Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Analysis and approximation of one-dimensional scalar conservation laws with general point constraints on the flux
2016
We introduce and analyze a class of models with nonlocal point constraints for traffic flow through bottlenecks, such as exits in the context of pedestrians traffic and reduction of lanes on a road under construction in vehicular traffic. Constraints are defined based on data collected from non-local in space and/or in time observations of the flow. We propose a theoretical analysis and discretization framework that permits to include different data acquisition strategies; a numerical comparison is provided. Nonlocal constraint allows to model, e.g., the irrational behavior (" panic ") near the exit observed in dense crowds and the capacity drop at tollbooth in vehicular traffic. Existence …
Computational stability of an initially radial solution of a growth/dissolution problem in a nonradial implementation
1991
We consider a free boundary problem modelling the growth/dissolution of a crystal. The aim is to investigate the following question: Does the solution to the crystal growth problem posed in two dimensions with radially symmetric initial and boundary condition evolve as a radially symmetric solution?
An improved smoothed particle electromagnetics method in 3D time domain simulations
2011
In this paper, an enhanced variant of the meshless smoothed particle electromagnetics (SPEM) method is performed in order to solve PDEs in time domain describing 3D transient electromagnetic phenomena. The method appears to be very efficient in approximating spatial derivatives in the numerical treatment of Maxwell's curl equations. In many cases, very often, accuracy degradation, due to a lack of particle consistency, severely limits the usefulness of this approach. A numerical corrective strategy, which allows to restore the SPEM consistency, without any modification of the smoothing kernel function and its derivatives, is presented. The method allows to restore the same order of consiste…
Quasi-Newton approach to nonnegative image restorations
2000
Abstract Image restoration, or deblurring, is the process of attempting to correct for degradation in a recorded image. Typically the blurring system is assumed to be linear and spatially invariant, and fast Fourier transform (FFT) based schemes result in efficient computational image restoration methods. However, real images have properties that cannot always be handled by linear methods. In particular, an image consists of positive light intensities, and thus a nonnegativity constraint should be enforced. This constraint and other ways of incorporating a priori information have been suggested in various applications, and can lead to substantial improvements in the reconstructions. Neverth…
ELECTRE III to dynamically support the decision maker about the periodic replacements configurations for a multi-component system
2013
The problem tackled by the present paper concerns the selection of the elements of a repairable and stochastically deteriorating multi-component system to replace (replacements configuration) during each scheduled and periodical system stop within a finite optimization cycle, by ensuring the simultaneous minimization of both the expected total maintenance cost and the system unavailability. To solve the considered problem, a combined approach between multi-objective optimization problem (MOOP) and multi-criteria decision making (MCDM) resolution techniques is proposed. In particular, the @e constraint method is used to single out the optimal Pareto frontier whereas the ELECTRE III multi-cri…
Integration of Two Multiobjective Optimization Methods for Nonlinear Problems
2003
In this paper, we bring together two existing methods for solving multiobjective optimization problems described by nonlinear mathematical models and create methods that benefit from both heir strengths. We use the Feasible Goals Method and the NIMBUS method to form new hybrid approaches. The Feasible Goals Method (FGM) is a graphic decision support tool that combines ideas of goal programming and multiobjective methods. It is based on the transformation of numerical information given by mathematical models into a variety of feasible criterion vectors (that is, feasible goals). Visual interactive display of this variety provides information about the problem that helps the decision maker to…
Stochastic Decision Support Models and Optimal Stopping Rules in a New Product Lifetime Testing
2010
Determining when to stop a statistical test is an important management decision. Several stopping criteria have been proposed, including criteria based on statistical similarity, the probability that the system has a desired reliability, and the expected cost of remaining faults. This paper presents a new stopping rule in fixed-sample testing based on the statistical estimation of total costs involved in the decision to continue beyond an early failure as well as a stopping rule in sequential-sample testing to determine when testing should be stopped. The paper considers the problem that can be stated as follows. A new product is submitted for lifetime testing. The product will be accepted …
Stochastic multicriteria acceptability analysis using the data envelopment model
2006
Abstract Data envelopment analysis (DEA) and stochastic multicriteria acceptability analysis (SMAA-2) are methods for evaluating alternatives based on multiple criteria. While DEA is mainly an ex-post tool used for classifying alternatives into efficient and inefficient ones, SMAA-2 is an ex-ante tool for supporting multiple criteria decision-making. Both methods use a kind of value function where the importance of criteria is modeled using weights. Unlike many other methods, neither DEA nor SMAA-2 requires decision-makers’ weights as input. Instead, these so-called non-parametric methods explore the weight space in order to identify weights favorable for each alternative. This paper introd…
A Branch-Price-and-Cut Algorithm for the Min-Max k -Vehicle Windy Rural Postman Problem
2013
[EN] The min-max k -vehicles windy rural postman problem consists of minimizing the maximal distance traveled by a vehicle to find a set of balanced routes that jointly service all the required edges in a windy graph. This is a very difficult problem, for which a branch-and-cut algorithm has already been proposed, providing good results when the number of vehicles is small. In this article, we present a branch-price-and-cut method capable of obtaining optimal solutions for this problem when the number of vehicles is larger for the same set of required edges. Extensive computational results on instances from the literature are presented.
Optimal shape design and unilateral boundary value problems: Part II
2007
In the first part we give a general existence theorem and a regularization method for an optimal control problem where the control is a domain in R″ and where the system is governed by a state relation which includes differential equations as well as inequalities. In the second part applications for optimal shape design problems governed by the Dirichlet-Signorini boundary value problem are presented. Several numerical examples are included.