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BCC464/PCC174 — 2019/2Departamento de Computação — UFOP
Túlio A. M. Toffolohttp://www.toffolo.com.br
Otimização Linear e InteiraAula de Apresentação
/ 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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/ 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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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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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
/ 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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/ 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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/ 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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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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Regras!!!
/ 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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Regras: comportamento
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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?
