Schedulazione delle rotte marittime nel settore ortofrutticolo. Modelli e Metodi

Il trasporto marittimo è una delle modalità più utilizzate soprattutto per la movimentazione di grandi volumi di prodotti tra i continenti in quanto è a basso costo, sicuro e meno inquinante rispetto ad altri mezzi di movimentazione. Ai giorni nostri è responsabile di circa l’80% del commercio globale (in volume di carichi trasportati). Il settore del trasporto marittimo ha avuto una lunga tradizione di pianificazione manuale effettuata da progettisti esperti.
 L’obiettivo principale di questa trattazione è stato quello di implementare un modello matematico lineare (MILP, Mixed-Integer Linear Programming Model) per l’ottimizzazione delle rotte marittime nell’ambito del mercato orto-frutticolo che si sviluppa nel bacino del Mediterraneo (problema di Ship-Scheduling). Il modello fornito in questa trattazione è un valido strumento di supporto alle decisioni che può utilizzare uno spedizioniere nell’ambito della pianificazione delle rotte marittime della flotta di navi in suo possesso. Consente di determinare l’insieme delle rotte ottimali che devono essere svolte da un insieme di vettori al fine di massimizzare il profitto complessivo dello spedizioniere, generato nell’arco di tempo considerato. Inoltre, permette di ottenere, per ogni nave considerata, la ripartizione ottimale della merce (carico ottimale).

Exact Combinatorial Optimization with Graph Convolutional Neural Networks

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose to learn a variable selection policy for branch-and-bound in mixed-integer linear programming, by imitation learning on a diversified variant of the strong branching expert rule. We encode states as bipartite graphs and parameterize the policy as a graph convolutional neural network. Experiments on a series of synthetic problems demonstrate that our approach produces policies that can improve upon expert-designed branching rules on large problems, and generalize to instances significantly larger than seen during training.

Computing primal solutions with exact arithmetics in SCIP.

The research for exact solutions of mixed integer problems is an active topic in the scientific community. State-of-the-art MIP solvers exploit a floating- point numerical representation, therefore introducing small approximations. Although such MIP solvers yield reliable results for the majority of problems, there are cases in which a higher accuracy is required. Indeed, it is known that for some applications floating-point solvers provide falsely feasible solutions, i.e. solutions marked as feasible because of approximations that would not pass a check with exact arithmetic and cannot be practically implemented. The framework of the current dissertation is SCIP, a mixed integer programs solver mainly developed at Zuse Institute Berlin. In the same site we considered a new approach for exactly solving MIPs. Specifically, we developed a constraint handler to plug into SCIP, with the aim to analyze the accuracy of provided floating-point solutions and compute exact primal solutions starting from floating-point ones. We conducted a few computational experiments to test the exact primal constraint handler through the adoption of two main settings. Analysis mode allowed to collect statistics about current SCIP solutions' reliability. Our results confirm that floating-point solutions are accurate enough with respect to many instances. However, our analysis highlighted the presence of numerical errors of variable entity. By using the enforce mode, our constraint handler is able to suggest exact solutions starting from the integer part of a floating-point solution. With the latter setting, results show a general improvement of the quality of provided final solutions, without a significant loss of performances.

Asymmetries in Adversarial Settings

Even without formal guarantees of their effectiveness, adversarial attacks against Machine Learning models frequently fool new defenses. We identify six key asymmetries that contribute to this phenomenon and formulate four guidelines to build future-proof defenses by preventing such asymmetries. We also prove that attacking a classifier is NP-complete, while defending from such attacks is Sigma_2^P-complete. We then introduce Counter-Attack (CA), an asymmetry-free metadefense that determines whether a model is robust on a given input by estimating its distance from the decision boundary. Under specific assumptions CA can provide theoretical detection guarantees. Additionally, we prove that while CA is NP-complete, fooling CA is Sigma_2^P-complete. Even when using heuristic relaxations, we show that our method can reliably identify non-robust points. As part of our experimental evaluation, we introduce UG100, a new dataset obtained by applying a provably optimal attack to six limited-scale networks (three for MNIST and three for CIFAR10), each trained in three different manners.

Design and management of a supply chain: a joint location-inventory problem under uncertainty (Part A)

In this paper, a joint location-inventory model is proposed that simultaneously optimises strategic supply chain design decisions such as facility location and customer allocation to facilities, and tactical-operational inventory management and production scheduling decisions. All this is analysed in a context of demand uncertainty and supply uncertainty. While demand uncertainty stems from potential fluctuations in customer demands over time, supply-side uncertainty is associated with the risk of “disruption” to which facilities may be subject. The latter is caused by external factors such as natural disasters, strikes, changes of ownership and information technology security incidents. The proposed model is formulated as a non-linear mixed integer programming problem to minimise the expected total cost, which includes four basic cost items: the fixed cost of locating facilities at candidate sites, the cost of transport from facilities to customers, the cost of working inventory, and the cost of safety stock. Next, since the optimisation problem is very complex and the number of evaluable instances is very low, a "matheuristic" solution is presented. This approach has a twofold objective: on the one hand, it considers a larger number of facilities and customers within the network in order to reproduce a supply chain configuration that more closely reflects a real-world context; on the other hand, it serves to generate a starting solution and perform a series of iterations to try to improve it. Thanks to this algorithm, it was possible to obtain a solution characterised by a lower total system cost than that observed for the initial solution. The study concludes with some reflections and the description of possible future insights.

Fleet Management System for Search and Rescue Operations

Over one million people lost their lives in the last twenty years from natural disasters like wildfires, earthquakes and man-made disasters. In such scenarios the usage of a fleet of robots aims at the parallelization of the workload and thus increasing speed and capabilities to complete time sensitive missions. This work focuses on the development of a dynamic fleet management system, which consists in the management of multiple agents cooperating in order to accomplish tasks. We presented a Mixed Integer Programming problem for the management and planning of mission’s tasks. The problem was solved using both an exact and a heuristic approach. The latter is based on the idea of solving iteratively smaller instances of the complete problem. Alongside, a fast and efficient algorithm for estimation of travel times between tasks is proposed. Experimental results demonstrate that the proposed heuristic approach is able to generate quality solutions, within specific time limits, compared to the exact one.

New integer programming models for balanced multi-country kep

Le persone che soffrono di insufficienza renale terminale hanno due possibili trattamenti da affrontare: la dialisi oppure il trapianto di organo. Nel caso volessero seguire la seconda strada, oltre che essere inseriti nella lista d'attesa dei donatori deceduti, possono trovare una persona, come il coniuge, un parente o un amico, disposta a donare il proprio rene. Tuttavia, non sempre il trapianto è fattibile: donatore e ricevente possono, infatti, presentare delle incompatibilità a livello di gruppo sanguigno o di tessuto organico. Come risposta a questo tipo di problema nasce il KEP (Kidney Exchange Program), un programma, ampiamente avviato in diverse realtà europee e mondiali, che si occupa di raggruppare in un unico insieme le coppie donatore/ricevente in questa stessa situazione al fine di operare e massimizzare scambi incrociati di reni fra coppie compatibili. Questa tesi approffondisce tale questione andando a valutare la possibilità di unire in un unico insieme internazionale coppie donatore/ricevente provenienti da più paesi. Lo scopo, naturalmente, è quello di poter ottenere un numero sempre maggiore di trapianti effettuati. Lo studio affronta dal punto di vista matematico problematiche legate a tale collaborazione: i paesi che eventualmente accettassero di partecipare a un simile programma, infatti, devono avere la garanzia non solo di ricavarne un vantaggio, ma anche che tale vantaggio sia equamente distribuito fra tutti i paesi partecipanti.