Search

Among sub-optimal MAPF solvers, rule-based algorithms are particularly appealing since they are complete. Even in crowded scenarios, they allow finding a feasible solution that brings each agent to its target, preventing deadlock situations. However, generally, rule-based algorithms provide solutions that are much longer than the optimal one. The main contribution of this paper is the introduction of an iterative local search procedure in MAPF. We start from a feasible suboptimal solution and we perform a local search in a neighborhood of this solution, to find a shorter one. Iteratively, we repeat this procedure until the solution cannot be shortened any longer. At the end, we obtain a solution, that is still sub-optimal, but, in general, of much better quality than the initial one. We use dynamic programming for the local search procedure. Under this respect, the fact that our search is local is fundamental to reduce the time complexity of the algorithm. Indeed, if we apply a standard dynamic programming the number of explored states grows exponentially with the number of agents. As we will see, the introduction of a locality constraint allows solving the (local) dynamic programming problem in a time that grows only polynomially with respect to the number of agents.

In this paper we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration and jerk constraints. Such a problem arises in industrial contexts such as automated warehouses, where LGVs need to perform assigned tasks as fast as possible in order to increase productivity. It can be reformulated as an optimization problem with a convex objective function, linear velocity and acceleration constraints, and non-convex jerk constraints, which, thus, represent the main source of difficulty. While existing non-linear programming (NLP) solvers can be employed for the solution of this problem, it turns out that the performance and robustness of such solvers can be enhanced by the sequential line-search algorithm proposed in this paper. At each iteration a feasible direction, with respect to the current feasible solution, is computed, and a step along such direction is taken in order to compute the next iterate. The computation of the feasible direction is based on the solution of a linearized version of the problem, and the solution of the linearized problem, through an approach which strongly exploits its special structure, represents the main contribution of this work. The efficiency of the proposed approach with respect to existing NLP solvers is proved through different computational experiments.

In this work we present some exactness conditions for the Shor relaxation of diagonal QCQPs, which extend the conditions introduced in different recent papers about the same topic. It is shown that the Shor relaxation is equivalent to two convex quadratic relaxations. Then, sufficient conditions for the exactness of the relaxations are derived from their KKT systems. It will be shown that, in some cases, by this derivation previous conditions in the literature, which can be viewed as dual conditions, since they only involve the Lagrange multipliers appearing in the KKT systems, can be extended to primal-dual conditions, which also involve the primal variables appearing in the KKT systems.

We have experimentally investigated the expansion mechanism induced by laser irradiation of H2SO4 intercalated graphite. Intercalated graphite materials irradiated by laser allows to study reactions occurring in confined chemical conditions. We find that the laser-assisted reaction process is characterized by a threshold temperature of about 140{\deg}C followed by a fast rate of heating which produces a large amount of overheated gases and causes a violent expansion of the graphite crystal. We investigate the morphological changes undergone by irradiated graphite filaments using a combination of thermal and visible imaging technique which allows for the quantitative determination of temporal evolution of the thermal field during the heating stage and exfoliation of the grain., Comment: pag 12 figure 7

Silicon Photo-Multipliers (SiPM) are state of the art light detectors with unprecedented single photon sensitivity and photon number resolving capability, representing a breakthrough in several fundamental and applied Science domains. An educational experiment based on a SiPM set-up is proposed in this article, guiding the student towards a comprehensive knowledge of this sensor technology while experiencing the quantum nature of light and exploring the statistical properties of the light pulses emitted by a LED.