franklina m. b. toledo / alysson m. costa otimização em grafos traveling salesman problem...

Franklina M. B. Toledo / Alysson M. Costa 09:49 5 mar 2009.

Otimização em grafos

Traveling salesman problemIntrodução

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Caixeiro viajante

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The Travelling Salesman Problem: a computational study. Applegate, Bixby, Chvátal and Cook

FMBT/ AMC 10:08 5 mar 2009.

The Travelling Salesman Problem: a computational study. Applegate, Bixby, Chvátal and Cook

FMBT/ AMC 10:08 5 mar 2009.

The Travelling Salesman Problem: a computational study. Applegate, Bixby, Chvátal and Cook

FMBT/ AMC 10:08 5 mar 2009.

The Travelling Salesman Problem: a computational study. Applegate, Bixby, Chvátal and Cook

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http://www.cgl.uwaterloo.ca/~csk/projects/tsp/

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Caixeiro viajante (estética!)

The Travelling Salesman Problem: a computational study. Applegate, Bixby, Chvátal and Cook

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Polivanova, N. I.Functional and structural aspects of the visual components of intuition in problem solvingVoprosy Psikhologii, 1974, 4, 41-51

- problemas representados geometricamente £ problemas onde as distâncias são dadas para cada par de cidades.

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Vickers, D.; Butavicius, M.; Lee, M. & Medvedev, A.Human performance on visually presented Traveling Salesman problemsPsychological Research, 2001, 65, 34-45

Otimização x Estética

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Ormerod, T. C. & Chronicle, E. P.Global perceptual processes in problem solving: The case of the traveling salesperson.Perception & Psychophysics, 1999, 61, 1227-1238

Associar escala (1-melhor; 5-pior) a estética de soluções do TSP

FMBT/ AMC 10:08 5 mar 2009.

Caixeiro viajante (história)

Schrijver, A.Aardal, K.; Nemhauser, G. L. & Weismantel, R. (ed.)On the history of combinatorial optimization (till 1960),Handbooks in Operations Research and Management - Discrete Optimization, 2005, 12, 1–68.

David Applegate, Robert Bixby,Vašek Chvátal & William Cook.The Traveling Salesman Problem: A Computational Study Princeton Series in Applied Mathematics, February 2007. http://www.tsp.gatech.edu/

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Caixeiro viajante (história)

– Século XIX

• Sir William Rowan Hamilton (matemático irlandês)

• Thomas Penyngton (matemático britânico)

Hamilton Icosian game

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Caixeiro viajante (história) - cavaleiros...

O passeio do cavalo (the Knight's tour)Leonhard Paul Euler (1707 – 1783)

Knight's tour

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Caixeiro viajante (história) - cavaleiros...

Euller

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Caixeiro viajante (história) - cavaleiros...

Exercício: como transformar no TSP ?

?

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Caixeiro viajante (história)

– Século XIX - Um manual de 1832

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– Século XIX - Um manual de 1832

– Business leads the traveling salesman here and there, and there is not a good tour for all occurring cases; but through an expedient choice division of the tour so much time can be won that we feel compelled to give guidelines about this.

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– Século XIX - Um manual de 1832

– Everyone should use as much of the advice as he thinks useful for his application. We believe we can ensure as much that it will not be possible to plan the tours through Germany in consideration of the distances and the traveling back and fourth, which deserves the traveler’s special attention, with more economy. The main thing to remember is always to visit as many localities as possible without having to touch them twice.

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– Século XIX - Um manual de 1832

– Travelling salesperson ?

– "cuidado com as mulheres, nos negócios ou fora dele!"

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– Século XX

– "It appears to have been discussed informally among mathematicians at mathematics meetings for many years"

Dantzig, Fulkerson, Johnson (1954)

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– Século XX

– década de 30: K. Mergen– palestra em Harvard (Hassler Whitney)

– década de 40: estatísticos Mahalanobis (1940), Jessen (1942), Gosh (1948), Marks (1948)

Palestra em Princeton:Problema de encontrar a rota mais curtaentre os 48 estados dos EEUU (Flood)

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– Século XX– Flood - RAND (Research ANd

Development)– Dantzig, G. B.; Fulkerson, D. R. & Johnson,

S. M., Solution of a large-scale traveling-salesman problem,Operations Research, 1954, 2, 393-410