavori precedenti. In particolare identifichiamo due tipi possibili di combinazioni, una forte ed una debole, definendo le nozioni di coerenza agli estremi sui vincoli e sincronizzazione tra rappresentazioni. Il nostro studio propone alcune interessanti intuizioni sulle combinazioni esistenti, evidenziandone i limiti e svelando alcune sorprese. Inoltre forniamo un'analisi di complessità della sincronizzazione tra minlex, una rappresentazione in grado di propagare in maniera ottimale vincoli lessicografici, e le principali rappresentazioni esistenti.

Designing and Programming Organizational Infrastructures for Agents situated in Artifact-based Environments

Actual trends in software development are pushing the need to face a multiplicity of diverse activities and interaction styles characterizing complex and distributed application domains, in such a way that the resulting dynamics exhibits some grade of order, i.e. in terms of evolution of the system and desired equilibrium. Autonomous agents and Multiagent Systems are argued in literature as one of the most immediate approaches for describing such a kind of challenges. Actually, agent research seems to converge towards the definition of renewed abstraction tools aimed at better capturing the new demands of open systems. Besides agents, which are assumed as autonomous entities purposing a series of design objectives, Multiagent Systems account new notions as first-class entities, aimed, above all, at modeling institutional/organizational entities, placed for normative regulation, interaction and teamwork management, as well as environmental entities, placed as resources to further support and regulate agent work. The starting point of this thesis is recognizing that both organizations and environments can be rooted in a unifying perspective. Whereas recent research in agent systems seems to account a set of diverse approaches to specifically face with at least one aspect within the above mentioned, this work aims at proposing a unifying approach where both agents and their organizations can be straightforwardly situated in properly designed working environments. In this line, this work pursues reconciliation of environments with sociality, social interaction with environment based interaction, environmental resources with organizational functionalities with the aim to smoothly integrate the various aspects of complex and situated organizations in a coherent programming approach. Rooted in Agents and Artifacts (A&A) meta-model, which has been recently introduced both in the context of agent oriented software engineering and programming, the thesis promotes the notion of Embodied Organizations, characterized by computational infrastructures attaining a seamless integration between agents, organizations and environmental entities.

Algoritmi esatti per il Job Shop Scheduling: approcci Mathematical Programming

In questa tesi ci occuperemo di fornire un modello MIP di base e di alcune sue varianti, realizzate allo scopo di comprenderne il comportamento ed eventualmente migliorarne l’efficienza. Le diverse varianti sono state costruite agendo in particolar modo sulla definizione di alcuni vincoli, oppure sui bound delle variabili, oppure ancora nell’obbligare il risolutore a focalizzarsi su determinate decisioni o specifiche variabili. Sono stati testati alcuni dei problemi tipici presenti in letteratura e i diversi risultati sono stati opportunamente valutati e confrontati. Tra i riferimenti per tale confronto sono stati considerati anche i risultati ottenibili tramite un modello Constraint Programming, che notoriamente produce risultati apprezzabili in ambito di schedulazione. Un ulteriore scopo della tesi è, infatti, comparare i due approcci Mathematical Programming e Constraint Programming, identificandone quindi i pregi e gli svantaggi e provandone la trasferibilità al modello raffrontato.

Decomposition and reformulation of integer linear programming problems

This thesis deals with an investigation of Decomposition and Reformulation to solve Integer Linear Programming Problems. This method is often a very successful approach computationally, producing high-quality solutions for well-structured combinatorial optimization problems like vehicle routing, cutting stock, p-median and generalized assignment . However, until now the method has always been tailored to the specific problem under investigation. The principal innovation of this thesis is to develop a new framework able to apply this concept to a generic MIP problem. The new approach is thus capable of auto-decomposition and autoreformulation of the input problem applicable as a resolving black box algorithm and works as a complement and alternative to the normal resolving techniques. The idea of Decomposing and Reformulating (usually called in literature Dantzig and Wolfe Decomposition DWD) is, given a MIP, to convexify one (or more) subset(s) of constraints (slaves) and working on the partially convexified polyhedron(s) obtained. For a given MIP several decompositions can be defined depending from what sets of constraints we want to convexify. In this thesis we mainly reformulate MIPs using two sets of variables: the original variables and the extended variables (representing the exponential extreme points). The master constraints consist of the original constraints not included in any slaves plus the convexity constraint(s) and the linking constraints(ensuring that each original variable can be viewed as linear combination of extreme points of the slaves). The solution procedure consists of iteratively solving the reformulated MIP (master) and checking (pricing) if a variable of reduced costs exists, and in which case adding it to the master and solving it again (columns generation), or otherwise stopping the procedure. The advantage of using DWD is that the reformulated relaxation gives bounds stronger than the original LP relaxation, in addition it can be incorporated in a Branch and bound scheme (Branch and Price) in order to solve the problem to optimality. If the computational time for the pricing problem is reasonable this leads in practice to a stronger speed up in the solution time, specially when the convex hull of the slaves is easy to compute, usually because of its special structure.

Hybrid constraint programming and metaheuristic methods for large scale optimization problems

This work presents hybrid Constraint Programming (CP) and metaheuristic methods for the solution of Large Scale Optimization Problems; it aims at integrating concepts and mechanisms from the metaheuristic methods to a CP-based tree search environment in order to exploit the advantages of both approaches. The modeling and solution of large scale combinatorial optimization problem is a topic which has arisen the interest of many researcherers in the Operations Research field; combinatorial optimization problems are widely spread in everyday life and the need of solving difficult problems is more and more urgent. Metaheuristic techniques have been developed in the last decades to effectively handle the approximate solution of combinatorial optimization problems; we will examine metaheuristics in detail, focusing on the common aspects of different techniques. Each metaheuristic approach possesses its own peculiarities in designing and guiding the solution process; our work aims at recognizing components which can be extracted from metaheuristic methods and re-used in different contexts. In particular we focus on the possibility of porting metaheuristic elements to constraint programming based environments, as constraint programming is able to deal with feasibility issues of optimization problems in a very effective manner. Moreover, CP offers a general paradigm which allows to easily model any type of problem and solve it with a problem-independent framework, differently from local search and metaheuristic methods which are highly problem specific. In this work we describe the implementation of the Local Branching framework, originally developed for Mixed Integer Programming, in a CP-based environment. Constraint programming specific features are used to ease the search process, still mantaining an absolute generality of the approach. We also propose a search strategy called Sliced Neighborhood Search, SNS, that iteratively explores slices of large neighborhoods of an incumbent solution by performing CP-based tree search and encloses concepts from metaheuristic techniques. SNS can be used as a stand alone search strategy, but it can alternatively be embedded in existing strategies as intensification and diversification mechanism. In particular we show its integration within the CP-based local branching. We provide an extensive experimental evaluation of the proposed approaches on instances of the Asymmetric Traveling Salesman Problem and of the Asymmetric Traveling Salesman Problem with Time Windows. The proposed approaches achieve good results on practical size problem, thus demonstrating the benefit of integrating metaheuristic concepts in CP-based frameworks.

Theoretical and implementation aspects in the mechanization of the metatheory of programming languages

Interactive theorem provers are tools designed for the certification of formal proofs developed by means of man-machine collaboration. Formal proofs obtained in this way cover a large variety of logical theories, ranging from the branches of mainstream mathematics, to the field of software verification. The border between these two worlds is marked by results in theoretical computer science and proofs related to the metatheory of programming languages. This last field, which is an obvious application of interactive theorem proving, poses nonetheless a serious challenge to the users of such tools, due both to the particularly structured way in which these proofs are constructed, and to difficulties related to the management of notions typical of programming languages like variable binding. This thesis is composed of two parts, discussing our experience in the development of the Matita interactive theorem prover and its use in the mechanization of the metatheory of programming languages. More specifically, part I covers: - the results of our effort in providing a better framework for the development of tactics for Matita, in order to make their implementation and debugging easier, also resulting in a much clearer code; - a discussion of the implementation of two tactics, providing infrastructure for the unification of constructor forms and the inversion of inductive predicates; we point out interactions between induction and inversion and provide an advancement over the state of the art. In the second part of the thesis, we focus on aspects related to the formalization of programming languages. We describe two works of ours: - a discussion of basic issues we encountered in our formalizations of part 1A of the Poplmark challenge, where we apply the extended inversion principles we implemented for Matita; - a formalization of an algebraic logical framework, posing more complex challenges, including multiple binding and a form of hereditary substitution; this work adopts, for the encoding of binding, an extension of Masahiko Sato's canonical locally named representation we designed during our visit to the Laboratory for Foundations of Computer Science at the University of Edinburgh, under the supervision of Randy Pollack.

Programming Robots with an Agent-Oriented BDI-based Control Architecture: Explorations using the JaCa and Webots Platforms

La crescente disponibilità di dispositivi meccanici e -soprattutto - elettronici le cui performance aumentano mentre il loro costo diminuisce, ha permesso al campo della robotica di compiere notevoli progressi. Tali progressi non sono stati fatti unicamente per ciò che riguarda la robotica per uso industriale, nelle catene di montaggio per esempio, ma anche per quella branca della robotica che comprende i robot autonomi domestici. Questi sistemi autonomi stanno diventando, per i suddetti motivi, sempre più pervasivi, ovvero sono immersi nello stesso ambiente nel quale vivono gli essere umani, e interagiscono con questi in maniera proattiva. Essi stanno compiendo quindi lo stesso percorso che hanno attraversato i personal computer all'incirca 30 anni fa, passando dall'essere costosi ed ingombranti mainframe a disposizione unicamente di enti di ricerca ed università, ad essere presenti all'interno di ogni abitazione, per un utilizzo non solo professionale ma anche di assistenza alle attività quotidiane o anche di intrattenimento. Per questi motivi la robotica è un campo dell'Information Technology che interessa sempre più tutti i tipi di programmatori software. Questa tesi analizza per prima cosa gli aspetti salienti della programmazione di controllori per robot autonomi (ovvero senza essere guidati da un utente), quindi, come l'approccio basato su agenti sia appropriato per la programmazione di questi sistemi. In particolare si mostrerà come un approccio ad agenti, utilizzando il linguaggio di programmazione Jason e quindi l'architettura BDI, sia una scelta significativa, dal momento che il modello sottostante a questo tipo di linguaggio è basato sul ragionamento pratico degli esseri umani (Human Practical Reasoning) e quindi è adatto alla implementazione di sistemi che agiscono in maniera autonoma. Dato che le possibilità di utilizzare un vero e proprio sistema autonomo per poter testare i controllori sono ridotte, per motivi pratici, economici e temporali, mostreremo come è facile e performante arrivare in maniera rapida ad un primo prototipo del robot tramite l'utilizzo del simulatore commerciale Webots. Il contributo portato da questa tesi include la possibilità di poter programmare un robot in maniera modulare e rapida per mezzo di poche linee di codice, in modo tale che l'aumento delle funzionalità di questo risulti un collo di bottiglia, come si verifica nella programmazione di questi sistemi tramite i classici linguaggi di programmazione imperativi. L'organizzazione di questa tesi prevede un capitolo di background nel quale vengono riportare le basi della robotica, della sua programmazione e degli strumenti atti allo scopo, un capitolo che riporta le nozioni di programmazione ad agenti, tramite il linguaggio Jason -quindi l'architettura BDI - e perché tale approccio è adatto alla programmazione di sistemi di controllo per la robotica. Successivamente viene presentata quella che è la struttura completa del nostro ambiente di lavoro software che comprende l'ambiente ad agenti e il simulatore, quindi nel successivo capitolo vengono mostrate quelle che sono le esplorazioni effettuate utilizzando Jason e un approccio classico (per mezzo di linguaggi classici), attraverso diversi casi di studio di crescente complessità; dopodiché, verrà effettuata una valutazione tra i due approcci analizzando i problemi e i vantaggi che comportano questi. Infine, la tesi terminerà con un capitolo di conclusioni e di riflessioni sulle possibili estensioni e lavori futuri.

Reuse Mechanisms and Concurrency: From Actors to Agent-Oriented Programming

La presente tesi è dedicata al riuso nel software. Eccettuata un'introduzione organica al tema, l'analisi è a livello dei meccanismi offerti dai linguaggi di programmazione e delle tecniche di sviluppo, con speciale attenzione rivolta al tema della concorrenza. Il primo capitolo fornisce un quadro generale nel quale il riuso del software è descritto, assieme alle ragioni che ne determinano l'importanza e ai punti cruciali relativi alla sua attuazione. Si individuano diversi livelli di riuso sulla base dell'astrazione e degli artefatti in gioco, e si sottolinea come i linguaggi contribuiscano alla riusabilità e alla realizzazione del riuso. In seguito, viene esplorato, con esempi di codice, il supporto al riuso da parte del paradigma ad oggetti, in termini di incapsulamento, ereditarietà, polimorfismo, composizione. La trattazione prosegue analizzando differenti feature – tipizzazione, interfacce, mixin, generics – offerte da vari linguaggi di programmazione, mostrando come esse intervengano sulla riusabilità dei componenti software. A chiudere il capitolo, qualche parola contestualizzata sull'inversione di controllo, la programmazione orientata agli aspetti, e il meccanismo della delega. Il secondo capitolo abbraccia il tema della concorrenza. Dopo aver introdotto l'argomento, vengono approfonditi alcuni significativi modelli di concorrenza: programmazione multi-threaded, task nel linguaggio Ada, SCOOP, modello ad Attori. Essi vengono descritti negli elementi fondamentali e ne vengono evidenziati gli aspetti cruciali in termini di contributo al riuso, con esempi di codice. Relativamente al modello ad Attori, viene presentata la sua implementazione in Scala/Akka come caso studio. Infine, viene esaminato il problema dell'inheritance anomaly, sulla base di esempi e delle tre classi principali di anomalia, e si analizza la suscettibilità del supporto di concorrenza di Scala/Akka a riscontrare tali problemi. Inoltre, in questo capitolo si nota come alcuni aspetti relativi al binomio riuso/concorrenza, tra cui il significato profondo dello stesso, non siano ancora stati adeguatamente affrontati dalla comunità informatica. Il terzo e ultimo capitolo esordisce con una panoramica dell'agent-oriented programming, prendendo il linguaggio simpAL come riferimento. In seguito, si prova ad estendere al caso degli agenti la nozione di riuso approfondita nei capitoli precedenti.

Engineering Agent-Oriented Technologies and Programming Languages for Computer Programming and Software Development

Mainstream hardware is becoming parallel, heterogeneous, and distributed on every desk, every home and in every pocket. As a consequence, in the last years software is having an epochal turn toward concurrency, distribution, interaction which is pushed by the evolution of hardware architectures and the growing of network availability. This calls for introducing further abstraction layers on top of those provided by classical mainstream programming paradigms, to tackle more effectively the new complexities that developers have to face in everyday programming. A convergence it is recognizable in the mainstream toward the adoption of the actor paradigm as a mean to unite object-oriented programming and concurrency. Nevertheless, we argue that the actor paradigm can only be considered a good starting point to provide a more comprehensive response to such a fundamental and radical change in software development. Accordingly, the main objective of this thesis is to propose Agent-Oriented Programming (AOP) as a high-level general purpose programming paradigm, natural evolution of actors and objects, introducing a further level of human-inspired concepts for programming software systems, meant to simplify the design and programming of concurrent, distributed, reactive/interactive programs. To this end, in the dissertation first we construct the required background by studying the state-of-the-art of both actor-oriented and agent-oriented programming, and then we focus on the engineering of integrated programming technologies for developing agent-based systems in their classical application domains: artificial intelligence and distributed artificial intelligence. Then, we shift the perspective moving from the development of intelligent software systems, toward general purpose software development. Using the expertise maturated during the phase of background construction, we introduce a general-purpose programming language named simpAL, which founds its roots on general principles and practices of software development, and at the same time provides an agent-oriented level of abstraction for the engineering of general purpose software systems.

A farm-level programming model to compare the atmospheric impact of conventional and organic farming

A model is developed to represent the activity of a farm using the method of linear programming. Two are the main components of the model, the balance of soil fertility and the livestock nutrition. According to the first, the farm is supposed to have a total requirement of nitrogen, which is to be accomplished either through internal sources (manure) or through external sources (fertilisers). The second component describes the animal husbandry as having a nutritional requirement which must be satisfied through the internal production of arable crops or the acquisition of feed from the market. The farmer is supposed to maximise total net income from the agricultural and the zoo-technical activities by choosing one rotation among those available for climate and acclivity. The perspective of the analysis is one of a short period: the structure of the farm is supposed to be fixed without possibility to change the allocation of permanent crops and the amount of animal husbandry. The model is integrated with an environmental module that describes the role of the farm within the carbon-nitrogen cycle. On the one hand the farm allows storing carbon through the photosynthesis of the plants and the accumulation of carbon in the soil; on the other some activities of the farm emit greenhouse gases into the atmosphere. The model is tested for some representative farms of the Emilia-Romagna region, showing to be capable to give different results for conventional and organic farming and providing first results concerning the different atmospheric impact. Relevant data about the representative farms and the feasible rotations are extracted from the FADN database, with an integration of the coefficients from the literature.

Game programming: Grafica 3d

Tesi riguardante la creazione di tutte le risorse grafiche necessarie ad un videogioco tridimensionale in prima persona con Blender e Unity3D. Gli argomenti trattati sono: prgettazione, 3D modeling, texturing e shading.

Game programming: sviluppo di un gioco

La tesi riguarda tutto il processo di progettazione di un videogioco e l'implementazione dello stesso. Gli argomenti trattati sono: Unity, Design & Gameplay e l'implementazioni del progetto.

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.