The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform

Oleg V. Shylo - One of the best experts on this subject based on the ideXlab platform.

  • Path Relinking Scheme for the Max-Cut Problem within Global Equilibrium Search
    Recent Algorithms and Applications in Swarm Intelligence Research, 2020
    Co-Authors: Volodymyr P. Shylo, Oleg V. Shylo
    Abstract:

    In this paper, the potential of the path relinking method for the maximum cut problem is investigated. This method is embedded within Global Equilibrium search to utilize the set of high quality solutions provided by the latter. The computational experiment on a set of standard benchmark problems is provided to study the proposed approach. The empirical experiments reveal that the large sizes of the elite set lead to restart distribution of the running times, i.e., the algorithm can be accelerated by simply removing all of the accumulated data (set P) and re-initiating its execution after a certain number of elite solutions is obtained.

  • PPSN (2) - Global Equilibrium search algorithms for combinatorial optimization problems
    Lecture Notes in Computer Science, 2012
    Co-Authors: Oleg V. Shylo, Dmytro Korenkevych, Panos M. Pardalos
    Abstract:

    Global Equilibrium Search (GES) is a meta-heuristic framework that shares similar ideas with the simulated annealing method. GES accumulates a compact set of information about the search space to generate promising initial solutions for the techniques that require a starting solution, such as the simple local search method. GES has been successful for many classic discrete optimization problems: the unconstrained quadratic programming problem, the maximum satisfiability problem, the max-cut problem, the multidimensional knapsack problem and the job-shop scheduling problem. GES provides state-of-the-art performance on all of these domains when compared to the current best known algorithms from the literature. GES algorithm can be naturally extended for parallel computing as it performs search simultaneously in distinct areas of the solution space. In this talk, we provide an overview of Global Equilibrium Search and discuss some successful applications.

  • solving weighted max cut problem by Global Equilibrium search
    Cybernetics and Systems Analysis, 2012
    Co-Authors: Vladimir P. Shylo, Oleg V. Shylo, V A Roschyn
    Abstract:

    A new algorithm based on the Global Equilibrium search (GES) is developed to solve the weighted max-cut problem and is compared with currently the best solution algorithms. The advantages of the GES algorithm both in the performance and in the possibility of finding the best solutions are shown.

  • solving the maxcut problem by the Global Equilibrium search
    Cybernetics and Systems Analysis, 2010
    Co-Authors: Vladimir P. Shylo, Oleg V. Shylo
    Abstract:

    The authors propose an approach to the solution of the maxcut problem. It is based on the Global Equilibrium search method, which is currently one of the most efficient discrete programming methods. The efficiency of the proposed algorithm is analyzed.

  • Solving weighted MAX-SAT via Global Equilibrium search
    Operations Research Letters, 2008
    Co-Authors: Oleg V. Shylo, Oleg A. Prokopyev, Vladimir P. Shylo
    Abstract:

    In this note we investigate the performance of Global Equilibrium search based heuristics on the weighted MAX-SAT problem. Three variants of the approach are implemented and compared with other existing algorithms on publicly available benchmark instances. The reported computational results indicate high efficiency of the method considered.

Cedric Villani - One of the best experts on this subject based on the ideXlab platform.

  • on the trend to Global Equilibrium for spatially inhomogeneous kinetic systems the boltzmann equation
    Inventiones Mathematicae, 2005
    Co-Authors: Laurent Desvillettes, Cedric Villani
    Abstract:

    As part of our study of convergence to Equilibrium for spatially inhomogeneous kinetic equations, started in [21], we derive estimates on the rate of convergence to Equilibrium for solutions of the Boltzmann equation, like O(t-∞). Our results hold conditionally to some strong but natural estimates of smoothness, decay at large velocities and strict positivity, which at the moment have only been established in certain particular cases. Among the most important steps in our proof are 1) quantitative variants of Boltzmann’s H-theorem, as proven in [52,60], based on symmetry features, hypercontractivity and information-theoretical tools; 2) a new, quantitative version of the instability of the hydrodynamic description for non-small Knudsen number; 3) some functional inequalities with geometrical content, in particular the Korn-type inequality which we established in [22]; and 4) the study of a system of coupled differential inequalities of second order, by a treatment inspired from [21]. We also briefly point out the particular role of conformal velocity fields, when they are allowed by the geometry of the problem.

  • on the trend to Global Equilibrium in spatially inhomogeneous entropy dissipating systems the linear fokker planck equation
    Communications on Pure and Applied Mathematics, 2001
    Co-Authors: Laurent Desvillettes, Cedric Villani
    Abstract:

    We study the long-time behavior of kinetic equations in which transport and spatial confinement (in an exterior potential or in a box) are associated with a (degenerate) collision operator acting only in the velocity variable. We expose a general method, based on logarithmic Sobolev inequalities and the entropy, to overcome the well-known problem, due to the degeneracy in the position variable, of the existence of infinitely many local equilibria. This method requires that the solution be somewhat smooth. In this paper, we apply it to the linear Fokker-Planck equation and prove decay to Equilibrium faster than O(t−1/ϵ) for all ϵ > 0. © 2001 John Wiley & Sons, Inc.

Prasad Tetali - One of the best experts on this subject based on the ideXlab platform.

  • convergence to Global Equilibrium for fokker planck equations on a graph and talagrand type inequalities
    Journal of Differential Equations, 2016
    Co-Authors: Wen Huang, Yao Li, Prasad Tetali
    Abstract:

    Abstract In 2012, Chow, Huang, Li and Zhou [7] proposed the Fokker–Planck equations for the free energy on a finite graph, in which they showed that the corresponding Fokker–Planck equation is a nonlinear ODE defined on a Riemannian manifold of probability distributions. Different choices for inner products result in different Fokker–Planck equations. The unique Global Equilibrium of each equation is a Gibbs distribution. In this paper we proved that the exponential rate of convergence towards the Global Equilibrium of these Fokker–Planck equations. The rate is measured by both the decay of the L 2 norm and that of the (relative) entropy. With the convergence result, we also prove two Talagrand-type inequalities relating relative entropy and Wasserstein metric, based on two different metrics introduced in [7] . The first one is a local inequality, while the second is a Global inequality with respect to the “lower bound metric” from [7] .

  • Convergence to Global Equilibrium for Fokker–Planck equations on a graph and Talagrand-type inequalities
    Journal of Differential Equations, 2016
    Co-Authors: Wen Huang, Yao Li, Prasad Tetali
    Abstract:

    Abstract In 2012, Chow, Huang, Li and Zhou [7] proposed the Fokker–Planck equations for the free energy on a finite graph, in which they showed that the corresponding Fokker–Planck equation is a nonlinear ODE defined on a Riemannian manifold of probability distributions. Different choices for inner products result in different Fokker–Planck equations. The unique Global Equilibrium of each equation is a Gibbs distribution. In this paper we proved that the exponential rate of convergence towards the Global Equilibrium of these Fokker–Planck equations. The rate is measured by both the decay of the L 2 norm and that of the (relative) entropy. With the convergence result, we also prove two Talagrand-type inequalities relating relative entropy and Wasserstein metric, based on two different metrics introduced in [7] . The first one is a local inequality, while the second is a Global inequality with respect to the “lower bound metric” from [7] .

  • convergence to Global Equilibrium for fokker planck equations on a graph and talagrand type inequalities
    arXiv: Classical Analysis and ODEs, 2014
    Co-Authors: Wen Huang, Yao Li, Prasad Tetali
    Abstract:

    In recent work, Chow, Huang, Li and Zhou introduced the study of Fokker-Planck equations for a free energy function defined on a finite graph. When $N\ge 2$ is the number of vertices of the graph, they show that the corresponding Fokker-Planck equation is a system of $N$ nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. The different choices for inner products on the space of probability distributions result in different Fokker-Planck equations for the same process. Each of these Fokker-Planck equations has a unique Global Equilibrium, which is a Gibbs distribution. In this paper we study the {\em speed of convergence} towards Global Equilibrium for the solution of these Fokker-Planck equations on a graph, and prove that the convergence is indeed exponential. The rate as measured by the decay of the $L_2$ norm can be bound in terms of the spectral gap of the Laplacian of the graph, and as measured by the decay of (relative) entropy be bound using the modified logarithmic Sobolev constant of the graph. With the convergence result, we also prove two Talagrand-type inequalities relating relative entropy and Wasserstein metric, based on two different metrics introduced in [CHLZ] The first one is a local inequality, while the second is a Global inequality with respect to the "lower bound metric" from [CHLZ].

Vladimir P. Shylo - One of the best experts on this subject based on the ideXlab platform.

M.m. Gupta - One of the best experts on this subject based on the ideXlab platform.

  • Global Equilibrium stability of discrete-time analog neural networks
    Proceedings of 1995 IEEE International Conference on Fuzzy Systems., 1995
    Co-Authors: P.n. Nikiforuk, M.m. Gupta
    Abstract:

    In this paper, some Global stability criteria of an Equilibrium state for a general class of discrete-time dynamic neural networks are presented using a novel diagonal Lyapunov function approach, and the resulting criteria are described by the diagonal Lyapunov matrix equations. First, Globally diagonal Lyapunov function approaches are applied to study Equilibrium stability problem of a class of discrete-time dynamic neural networks without linear terms. Some novel stability conditions are then obtained for a general class of discrete-time dynamic neural networks.