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BCC464/PCC174 — 2019/2 Departamento de Computação — UFOP Túlio A. M. Toffolo http://www.toffolo.com.br Otimização Linear e Inteira Aula de Apresentação

Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

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Page 1: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

BCC464/PCC174 — 2019/2Departamento de Computação — UFOP

Túlio A. M. Toffolohttp://www.toffolo.com.br

Otimização Linear e InteiraAula de Apresentação

Page 2: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação

ObjetivosThe football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Apresentar ao aluno diversos aspectos práticos e teóricos de otimização linear e inteira.

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Ensinar as técnicas de modelagem de problemas em diversas áreas de aplicação.

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Apresentar os métodos de resolução e os programas computacionais para problemas lineares e inteiros.

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Page 3: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação

EmentaThe football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Modelagem em Programação Linear

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Algoritmo Simplex

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Dualidade

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Análise de sensibilidade

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Geração de colunas

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Métodos de decomposição de Dantzig-Wolfe

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Modelagem em Programação Inteira

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Enumeração Implícita

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Planos de Corte

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Limites e Relaxações

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Page 4: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação

AvaliaçãoThe football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

3 Provas (60% da nota):17/Set: 20% da nota22/Out: 20% da nota26/Nov: 20% da nota

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Trabalho prático (40% da nota):Problema deve ser definido em comum acordo entre o aluno e o professor da disciplina.Apresentação de resultados em formato de artigo e seminário no final do semestre.

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Page 5: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação

Túlio Ângelo Machado To!olo

Segunda-feira Terça-feira Quarta-feira Quinta-feira Sexta-feira Sábado

Resumo da composição da carga horária:

Aula: 8h (horas/aula)Atendimento: 4hAdministrativo: 4hPesquisa: 8hOrientação: 8hPrep. Aulas: 8hTotal: 40 horas

07h - 08h

08h - 09h

09h - 10h

10h - 11h

11h - 12h

12h - 13h

13h - 14h

14h - 15h

15h - 16h

16h - 17h

17h - 18h

18h - 19h

19h - 20h

20h - 21h

21h - 22h

Administrativo

Prep. Aulas

BCC201

BCC464 PCC174

Atendimento

Orientação

Prep. Aulas

Orientação

BCC201

BCC464 PCC174(P)

Atendimento

Orientação

Pesquisa

Horários de atendimento

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Túlio Ângelo Machado Toffolo

Segunda­feira  Terça­feira  Quarta­feira  Quinta­feira  Sexta­feira  Sábado 

Valéria de Carvalho Santos

Vinicius Antonio de Oliveira Martins

Departamento de Computação  |  ICEB  |  Universidade Federal de Ouro Preto 

Campus Universitário Morro do Cruzeiro  |  CEP 35400­000  |  Ouro Preto ­ MG, Brasil 

Telefone: +55 31 3559­1692  |  [email protected]

 

07h ­ 08h

08h ­ 09h

09h ­ 10h

10h ­ 11h

11h ­ 12h

12h ­ 13h

13h ­ 14h

14h ­ 15h

15h ­ 16h

16h ­ 17h

17h ­ 18h

18h ­ 19h

Atendimento

Túlio Ângelo Machado Toffolo

Segunda­feira  Terça­feira  Quarta­feira  Quinta­feira  Sexta­feira  Sábado 

Valéria de Carvalho Santos

Vinicius Antonio de Oliveira Martins

Departamento de Computação  |  ICEB  |  Universidade Federal de Ouro Preto 

Campus Universitário Morro do Cruzeiro  |  CEP 35400­000  |  Ouro Preto ­ MG, Brasil 

Telefone: +55 31 3559­1692  |  [email protected]

 

07h ­ 08h

08h ­ 09h

09h ­ 10h

10h ­ 11h

11h ­ 12h

12h ­ 13h

13h ­ 14h

14h ­ 15h

15h ­ 16h

16h ­ 17h

17h ­ 18h

18h ­ 19h

Atendimento

Page 6: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação

Bibliografia recomendada

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Wolsey, Laurence A. Integer Programming, Wiley, New York, 1998.

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Page 7: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação

Bibliografia recomendada

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Goldbarg, Marco Cesar & Luna, Henrique Paca L. Otimização Combinatória e Programação Linear. 2a.ed. Campus/Elsevier, 2005.

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Page 8: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação

Bibliografia recomendada

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Murolo, A.C. et al. Pesquisa operacional para os cursos de: economia, administração e ciências contábeis. Atlas, 1998.

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Page 9: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação

Site da disciplina

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Todas as informações relacionadas ao curso, incluindo notas de aulas, notas e notícias referentes à disciplina estarão disponíveis no site http://www.toffolo.com.br

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Calendário programático também poderá ser baixado no site da disciplina.

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Page 10: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

Regras!!!

Page 11: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação

Regras: horárioThe football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

O aluno que perder mais de 25% das aulas será reprovadoAtenção: é regra da UFOP, não escolha minha

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Seja rigoroso com o horário!!

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Horário das aulas:15h20 — 17h

The football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Se você vive atrasadoaula começa às 15h… (ou às 14h30)

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Page 12: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação

Regras: comportamento

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Page 13: Aula de Apresentação - decom.ufop.br · / 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação Objetivos The football leagues grouping problem Problem

/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação

Regras: cópiaThe football leagues grouping problem

Problem constraints:

Leagues must comprise between m� and m+ teams.At most 2 teams from the same club can be in a league.There is a limit on the level difference between teams inthe same league.There is a limit on the travel time/distance between teamsin the same league.

It’s a generalization of the clique partitioning problem withminimum clique size requirement.

7 / 25 Toffolo et al. – IP heuristics for nesting problems

Colar nas provas, trabalhos e listas de exercícios, garante nota 0 para os envolvidos

Tanto para quem passou quanto para quem recebeu a cola.Isso sem falar em um possível processo administrativo (…)

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Perguntas?