This paper examines the Aircraft Sequencing Problem (ASP) over multiple runways, under mixed mode operations with the objective of minimizing the total weighted tardiness of aircraft landings and departures simultaneo...
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This paper examines the Aircraft Sequencing Problem (ASP) over multiple runways, under mixed mode operations with the objective of minimizing the total weighted tardiness of aircraft landings and departures simultaneously. The ASP can be modeled as a parallel machine scheduling problem with unequal ready-times, target times and deadlines. Furthermore, sequence-dependent separation times on each runway are considered to prevent the dangers associated with wake-vortex effects. Due to the problem being NP-hard, greedy heuristics and metaheuristics are applied in this paper to obtain solutions in reasonable computation times. The algorithms' solutions are compared to optimal solutions and their performances are evaluated in terms of solution quality and CPU time. (C) 2013 Elsevier Ltd. All rights reserved.
We present a novel stagewise strategy for improving greedy algorithms for sparse recovery. We demonstrate its efficiency both for synthesis and analysis sparse priors, where in both cases we demonstrate its computatio...
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We present a novel stagewise strategy for improving greedy algorithms for sparse recovery. We demonstrate its efficiency both for synthesis and analysis sparse priors, where in both cases we demonstrate its computational efficiency and competitive reconstruction accuracy. In the synthesis case, we also provide theoretical guarantees for the signal recovery that are on par with the existing perfect reconstruction bounds for the relaxation based solvers and other sophisticated greedy algorithms.
We develop greedy algorithms to approximate the optimal solution to the multi-fidelity sensor selection problem, which is a cost constrained optimization problem prescribing the placement and number of cheap (low sign...
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We develop greedy algorithms to approximate the optimal solution to the multi-fidelity sensor selection problem, which is a cost constrained optimization problem prescribing the placement and number of cheap (low signal-to-noise) and expensive (high signal-to-noise) sensors in an environment or state space. Specifically, we evaluate the composition of cheap and expensive sensors, along with their placement, required to achieve accurate reconstruction of a high-dimensional state. We use the column-pivoted QR decomposition to obtain preliminary sensor positions. How many of each type of sensor to use is highly dependent upon the sensor noise levels, sensor costs, overall cost budget, and the singular value spectrum of the data measured. Such nuances allow us to provide sensor selection recommendations based on computational results for asymptotic regions of parameter space. We also present a systematic exploration of the effects of the number of modes and sensors on reconstruction error when using one type of sensor. Our extensive exploration of multi-fidelity sensor composition as a function of data characteristics is the first of its kind to provide guidelines towards optimal multi-fidelity sensor selection.
This paper presents principles for the classification of greedy algorithms for optimization problems. These principles are made precise by their expression in the relational calculus, and illustrated by various exampl...
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This paper presents principles for the classification of greedy algorithms for optimization problems. These principles are made precise by their expression in the relational calculus, and illustrated by various examples. A discussion compares this work to other greedy algorithms theory. (C) 2003 Elsevier B.V. All rights reserved.
The reduced basis method was introduced for the accurate online evaluation of solutions to a parameter dependent family of elliptic PDEs. Abstractly, it can be viewed as determining a "good" n-dimensional sp...
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The reduced basis method was introduced for the accurate online evaluation of solutions to a parameter dependent family of elliptic PDEs. Abstractly, it can be viewed as determining a "good" n-dimensional space H(n) to be used in approximating the elements of a compact set F in a Hilbert space H. One by now popular computational approach is to find H(n) through a greedy strategy. It is natural to compare the approximation performance of the H(n) generated by this strategy with that of the Kolmogorov widths d(n)(F) since the latter gives the smallest error that can be achieved by subspaces of fixed dimension n. The first such comparisons, given in [A. Buffa et al., ESAIM Math. Model. Numer. Anal., 2011, to appear], show that the approximation error, sigma(n)(F) := dist(F, H(n)), obtained by the greedy strategy satisfies sigma(n)(F) <= Cn2(n)d(n)(F). In this paper, various improvements of this result will be given. Among these, it is shown that whenever d(n)(F) <= Mn(-alpha) for all n > 0 and some M, alpha > 0, we also have sigma(n)(F) <= C(alpha)Mn(-alpha) for all n > 0, where C(alpha) depends only on alpha. Similar results are derived for generalized exponential rates of the form Me(-an alpha). The exact greedy algorithm is not always computationally feasible, and a commonly used computationally friendly variant can be formulated as a "weak greedy algorithm." The results of this paper are established for this version as well.
Costs and benefits are recurrent issues that concern all the computing areas, including computer and software engineering. Mastery of optimization algorithms is essential in these fields, but their didactics hardly ha...
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Costs and benefits are recurrent issues that concern all the computing areas, including computer and software engineering. Mastery of optimization algorithms is essential in these fields, but their didactics hardly has received any attention. To fill this gap, the interactive system GreedEx was designed to support the active learning of greedy algorithms by means of experimentation. In this article we describe GreedExCol, a collaborative extension of GreedEx that complements its experimental phase with a discussion phase held by the students in each team. The contributions of the article are threefold. Firstly, we present GreedExCol, a CSCL system aimed at supporting collaborative discussion on experimental results of optimality for greedy algorithms. Secondly, GreedExCol was evaluated with respect to educational effectiveness, obtaining statistically significant improvements of the collaborative, experimental approach over an individual, experimental approach without the support of GreedExCol. Thirdly, GreedExCol was evaluated in the same two groups with respect to motivation, obtaining a statistically significant increase of implicit motivation for students in the experimental group. Overall, we present a medium-term effort for developing an innovative learning system and a comprehensive evaluation of its impact over the students. (C) 2015 Wiley Periodicals, Inc.
In this paper, we consider three simple and natural greedy algorithms for the maximum weighted independent set problem. We show that two of them output an independent set of weight at least Sigma(vis an element ofV(G)...
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In this paper, we consider three simple and natural greedy algorithms for the maximum weighted independent set problem. We show that two of them output an independent set of weight at least Sigma(vis an element ofV(G)) W(v)/[d(v) + 1] and the third algorithm outputs an independent set of weight at least Sigma(vis an element ofV(G)) W(v)(2)/[Sigma(uis an element ofNG+(v)) W(u)]. These results are generalization of theorem of Caro and Wei. (C) 2002 Elsevier Science B.V. All rights reserved.
This paper presents the evolution experienced by GreedEx, an interactive application to learn greedy algorithms. It shows the four different versions currently available. A first original version for computers, two ve...
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This paper presents the evolution experienced by GreedEx, an interactive application to learn greedy algorithms. It shows the four different versions currently available. A first original version for computers, two versions for iPad, and another version for smartphones. Besides, it describes the evaluation performed for each version, which has served so as to justify such evolution.
Actuator placement is an active field of research, which has received significant attention for its applications in complex dynamical networks. In this article, we study the problem of finding a set of actuator placem...
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Actuator placement is an active field of research, which has received significant attention for its applications in complex dynamical networks. In this article, we study the problem of finding a set of actuator placements minimizing the metric that measures the average energy consumed for state transfer by the controller, while satisfying a structural controllability requirement and a cardinality constraint on the number of actuators allowed. As no computationally efficient methods are known to solve such combinatorial set function optimization problems, two greedy algorithms, forward and reverse, are proposed to obtain approximate solutions. We first show that the constraint sets these algorithms explore can be characterized by matroids. We then obtain performance guarantees for the forward and reverse greedy algorithms applied to the general class of matroid optimization problems by exploiting properties of the objective function such as the submodularity ratio and the curvature. Finally, we propose feasibility check methods for both algorithms based on maximum flow problems on certain auxiliary graphs originating from the network graph. Our results are verified with case studies over large networks.
This paper introduces the concept of sensing dictionaries. It presents an alteration of greedy algorithms like thresholding or (orthogonal) matching pursuit which improves their performance in finding sparse signal re...
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This paper introduces the concept of sensing dictionaries. It presents an alteration of greedy algorithms like thresholding or (orthogonal) matching pursuit which improves their performance in finding sparse signal representations in redundant dictionaries while maintaining the same complexity. These algorithms can be split into a sensing and a reconstruction step, and the former will fail to identify correct atoms if the cumulative coherence of the dictionary is too high. We thus modify the sensing step by introducing a special sensing dictionary. The correct selection of components is then determined by the cross cumulative coherence which can be considerably lower than the cumulative coherence. We characterize the optimal sensing matrix and develop a constructive method to approximate it. Finally, we compare the performance of thresholding and OMP using the original and modified algorithms.
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