Diarrassouba I.,University of Le Havre
Discrete Optimization | Year: 2017
In this paper, we are interested in the separation problem for the so-called rounded capacity inequalities which are valid for the CVRP (Capacitated Vehicle Routing Problem) polytope. Rounded capacity inequalities, as well as the associated separation problem, are of particular interest for solving the CVRP, especially when dealing with the two-index formulation of the CVRP and Branch-and-Cut algorithms based on this formulation. To the best of our knowledge, it is not known in the literature whether this separation problem is NP-hard or polynomial (see for instance Augerat et al. (1998) and Letchford and Salazar (2015)), and it has been conjectured that the problem is NP-hard. In this paper, we prove this conjecture. We also show that the separation problem for rounded capacity inequalities is strongly NP-hard when the considered solution belongs to a particular relaxation of the problem and the clients have all the same demand. © 2017 Elsevier B.V.
Duchemin B.,University of Le Havre
Cellulose | Year: 2017
X-ray powder diffraction is one of the most commonly used methods in cellulose science. This technique is used to identify the cellulose allomorphs, their crystallinity, and the size of their crystallites. In this paper, a novel model is introduced that implicitly takes into account the shape and size of cellulose Iβ crystallites in the interpretation of powder diffractograms. Because of the limited amount of data in cellulose powder patterns, this model focuses on a small number of adjustable parameters. The method hypothesizes that cellulose Iβ crystallites are straight crystalline rods with superelliptical cross-sections. This superellipse is a parametric curve that can, for example, describe various crystallite shapes as rectangles or ellipses. Additionally, preferred orientation along the (0 0 1) crystallographic planes can be modelled using the March–Dollase approach. The simulated background has a semi-empirical form. An initial model comprised cellulose Iβ crystallites and the amorphous background. A second model comprised a biphasic distribution of crystallites and the same amorphous background. In this second model, large cellulose Iβ crystallites coexisted with more slender crystallites, usually less than 20 Å in lateral size. Cellulose IVI nanocrystals were selected as a modeling construct to represent these small and distorted forms of native cellulose. Both models produced simulations in excellent agreement with the experimental measurements. © 2017 Springer Science+Business Media Dordrecht
Lique F.,University of Le Havre |
Klos J.,University of Maryland University College
Monthly Notices of the Royal Astronomical Society: Letters | Year: 2011
Modelling of molecular emission spectra from interstellar clouds requires the calculation of rates for excitation by collisions with the most-abundant species. We calculate hyperfine structure resolved excitation rate coefficients of the cyano radical (CN) by He. State-tostate rate coefficients between the 37 lowest hyperfine levels of CN were calculated for low temperatures in the range 5-30 K. The new rate coefficients will help significantly in the interpretation of the CN emission lines observed with current and future telescopes, and enable this molecule to become a powerful astrophysical tool. © 2011 The Authors. Monthly Notices of the Royal Astronomical Society © 2011 RAS.
Michel S.,University of Le Havre |
Vanderbeck F.,University of Bordeaux 1
Operations Research | Year: 2012
Inventory routing problems combine the optimization of product deliveries (or pickups) with inventory control at customer sites. The application that motivates this paper concerns the planning of single-product pickups over time; each site accumulates stock at a deterministic rate; the stock is emptied on each visit. At the tactical planning stage considered here, the objective is to minimize a surrogate measure of routing cost while achieving some form of regional clustering by partitioning the sites between the vehicles. The fleet size is given but can potentially be reduced. Planning consists of assigning customers to vehicles in each time period, but the routing, i.e., the actual sequence in which vehicles visit customers, is considered an "operational" decision. The planning is due to be repeated over the time horizon with constrained periodicity. We develop a truncated branch-and-price-and-cut algorithm combined with rounding and local search heuristics that yield both primal solutions and dual bounds. On a large-scale industrial test problem (with close to 6,000 customer visits to schedule), we obtain a solution within 6.25% deviation from the optimal to our model. A rough comparison between an operational routing resulting from our tactical solution and the industrial practice shows a 10% decrease in the number of vehicles as well as in the travel distance. The key to the success of the approach is the use of a state-space relaxation technique in formulating the master program to avoid the symmetry in time. © 2012 INFORMS.
Lefebvre D.,University of Le Havre
Nonlinear Analysis: Hybrid Systems | Year: 2011
Reliability analysis is often based on stochastic discrete event models like stochastic Petri nets (SPNs). For large dynamical systems with numerous components, the analytical expression of the SPNs steady state is full of complexities because of the combinatory explosion with discrete models. Moreover, the estimation of mean markings thanks to simulations is time consuming in case of rare events. For these reasons, Petri net fluidification may be an interesting alternative to provide a reasonable estimate of the asymptotic behavior of stochastic processes. Unfortunately, the steady states of SPNs and timed continuous Petri nets (contPNs) with the same structure, same initial marking and same firing rates are mainly often different. The region of SPN steady states (when firing rates are defined in a polyhedral area) contrasts with that of contPN ones. The purpose of this paper is to illuminate this issue in taking advantage of the piecewise-affine hybrid structure of contPNs. Regions and critical regions are defined in the marking space in order to characterize this structure. Based on this characterization, the main contribution is to propose a transformation of the considered SPN into a contPN with the same structure, modified firing rates and homothetic initial marking so that the corrected contPN converges partially to the same mean marking than the SPN. Consequently, a global understanding of an SPN steady state can be obtained according to the corrected contPN. © 2011 Elsevier Ltd.
Lefebvre D.,University of Le Havre
Nonlinear Analysis: Hybrid Systems | Year: 2012
Reliability analysis is based on stochastic discrete event models like stochastic Petri nets. For complex dynamical systems with numerous components, analytical expressions of the steady state are tedious to work out because of the combinatory explosion with discrete models. For this reason, fluidification is investigated to estimate the asymptotic behavior of stochastic processes and the stationary indicators used for reliability issues. Unfortunately, the asymptotic mean markings of stochastic and continuous Petri nets are mainly often different. This paper proposes approximations of the stochastic steady state according to a set of reference data and to the classification of the firing rates, based on a k-nearest-neighbor method. This method maps the parameters of the stochastic model with the ones of the fluid model. It leads to the design of modified timed continuous Petri nets suitable to approximate the steady state of any stochastic Petri net. © 2012 Elsevier Ltd.
Odibat Z.M.,University of Le Havre
Nonlinear Dynamics | Year: 2010
This paper addresses the reliable synchronization problem between two non-identical chaotic fractional order systems. In this work, we present an adaptive feedback control scheme for the synchronization of two coupled chaotic fractional order systems with different fractional orders. Based on the stability results of linear fractional order systems and Laplace transform theory, using the master-slave synchronization scheme, sufficient conditions for chaos synchronization are derived. The designed controller ensures that fractional order chaotic oscillators that have non-identical fractional orders can be synchronized with suitable feedback controller applied to the response system. Numerical simulations are performed to assess the performance of the proposed adaptive controller in synchronizing chaotic systems. © 2009 Springer Science+Business Media B.V.
Odibat Z.M.,University of Le Havre
Computers and Mathematics with Applications | Year: 2010
An analytic study on linear systems of fractional differential equations with constant coefficients is presented. We briefly describe the issues of existence, uniqueness and stability of the solutions for two classes of linear fractional differential systems. This paper deals with systems of differential equations of fractional order, where the orders are equal to real number or rational numbers between zero and one. Exact solutions for initial value problems of linear fractional differential systems are analytically derived. Existence and uniqueness results are proved for two classes. The presented results are illustrated by analyzing some examples to demonstrate the effectiveness of the presented analytical approaches. © 2009 Elsevier Ltd. All rights reserved.
Lefebvre D.,University of Le Havre
IEEE Transactions on Automatic Control | Year: 2014
This technical note concerns fault detection and diagnosis for discrete event systems modeled with partially observed Petri nets. The proposed method provides diagnosis decisions via the analysis of observation sequences that include some observable events and the partial measurement of the successive states visited by the system. To this end, the observation sequences are decomposed into elementary observation sequences, linear matrix inequalities are used to compute the firing sequences consistent with each elementary observation sequence and an algorithm of linear complexity with respect to the length of the observation sequences is proposed to provide on-line diagnosis decisions. © 1963-2012 IEEE.
University of Le Havre | Date: 2010-02-05
An embodiment relates to a molding device that may be used to produce a part made from a composite material. The molding device includes an inductive flexible membrane and an electrically conductive rigid portion. The inductive flexible membrane generates a magnetic field which creates eddy currents in the rigid portion, thereby creating a heat flow. This heat flow heats the part made from composite material by means of conduction.