Automatic text summarization tools have a great impact on many fields, such as medicine, law, and scientific research in general. As information overload increases, automatic summaries allow handling the growing volume of documents, usually by assigning weights to the extracted phrases based on their significance in the expected summary. Obtaining the main contents of any given document in less time than it would take to do that manually is still an issue of interest. In~this~ article, a new method is presented that allows automatically generating extractive summaries from documents by adequately weighting sentence scoring features using \textit{Particle Swarm Optimization}. The key feature of the proposed method is the identification of those features that are closest to the criterion used by the individual when summarizing. The proposed method combines a binary representation and a continuous one, using an original variation of the technique developed by the authors of this paper. Our paper shows that using user labeled information in the training set helps to find better metrics and weights. The empirical results yield an improved accuracy compared to previous methods used in this field

The quantum approximate optimization algorithm (QAOA) has rapidly become a cornerstone of contemporary quantum algorithm development. Despite a growing range of applications, only a few results have been developed towards understanding the algorithms ultimate limitations. Here we report that QAOA exhibits a strong dependence on a problem instances constraint to variable ratio - this problem density places a limiting restriction on the algorithms capacity to minimize a corresponding objective function (and hence solve optimization problems). Such 'reachability deficits' persist even in the absence of barren plateaus [McClean et al., 2018] and are outside of the recently reported level-1 QAOA limitations [Hastings 2019]. Building on general numerical experiments, we compare the presence of reachability deficits with analytic solutions of the variational model of Grover's search algorithm.

We introduce a method to design lightweight shell objects that are structurally robust under the external forces they may experience during use. Given an input 3D model and a general description of the external forces, our algorithm generates a structurally-sound minimum weight shell object. Our approach works by altering the local shell thickness repeatedly based on the stresses that develop inside the object. A key issue in shell design is that large thickness values might result in self-intersections on the inner boundary creating a significant computational challenge during optimization. To address this, we propose a shape parametrization based on the solution to the Laplace's equation that guarantees smooth and intersection-free shell boundaries. Combined with our gradient-free optimization algorithm, our method provides a practical solution to the structural design of hollow objects with a single inner cavity. We demonstrate our method on a variety of problems with arbitrary 3D models under complex force configurations and validate its performance with physical experiments.

This article describes the application of soft computing methods for solving the problem of locating garbage accumulation points in urban scenarios. This is a relevant problem in modern smart cities, in order to reduce negative environmental and social impacts in the waste management process, and also to optimize the available budget from the city administration to install waste bins. A specific problem model is presented, which accounts for reducing the investment costs, enhance the number of citizens served by the installed bins, and the accessibility to the system. A family of single- and multi-objective heuristics based on the PageRank method and two mutiobjective evolutionary algorithms are proposed. Experimental evaluation performed on real scenarios on the cities of Montevideo (Uruguay) and Bahia Blanca (Argentina) demonstrates the effectiveness of the proposed approaches. The methods allow computing plannings with different trade-off between the problem objectives. The computed results improve over the current planning in Montevideo and provide a reasonable budget cost and quality of service for Bahia Blanca.

Trajectory replanning for quadrotors is essential to enable fully autonomous flight in unknown environments. Hierarchical motion planning frameworks, which combine path planning with path parameterization, are popular due to their time efficiency. However, the path planning cannot properly deal with non-static initial states of the quadrotor, which may result in non-smooth or even dynamically infeasible trajectories. In this paper, we present an efficient kinodynamic replanning framework by exploiting the advantageous properties of the B-spline, which facilitates dealing with the non-static state and guarantees safety and dynamical feasibility. Our framework starts with an efficient B-spline-based kinodynamic (EBK) search algorithm which finds a feasible trajectory with minimum control effort and time. To compensate for the discretization induced by the EBK search, an elastic optimization (EO) approach is proposed to refine the control point placement to the optimal location. Systematic comparisons against the state-of-the-art are conducted to validate the performance. Comprehensive onboard experiments using two different vision-based quadrotors are carried out showing the general applicability of the framework.

Planning safe trajectories for autonomous vehicles in complex urban environments is challenging since there are numerous semantic elements (such as dynamic agents, traffic lights and speed limits) to consider. These semantic elements may have different mathematical descriptions such as obstacle, constraint and cost. It is non-trivial to tune the effects from different combinations of semantic elements for a stable and generalizable behavior. In this paper, we propose a novel unified spatio-temporal semantic corridor (SSC) structure, which provides a level of abstraction for different types of semantic elements. The SSC consists of a series of mutually connected collision-free cubes with dynamical constraints posed by the semantic elements in the spatio-temporal domain. The trajectory generation problem then boils down to a general quadratic programming (QP) formulation. Thanks to the unified SSC representation, our framework can generalize to any combination of semantic elements. Moreover, our formulation provides a theoretical guarantee that the entire trajectory is safe and constraint-satisfied, by using the convex hull and hodograph properties of piecewise Bezier curve parameterization. We also release the code of our method to accommodate benchmarking.

We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the cardinality constrained likelihood problem to certifiable optimality. The approach uses techniques from mixed-integer optimization and convex optimization, and provides a high-quality solution with a guarantee on its suboptimality, even if the algorithm is terminated early. Using a variety of synthetic and real datasets, we demonstrate that our approach can solve problems where the dimension of the inverse covariance matrix is up to 1,000s. We also demonstrate that our approach produces significantly sparser solutions than Glasso and other popular learning procedures, makes less false discoveries, while still maintaining state-of-the-art accuracy.

There has been much recent interest in hierarchies of progressively stronger convexifications of polynomial optimisation problems (POP). These often converge to the global optimum of the POP, asymptotically, but prove challenging to solve beyond the first level in the hierarchy for modest instances. We present a finer-grained variant of the Lasserre hierarchy, together with first-order methods for solving the convexifications, which allow for efficient warm-starting with solutions from lower levels in the hierarchy.

Mixed Integer Programming (MIP) is one of the most widely used modeling techniques to deal with combinatorial optimization problems. In many applications, a similar MIP model is solved on a regular basis, maintaining remarkable similarities in model structures and solution appearances but differing in formulation coefficients. This offers the opportunity for machine learning method to explore the correlations between model structures and the resulting solution values. To address this issue, we propose to represent an MIP instance using a tripartite graph, based on which a Graph Convolutional Network (GCN) is constructed to predict solution values for binary variables. The predicted solutions are used to generate a local branching cut to the model which accelerate the solution process for MIP. Computational evaluations on 8 distinct types of MIP problems show that the proposed framework improves the performance of a state-of-the-art open source MIP solver significantly in terms of running time and solution quality.

Existing graph-based methods for extractive document summarization represent sentences of a corpus as the nodes of a graph or a hypergraph in which edges depict relationships of lexical similarity between sentences. Such approaches fail to capture semantic similarities between sentences when they express a similar information but have few words in common and are thus lexically dissimilar. To overcome this issue, we propose to extract semantic similarities based on topical representations of sentences. Inspired by the Hierarchical Dirichlet Process, we propose a probabilistic topic model in order to infer topic distributions of sentences. As each topic defines a semantic connection among a group of sentences with a certain degree of membership for each sentence, we propose a fuzzy hypergraph model in which nodes are sentences and fuzzy hyperedges are topics. To produce an informative summary, we extract a set of sentences from the corpus by simultaneously maximizing their relevance to a user-defined query, their centrality in the fuzzy hypergraph and their coverage of topics present in the corpus. We formulate a polynomial time algorithm building on the theory of submodular functions to solve the associated optimization problem. A thorough comparative analysis with other graph-based summarization systems is included in the paper. Our obtained results show the superiority of our method in terms of content coverage of the summaries.