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Ant Colony Optimisation: models and applications.

Oscar Cordón, Francisco Herrera, Thomas Stützle (2002)

Mathware and Soft Computing

Ant Colony Optimization (ACO) is a metaheuristic that is inspired by the shortest path searching behavior of various ant species [1,2]. The initial work of Dorigo, Maniezzo and Colorni [3,4] who proposed the first ACO algorithm called Ant System, has stimulated a still strongly increasing number of researchers to develop more sophisticated and better performing ACO algorithms that are used to successfully solve a large number of hard combinatorial optimization problems such as the traveling salesman...

Applications of nonnegative operators to a class of optimization problems

K. C. Sivakumar (2008)

Banach Center Publications

Let X be a partially ordered real Banach space, a,b ∈ X with a ≤ b. Let ϕ be a bounded linear functional on X. We call X a Ben-Israel-Charnes space (or a B-C space) if the linear program defined by Maximize ϕ(x) subject to a ≤ x ≤ b has an optimal solution for any ϕ, a and b. Such problems arise naturally in solving a class of problems known as Interval Linear Programs. B-C spaces were introduced in the author's doctoral thesis and were subsequently studied in [8] and [9]. In this article, we review...

Applications of the Fréchet subdifferential

Durea, M. (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 46A30, 54C60, 90C26.In this paper we prove two results of nonsmooth analysis involving the Fréchet subdifferential. One of these results provides a necessary optimality condition for an optimization problem which arise naturally from a class of wide studied problems. In the second result we establish a sufficient condition for the metric regularity of a set-valued map without continuity assumptions.

Approximate dynamic programming based on high dimensional model representation

Miroslav Pištěk (2013)

Kybernetika

This article introduces an algorithm for implicit High Dimensional Model Representation (HDMR) of the Bellman equation. This approximation technique reduces memory demands of the algorithm considerably. Moreover, we show that HDMR enables fast approximate minimization which is essential for evaluation of the Bellman function. In each time step, the problem of parametrized HDMR minimization is relaxed into trust region problems, all sharing the same matrix. Finding its eigenvalue decomposition, we...

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