Search results for " optimization"
showing 10 items of 2367 documents
Sparse Dynamic Programming for Longest Common Subsequence from Fragments
2002
Sparse Dynamic Programming has emerged as an essential tool for the design of efficient algorithms for optimization problems coming from such diverse areas as computer science, computational biology, and speech recognition. We provide a new sparse dynamic programming technique that extends the Hunt?Szymanski paradigm for the computation of the longest common subsequence (LCS) and apply it to solve the LCS from Fragments problem: given a pair of strings X and Y (of length n and m, respectively) and a set M of matching substrings of X and Y, find the longest common subsequence based only on the symbol correspondences induced by the substrings. This problem arises in an application to analysis…
The shortest-path problem with resource constraints with -loop elimination and its application to the capacitated arc-routing problem
2014
Abstract In many branch-and-price algorithms, the column generation subproblem consists of computing feasible constrained paths. In the capacitated arc-routing problem (CARP), elementarity constraints concerning the edges to be serviced and additional constraints resulting from the branch-and-bound process together impose two types of loop-elimination constraints. To fulfill the former constraints, it is common practice to rely on a relaxation where loops are allowed. In a k-loop elimination approach all loops of length k and smaller are forbidden. Following Bode and Irnich (2012) for solving the CARP, branching on followers and non-followers is the only known approach to guarantee integer …
Symmetries and Covariance of the Maxwell Equations
2012
Already within a given, fixed division of four-dimensional spacetime into the space where experiments are performed, and the laboratory time variable, Maxwell’s equations show interesting transformation properties under continuous and discrete space-time transformations. However, only the action of the whole Lorentz group on them reveals their full symmetry structure. A good example that illustrates the covariance of Maxwell’s equations is provided by the electromagnetic fields of a point charge uniformly moving along a straight line.
From First Principles to the Burrows and Wheeler Transform and Beyond, via Combinatorial Optimization
2007
AbstractWe introduce a combinatorial optimization framework that naturally induces a class of optimal word permutations with respect to a suitably defined cost function taking into account various measures of relatedness between words. The Burrows and Wheeler transform (bwt) (cf. [M. Burrows, D. Wheeler, A block sorting lossless data compression algorithm, Technical Report 124, Digital Equipment Corporation, 1994]), and its analog for labelled trees (cf. [P. Ferragina, F. Luccio, G. Manzini, S. Muthukrishnan, Structuring labeled trees for optimal succinctness, and beyond, in: Proc. of the 45th Annual IEEE Symposium on Foundations of Computer Science, 2005, pp. 198–207]), are special cases i…
Stationary and Initial-Terminal Value Problem for Collective Decision Making via Mean-Field Games
2017
Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, following some optimality criteria. The optimal transition rates are based on the players' knowledge of their current state and of the distribution of all the other players, thus introducing mean-field terms in the running and the terminal cost. The first contribution is a mean-field model that takes into account the macroscopic and the microscopic dynamics. The second contribution is the study of the mean-field equilibrium resulting from solving the initial-terminal value problem, involving the Kolmogorov equat…
Disturbance tolerance and rejection of discrete switched systems with time-varying delay and saturating actuator
2015
Abstract This paper is concerned with the problems of disturbance tolerance and rejection of discrete switched systems with time-varying delay and saturating actuator. Using the switched Lyapunov function approach, a sufficient condition for the existence of a state feedback controller is proposed such that the disturbance tolerance capability of the closed-loop system is ensured. By solving a convex optimization problem with linear matrix inequality (LMI) constraints, the maximal disturbance tolerance is estimated. In addition, the problem of disturbance rejection of the closed-loop system is solved. Two examples are given to illustrate the effectiveness of the proposed method.
Stability analysis and H∞ controller synthesis of discrete-time switched systems with time delay
2014
Abstract This paper studies the problems of stability analysis and H ∞ controller synthesis of switched systems with time-varying delay based on an input–output approach. The attention is focused on developing a new method to further reduce the conservatism of the existing results. The system under consideration is transformed into an interconnection system, and the scaled small gain condition for the interconnection systems is introduced. Based on the system transformation and the scaled small gain theorem, an improved delay-dependent stability criterion is proposed such that the interconnection system is asymptotically stable, which is also proved to guarantee the asymptotic stability of …
Exponential Transients in Continuous-Time Symmetric Hopfield Nets
2001
We establish a fundamental result in the theory of continuous-time neural computation, by showing that so called continuous-time symmetric Hopfield nets, whose asymptotic convergence is always guaranteed by the existence of a Liapunov function may, in the worst case, possess a transient period that is exponential in the network size. The result stands in contrast to e.g. the use of such network models in combinatorial optimization applications. peerReviewed
Local Capacity $H_{\infty}$ Control for Production Networks of Autonomous Work Systems With Time-Varying Delays
2010
This paper considers the problem of local capacity H∞ control for a class of production networks of autonomous work systems with time-varying delays in the capacity changes. The system under consideration is modeled in a discrete-time singular form. Attention is focused on the design of a controller gain for the local capacity adjustments which maintains the work-in-progress (WIP) in each work system in the vicinity of planned levels and guarantees the asymptotic stability of the system and reduces the effect of the disturbance input on the controlled output to a prescribed level. In terms of a matrix inequality, a sufficient condition for the solvability of this problem is presented using …
A Lyapunov–Razumikhin approach for stability analysis of logistics networks with time-delays
2012
Logistics network represents a complex system where different elements that are logistic locations interact with each other. This interaction contains delays caused by time needed for delivery of the material. Complexity of the system, time-delays and perturbations in a customer demand may cause unstable behaviour of the network. This leads to the loss of the customers and high inventory costs. Thus the investigation of the network on stability is desired during its design. In this article we consider local input-to-state stability of such logistics networks. Their behaviour is described by a functional differential equation with a constant time-delay. We are looking for verifiable conditio…