Search results for "Mathematical optimization"
showing 10 items of 1300 documents
On basins of attraction for a predator-prey model via meshless approximation
2016
Abstract. In this work an epidemiological predator-prey model is studied. It analyzes the spread of an infectious disease with frequency-dependent and vertical transmission within the predator population. In particular we consider social predators, i.e. they cooperate in groups to hunt. The result is a three-dimensional system in which the predator population is divided into susceptible and infected individuals. Studying the dynamical system and bifurcation diagrams, a scenario was identified in which the model shows multistability but the domain of attraction of one equilibrium point can be so small that it is almost the point itself. From a biological point of view it is important to anal…
A computational proposal for a robust estimation of the Pareto tail index: An application to emerging markets
2022
Abstract In this work, we backtest and compare, under the VaR risk measure, the fitting performances of three classes of density distributions (Gaussian, Stable and Pareto) with respect to three different types of emerging markets: Egypt, Qatar and Mexico. We also propose a new technique for the estimation of the Pareto tail index by means of the Threshold Accepting (TAVaR) and the Hybrid Particle Swarm Optimization algorithm (H-PSOVaR). Furthermore, we test the accuracy and robustness of our estimates demonstrating the effectiveness of the proposed approach.
Combining flow routing modelling and direct velocity measurement for optimal discharge estimation
2011
Abstract. A new procedure is proposed for estimating river discharge hydrographs during flood events, using only water level data measured at a gauged site, as well as 1-D shallow water modelling and sporadic maximum surface flow velocity measurements. During flood, the piezometric level is surmised constant in the vertical plane of the river section, where the top of the banks is always above the river level, and is well represented by the recorded stage hydrograph. The river is modelled along the reach directly located downstream the upstream gauged section, where discharge hydrograph is sought after. For the stability with respect to the topographic error, as well as for the simplicity o…
Mass transport problems for the Euclidean distance obtained as limits of p-Laplacian type problems with obstacles
2014
In this paper we analyze a mass transportation problem that consists in moving optimally (paying a transport cost given by the Euclidean distance) an amount of a commodity larger than or equal to a fixed one to fulfil a demand also larger than or equal to a fixed one, with the obligation of paying an extra cost of −g1(x) for extra production of one unit at location x and an extra cost of g2(y) for creating one unit of demand at y. The extra amounts of mass (commodity/demand) are unknowns of the problem. Our approach to this problem is by taking the limit as p→∞ to a double obstacle problem (with obstacles g1, g2) for the p-Laplacian. In fact, under a certain natural constraint on the extra …
A New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal
1999
In this paper we summarize the main features of a new time dependent model to approximate the solution to the nonlinear total variation optimization problem for deblurring and noise removal introduced by Rudin, Osher and Fatemi. Our model is based on level set motion whose steady state is quickly reached by means of an explicit procedure based on an ENO Hamilton-Jacobi version of Roe's scheme. We show numerical evidence of the speed, resolution and stability of this simple explicit procedure in two representative 1D and 2D numerical examples.
Fuzzy portfolio optimization under downside risk measures
2007
This paper presents two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained by a given expected return. We assume that the rates of returns on securities are approximated as LR-fuzzy numbers of the same shape, and that the expected return and risk are evaluated by interval-valued means. We establish the relationship between those mean-interval definitions for a given fuzzy portfolio by using suitable ordering relations. Finally, we formulate the portfolio selection problem as a linear program when the returns on the assets are of trapezoidal form.
Efficiency improvement of DC* through a Genetic Guidance
2017
DC∗ is a method for generating interpretable fuzzy information granules from pre-classified data. It is based on the subsequent application of LVQ1 for data compression and an ad-hoc procedure based on A∗ to represent data with the minimum number of fuzzy information granules satisfying some interpretability constraints. While being efficient in tackling several problems, the A∗ procedure included in DC∗ may happen to require a long computation time because the A∗ algorithm has exponential time complexity in the worst case. In this paper, we approach the problem of driving the search process of A∗ by suggesting a close-to-optimal solution that is produced through a Genetic Algorithm (GA). E…
A multiagent system approach for image segmentation using genetic algorithms and extremal optimization heuristics
2006
We propose a new distributed image segmentation algorithm structured as a multiagent system composed of a set of segmentation agents and a coordinator agent. Starting from its own initial image, each segmentation agent performs the iterated conditional modes method, known as ICM, in applications based on Markov random fields, to obtain a sub-optimal segmented image. The coordinator agent diversifies the initial images using the genetic crossover and mutation operators along with the extremal optimization local search. This combination increases the efficiency of our algorithm and ensures its convergence to an optimal segmentation as it is shown through some experimental results.
Strategies for accelerating ant colony optimization algorithms on graphical processing units
2007
Ant colony optimization (ACO) is being used to solve many combinatorial problems. However, existing implementations fail to solve large instances of problems effectively. In this paper we propose two ACO implementations that use graphical processing units to support the needed computation. We also provide experimental results by solving several instances of the well-known orienteering problem to show their features, emphasizing the good properties that make these implementations extremely competitive versus parallel approaches.
CLEAR: Covariant LEAst-Square Refitting with Applications to Image Restoration
2017
International audience; In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for $\ell_1$ regularization, we develop an approach re-fitting the results of standard methods towards the input data. Total variation regularizations and non-local means are special cases of interest. We identify important covariant information that should be preserved by the re-fitting method, and emphasize the importance of preserving the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we provide an approach that has a ``twicing'' flavor a…