Spelling suggestions: "subject:"combinatorial aptimization"" "subject:"combinatorial foptimization""
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Dynamic Fuzzy Logic Control of GeneticAlgorithm ProbabilitiesFeng, Yi January 2008 (has links)
Genetic algorithms are commonly used to solve combinatorial optimizationproblems. The implementation evolves using genetic operators (crossover, mutation,selection, etc.). Anyway, genetic algorithms like some other methods have parameters(population size, probabilities of crossover and mutation) which need to be tune orchosen.In this paper, our project is based on an existing hybrid genetic algorithmworking on the multiprocessor scheduling problem. We propose a hybrid FuzzyGenetic Algorithm (FLGA) approach to solve the multiprocessor scheduling problem.The algorithm consists in adding a fuzzy logic controller to control and tunedynamically different parameters (probabilities of crossover and mutation), in anattempt to improve the algorithm performance. For this purpose, we will design afuzzy logic controller based on fuzzy rules to control the probabilities of crossoverand mutation. Compared with the Standard Genetic Algorithm (SGA), the resultsclearly demonstrate that the FLGA method performs significantly better.

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Ant colony for TSPFeng, Yinda January 2010 (has links)
The aim of this work is to investigate Ant Colony Algorithm for the traveling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. This paper is based on the ideas of ant colony algorithm and analysis the main parameters of the ant colony algorithm. Experimental results for solving TSP problems with ant colony algorithm show great effectiveness.

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Intractability results for problems in computational learning and approximationSaket, Rishi. January 2009 (has links)
Thesis (Ph.D)Computing, Georgia Institute of Technology, 2009. / Committee Chair: Khot, Subhash; Committee Member: Tetali, Prasad; Committee Member: Thomas, Robin; Committee Member: Vempala, Santosh; Committee Member: Vigoda, Eric. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Characterizing neighborhoods favorable to local search techniquesDimova, Boryana Slavcheva 28 August 2008 (has links)
Not available / text

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A group theoretic approach to metaheuristic local search for partitioning problemsKinney, Gary W. 28 August 2008 (has links)
Not available / text

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Integrated modernheuristic and B/B approach for the classical traveling salesman problem on a parallel computer李寶榮, Lee, Powing. January 1999 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy

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Geometric Ramifications of the Lovász Theta Function and Their Interplay with Dualityde Carli Silva, Marcel Kenji January 2013 (has links)
The Lovasz theta function and the associated convex sets known as theta bodies are fundamental objects in combinatorial and
semidefinite optimization. They are accompanied by a rich duality theory and
deep connections to the geometric concept of orthonormal representations of graphs. In this thesis, we investigate several ramifications of the theory underlying these objects, including those arising from the illuminating viewpoint of duality. We study some optimization problems over unitdistance representations of graphs, which are intimately related to the Lovasz theta function and orthonormal representations. We also strengthen some known results about dual descriptions of theta bodies and their variants. Our main goal throughout the thesis is to lay some of the foundations for using semidefinite optimization and convex analysis in a way analogous to how polyhedral combinatorics has been using linear optimization to prove minmax theorems.
A unitdistance representation of a graph $G$ maps its nodes to some Euclidean space so that adjacent nodes are sent to pairs of points at distance one. The hypersphere number of $G$, denoted by $t(G)$, is the (square of the) minimum radius of a hypersphere that contains a unitdistance representation of $G$. Lovasz proved a minmax relation describing $t(G)$ as a function of $\vartheta(\overline{G})$, the theta number of the complement of $G$. This relation provides a dictionary between unitdistance representations in hyperspheres and orthonormal representations, which we exploit in a number of ways: we develop a weighted generalization of $t(G)$, parallel to the weighted version of $\vartheta$; we prove that $t(G)$ is equal to the (square of the) minimum radius of an Euclidean ball that contains a unitdistance representation of $G$; we abstract some properties of $\vartheta$ that yield the famous Sandwich Theorem and use them to define another weighted generalization of $t(G)$, called ellipsoidal number of $G$, where the unitdistance representation of $G$ is required to be in an ellipsoid of a given shape with minimum volume. We determine an analytic formula for the ellipsoidal number of the complete graph on $n$ nodes whenever there exists a Hadamard matrix of order $n$.
We then study several duality aspects of the description of the theta body $\operatorname{TH}(G)$. For a graph $G$, the convex corner $\operatorname{TH}(G)$ is known to be the projection of a certain convex set, denoted by $\widehat{\operatorname{TH}}(G)$, which lies in a much higherdimensional matrix space. We prove that the vertices of $\widehat{\operatorname{TH}}(G)$ are precisely the symmetric tensors of incidence vectors of stable sets in $G$, thus broadly generalizing previous results about vertices of the elliptope due to Laurent and Poljak from 1995. Along the way, we also identify all the vertices of several variants of $\widehat{\operatorname{TH}}(G)$ and of the elliptope. Next we introduce an axiomatic framework for studying generalized theta bodies, based on the concept of diagonally scaling invariant cones, which allows us to prove in a unified way several characterizations of $\vartheta$ and the variants $\vartheta'$ and $\vartheta^+$, introduced independently by Schrijver, and by McEliece, Rodemich, and Rumsey in the late 1970's, and by Szegedy in 1994. The beautiful duality equation which states that the antiblocker of $\operatorname{TH}(G)$ is $\operatorname{TH}(\overline{G})$ is extended to this setting. The framework allows us to treat the stable set polytope and its classical polyhedral relaxations as generalized theta bodies, using the completely positive cone and its dual, and it allows us to derive a (weighted generalization of a) copositive formulation for the fractional chromatic number due to Dukanovic and Rendl in 2010 from a completely positive formulation for the stability number due to de Klerk and Pasechnik in 2002. Finally, we study a nonconvex constraint for semidefinite programs (SDPs) that may be regarded as analogous to the usual integrality constraint for linear programs. When applied to certain classical SDPs, it specializes to the standard rankone constraint. More importantly, the nonconvex constraint also applies to the dual SDP, and for a certain SDP formulation of $\vartheta$, the modified dual yields precisely the clique covering number. This opens the way to study some exactness properties of SDP relaxations for combinatorial optimization problems akin to the corresponding classical notions from polyhedral combinatorics, as well as approximation algorithms based on SDP relaxations.

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Short horizon optimal control of nonlinear systems via discrete state space realizationFoley, Dawn Christine 05 1900 (has links)
No description available.

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Application of genetic algorithms to Visual Interactive Simulation optimisationGibson, Gary M January 1995 (has links)
Thesis (PhD in Computer and Information Science)University of South Australia, 1995

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Application of genetic algorithms to Visual Interactive Simulation optimisationGibson, Gary M January 1995 (has links)
Thesis (PhD in Computer and Information Science)University of South Australia, 1995

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