Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Uncertainty quantification in simulations of epidemics using polynomial chaos.
2012
Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equa…
Robust consensus in social networks and coalitional games
2014
We study an n-player averaging process with dynamics subject to controls and adversarial disturbances. The model arises in two distinct application domains: i) coalitional games with transferable utilities (TU) and ii) opinion propagation. We study conditions under which the average allocations achieve robust consensus to some predefined target set.
Closedness properties in team learning of recursive functions
1997
This paper investigates closedness properties in relation with team learning of total recursive functions. One of the first problems solved for any new identification types is the following: “Does the identifiability of classes U1 and U2 imply the identifiability of U1∪U2?” In this paper we are interested in a more general question: “Does the identifiability of every union of n−1 classes out of U1,...,Un imply the identifiability of U1∪...∪Un?” If the answer is positive, we call such identification type n-closed. We show that n-closedness can be equivalently formulated in terms of team learning. After that we find for which n team identification in the limit and team finite identification t…
Introduction to General Duality Theory for Multi-Objective Optimization
1992
This is intended as a comprehensive introduction to the duality theory for vector optimization recently developed by C. Malivert and the present author [3]. It refers to arbitrarily given classes of mappings (dual elements) and extends the general duality theory proposed for scalar optimization by E. Balder, S. Kurcyusz and the present author [1] and P. Lindberg.
GRASP with exterior path-relinking and restricted local search for the multidimensional two-way number partitioning problem
2017
In this work, we tackle multidimensional two-way number partitioning (MDTWNP) problem by combining GRASP with Exterior Path Relinking. In the last few years, the combination of GRASP with path relinking (PR) has emerged as a highly effective tool for finding high-quality solutions for several difficult problems in reasonable computational time. However, in most of the cases, this hybridisation is limited to the variant known as interior PR. Here, we couple GRASP with the "exterior form" of path relinking and perform extensive experimentation to evaluate this variant. In addition, we enhance our GRASP with PR method with a novel local search method specially designed for the MDTWNP problem. …
An environment based approach for the ant colony convergence
2020
Abstract Ant colony optimization (ACO) algorithms are a bio inspired solutions which have been very successful in combinatorial problem solving, also known as NP-hard problems, including transportation system optimization. As opposed to exact methods, which could give the best results of a tested problem, this meta-heuristics is based on the stochastic logic but not on theoretical mathematics demonstration (or only on certain well defined applications). According to this, the weak point of this meta-heuristics is his convergence, its termination condition. We can finds many different termination criteria in the scientific literature, yet most of them are costly in resources and unsuitable f…
Electromagnetic Sensitivity Analysis and Shape Optimization Using Method of Moments and Automatic Differentiation
2009
Sensitivity analysis is an important part of gradient-based optimization of electromagnetic devices. We demonstrate how sensitivity analysis can be incorporated into an existing in-house method of moments solver with a relatively small amount of labor by using a technique called automatic differentiation (AD). This approach enables us to obtain (geometrical) sensitivities of the discrete solution with accuracy up to numerical precision. We compare the assembly time and memory usage of the modified and original solvers. Moreover, we optimize the shape of a dipole antenna and the dimensions of a Yagi-Uda array using the presented AD technique, traditional response level finite difference sens…
On spline methods of approximation under L-fuzzy information
2011
This work is closely related to our previous papers on algorithms of approximation under L-fuzzy information. In the classical theory of approximation central algorithms were worked out on the basis of usual, that is crisp splines. We describe central methods for solution of linear problems with balanced L-fuzzy information and develop the concept of L-fuzzy splines.
Real-time clothoid approximation by Rational Bezier curves
2008
This paper presents a novel technique for implementing Clothoidal real-time paths for mobile robots. As first step, rational Bezier curves are obtained as approximation of the Fresnel integrals. By rescaling, rotating and translating the previously computed RBC, an on-line Clothoidal path is obtained. In this process, coefficients, weights and control points are kept invariant. This on-line approach guarantees that an RBC has the same behavior as the original Clothoid using a low curve order. The resulting Clothoidal path allows any two arbitrary poses to be joined in a plane. RBCs working as Clothoids are also used to search for the shortest bounded-curvature path with a significant comput…
Reduced complexity models in the identification of dynamical networks: Links with sparsification problems
2009
In many applicative scenarios it is important to derive information about the topology and the internal connections of more dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology. We cast the problem as the optimization of a cost function operating a trade-off between accuracy and complexity in the final model. We address the problem of reducing the complexity by fixing a certain degree of sparsity, and trying to find the solution that “better” satisfi…