Embed Size (px)
Citation preview
BCC464/PCC174 — 2018/2Departamento 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.
�2
/ 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
�3
/ 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):18/Set: 20% da nota23/Out: 20% da nota27/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.
�4
/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação
Horários de atendimento
MENU - ADMIN
Página Inicial
Meu Plano de Trabalho
Administração Django
Aulas da Computação
Aulas / Professor
Planos / Professores
Resumo Professores
Gerar CSV Disciplinas
Logout
Meu Plano de Trabalho - Túlio Ângelo Machado Toffolo (Semestre: 2018-2)
2018-2
Passo 1: Inserir, remover ou alterar as atividades
Administrativo Atividades administrativas 2h
Atendimento Atendimento a alunos 4h
Prep. Aulas Preparação de aulas 8h
Orientação Orientação de alunos 4h
Pesquisa Pesquisa 14h
Passo 2: Verificar grade de horários
Segunda-feira Terça-feira Quarta-feira Quinta-feira Sexta-feira Sábado
Resumo da composição da carga horária:
Aula: 8h (horas/aula)Atendimento: 4h
Administrativo: 2h
Pesquisa: 14h
Orientação: 4h
Prep. Aulas: 8h
Total: 40 horas
Passo 3: Checar ementa e demais informações das suas disciplinas
BCC201 - Introdução à Programação ( ementa em PDF)BCC464 - Otimização Linear e Inteira ( ementa em PDF)PCC174 - Otimização Linear e Inteira ( ementa em PDF)
PPGCC - Programa de Pós-Graduação em Ciência da ComputaçãoDepartamento de Computação | ICEB | Universidade Federal de Ouro Preto
Campus Universitário Morro do Cruzeiro | CEP 35400-000 | Ouro Preto - MG, BrasilTelefone: +55 31 3559-1692 | [email protected]
Você está logado no Sistema de Administração do DECOM. Por favor, utilize o Menu Lateral. Voltar ao site do DECOM
07h - 08h
08h - 09h
09h - 10h
10h - 11h
11h - 12h
12h - 13h
13h - 14h
14h - 15h
15h - 16h
16h - 17h
17h - 18h
18h - 19h
Orientação
Pesquisa
BCC201
BCC464 PCC174
Prep. Aulas
Prep. Aulas
Administrativo
Atendimento
Pesquisa
BCC201
BCC464 PCC174
Prep. Aulas
Prep. Aulas
Pesquisa
Pesquisa
MENU - ADMIN
Página Inicial
Meu Plano de Trabalho
Administração Django
Aulas da Computação
Aulas / Professor
Planos / Professores
Resumo Professores
Gerar CSV Disciplinas
Logout
Meu Plano de Trabalho - Túlio Ângelo Machado Toffolo (Semestre: 2018-2)
2018-2
Passo 1: Inserir, remover ou alterar as atividades
Administrativo Atividades administrativas 1h
Atendimento Atendimento 4h
Prep. Aulas Preparação de aulas 8h
Orientação Orientação de alunos 4h
Pesquisa Pesquisa 15h
Passo 2: Verificar grade de horários
Segunda-feira Terça-feira Quarta-feira Quinta-feira Sexta-feira Sábado
Resumo da composição da carga horária:
Aula: 8h (horas/aula)Atendimento: 4h
Administrativo: 1h
Pesquisa: 15h
Orientação: 4h
Prep. Aulas: 8h
Total: 40 horas
Passo 3: Checar ementa e demais informações das suas disciplinas
BCC201 - Introdução à Programação ( ementa em PDF)BCC464 - Otimização Linear e Inteira ( ementa em PDF)PCC174 - Otimização Linear e Inteira ( ementa em PDF)
PPGCC - Programa de Pós-Graduação em Ciência da ComputaçãoDepartamento de Computação | ICEB | Universidade Federal de Ouro Preto
Campus Universitário Morro do Cruzeiro | CEP 35400-000 | Ouro Preto - MG, BrasilTelefone: +55 31 3559-1692 | [email protected]
Você está logado no Sistema de Administração do DECOM. Por favor, utilize o Menu Lateral. Voltar ao site do DECOM
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
Modo de edição LogoutPágina
�5
/ 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.
�6
/ 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.
�7
/ 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.
�8
/ 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.
�9
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)
�11
/ 12/ 13 Túlio Toffolo — Otimização Linear e Inteira — Aula de Apresentação
Regras: comportamento
�12
/ 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 (…)
�13
/ 12
Perguntas?
