Progetto di un sistema di navigazione pedonale al coperto

Quest’articolo ha lo scopo di porre le basi per il progetto di un sistema di navigazione dedicato all’uso pedonale e in ambienti chiusi. Si vuole, infatti, progettare un sistema di posizionamento alternativo al GPS che sia in grado di sostituirlo in ambienti in cui non sia possibile ricevere il segnale satellitare. Questo avviene tramite l’utilizzo del Map Matching che, con l’aiuto di un modulo INS e l’applicazione del filtro di Kalman, dovrebbe poter permettere la creazione di un software per la navigazione assistita pedonale indoor.ope

A MILP model for quasi-periodic strategic train timetabling

In railways, the long-term strategic planning is the process of evaluating improvements to the railway network (e.g., upgrading a single track line to a double track line) and changes to the composition/frequency of train services (e.g., adding 1 train per hour along a certain route). The effects of different combinations of infrastructure upgrades and updated train services (also called scenarios), are usually evaluated by creating new feasible timetables followed by extensive simulation. Strategic Train Timetabling (STT) is indeed the task of producing new tentative timetables for these what-if scenarios. Unlike the more classic train timetabling, STT can often overlook (or at least give less importance to) some complementary aspects, such as crew and rolling stock scheduling. On the other hand, the different scenarios are likely to lead to very different timetables, hindering the common and effective practice of using existing timetables to warm start the solution process. We introduce the concept of quasi-periodic timetables, that are timetables where certain subsets of trains need to start at almost (rather than precisely) the same minute of every period. The additional flexibility offered by quasi-periodic timetables turned out to be crucial in real-life scenarios characterized by elevated train traffic. We describe a MILP based approach for strategic quasi-periodic train timetabling and we test it on 4 different realistic what-if scenarios for an important line in Norway. The timetables produced by our algorithm were ultimately used by the Norwegian Railway Directorate to select 3 out of the 4 scenarios for phasing the progressive expansion of the JȪren line.publishedVersio

Efficient encoding of the weighted MAX k-CUT on a quantum computer using QAOA

The weighted MAX k-CUT problem consists of finding a k-partition of a given weighted undirected graph G(V,E) such that the sum of the weights of the crossing edges is maximized. The problem is of particular interest as it has a multitude of practical applications. We present a formulation of the weighted MAX k-CUT suitable for running the quantum approximate optimization algorithm (QAOA) on noisy intermediate scale quantum (NISQ)-devices to get approximate solutions. The new formulation uses a binary encoding that requires only |V|log_2(k) qubits. The contributions of this paper are as follows: i) A novel decomposition of the phase separation operator based on the binary encoding into basis gates is provided for the MAX k-CUT problem for k >2. ii) Numerical simulations on a suite of test cases comparing different encodings are performed. iii) An analysis of the resources (number of qubits, CX gates) of the different encodings is presented. iv) Formulations and simulations are extended to the case of weighted graphs. For small k and with further improvements when k is not a power of two, our algorithm is a possible candidate to show quantum advantage on NISQ devices.Comment: 14 page

A MIP-and-refine matheuristic for smart grid energy management

Abstract In the last years we have witnessed an increasing interest in smart buildings, in particular for what concerns optimal energy management, renewable energy sources, and smart appliances. In this paper we investigate the problem of scheduling smart appliance operation in a given time horizon with a set of energy sources and accumulators. Appliance operation is modeled in terms of uninterruptible sequential phases with a given power demand, with the goal of minimizing the energy bill fulfilling duration, energy, and user preference constraints. A Mixed Integer Linear Programming (MIP) model and a greedy heuristic algorithm are given, intended to be used in a synergic way. We show how a general purpose (off-the-shelf) MIP refining procedure can effectively be used for improving, in short computing time, the quality of the solutions provided by the initial greedy heuristic. Computational results confirm the viability of the overall approach, in terms of both solution quality and speed

Constraint Preserving Mixers for the Quantum Approximate Optimization Algorithm

The quantum approximate optimization algorithm/quantum alternating operator ansatz (QAOA) is a heuristic to find approximate solutions of combinatorial optimization problems. Most of the literature is limited to quadratic problems without constraints. However, many practically relevant optimization problems do have (hard) constraints that need to be fulfilled. In this article, we present a framework for constructing mixing operators that restrict the evolution to a subspace of the full Hilbert space given by these constraints. We generalize the “XY”-mixer designed to preserve the subspace of “one-hot” states to the general case of subspaces given by a number of computational basis states. We expose the underlying mathematical structure which reveals more of how mixers work and how one can minimize their cost in terms of the number of CX gates, particularly when Trotterization is taken into account. Our analysis also leads to valid Trotterizations for an “XY”-mixer with fewer CX gates than is known to date. In view of practical implementations, we also describe algorithms for efficient decomposition into basis gates. Several examples of more general cases are presented and analyzed.publishedVersio