Compact Extended Linear Programming Models:
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham
Springer
2018
|
| Series: | EURO Advanced Tutorials on Operational Research
|
| Subjects: | |
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| Physical Description: | 1 Online-Ressource (IX, 208 Seiten) 37 Illustrationen |
| ISBN: | 9783319639765 |
| DOI: | 10.1007/978-3-319-63976-5 |
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Record in the Search Index
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| _version_ | 1824554639376252929 |
| adam_text | Titel: Compact extended linear programming models
Autor: Lancia, Giuseppe
Jahr: 2018
Contents
1 Introduction..........................................................................................1
2 Polyhedra..............................................................................................7
2.1 Basic Definitions..........................................................................7
2.2 Convex Hulls of Infinitely Many Points......................................11
2.3 The Slack Matrix........................................................................12
2.4 Projections of Polyhedra..............................................................13
2.5 Union of Polyhedra Defined by Inequalities................................24
2.6 Union of Polyhedra Defined by Vertices and Extreme Rays. ... 28
3 Linear Programming............................................................................33
3.1 Basic Definitions..........................................................................33
3.2 Polyhedral Characterization........................................................35
3.3 Duality........................................................................................36
3.4 Algorithms..................................................................................39
4 Integer Linear Programming..............................................................43
4.1 Basic Definitions..........................................................................43
4.2 Modeling....................................................................................45
4.3 Formulations with Integral LP-Relaxation....................................48
4.4 The Branch-and-Bound Approach................................................51
4.5 The Cutting-Plane Approach........................................................58
4.6 General-Purpose MILP Solvers....................................................65
5 Large-Scale Linear Programming......................................................67
5.1 LP with Exponentially Many Columns........................................68
5.2 Column Generation and Branch-and-Bound................................70
5.3 LP with Exponentially Many Rows............................................71
5.4 LP with Exponentially Many Columns and Rows......................72
V
vi Contents
6 General Techniques for Compact Formulations................................75
6.1 Primal Compact Extended Formulations......................................75
6.2 Two Examples of Compact Extended Formulations....................78
6.3 Compact Equivalent Formulations..............................................81
6.4 A First Example of Compact Equivalent Formulation................84
6.5 A Second Example of Compact Equivalent Formulation............86
6.6 A Common Feature for Path Problems........................................90
6.7 The Dantzig-Wolfe Decomposition Technique............................92
6.8 Projections and Slack Matrix Factorization..................................94
6.9 Union of Polyhedra....................................................................99
7 The Permutahedron............................................................................103
7.1 Basic Definitions..........................................................................103
7.2 A Compact Extended Formulation by LP Techniques................106
7.3 A Direct Compact Extended Formulation....................................108
7.4 A Minimal Compact Extended Formulation................................109
8 The Parity Polytope..............................................................................H3
8.1 External Representation of the Parity Polytope............................114
8.2 A Compact Extended Formulation by Union of Polyhedra..........117
8.3 A Compact Extended Formulation by LP Techniques................118
9 Trees....................................................................................................123
9.1 Steiner and Spanning Trees........................................................123
9.2 Spanning Trees............................................................................125
9.3 Bounded-Degree Spanning Trees................................................131
9.4 Minimum Routing Cost Trees....................................................133
10 Cuts and Induced Bipartite Subgraphs..............................................137
10.1 Basic Definitions..........................................................................137
10.2 Max-Cut and Edge-Induced Bipartite Subgraphs........................138
10.3 Compact Versions........................................................................141
10.4 Model Comparison......................................................................144
10.5 Node-Induced Bipartite Subgraphs..............................................146
11 Stable Sets............................................................................................149
11.1 Basic Definitions..........................................................................149
11.2 Compact Models..........................................................................150
11.3 Comparability Graphs..................................................................152
12 Traveling Salesman Problems..............................................................155
12.1 Separation of Subtour Inequalities..............................................156
12.2 A Column Generation Model for the ATSP................ 157
12.3 ATSP - A Compact Reformulation....................... 160
12.4 Time-Window ATSP................................. 161
Contents vii
13 Packing................................................ 165
13.1 Bin Packing........................................ 165
13.2 Robust Knapsack........................................................................169
13.3 Cycle Packing....................................... 170
14 Scheduling............................................................................................173
14.1 The Job-Shop Problem................................................................173
14.2 The One Machine Problem............................. 178
15 Computational Biology Problems............................ 183
15.1 Introduction........................................ 183
15.2 Sorting by Reversals and Alternating Cycles............... 184
15.3 Alignments and Longest Common Subsequences............ 190
15.4 Protein Fold Comparison.............................. 193
References.................................................. 197
Index............................................................................................................205
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| id | DE-604.BV044531003 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-20T06:54:58Z |
| institution | BVB |
| isbn | 9783319639765 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029930293 |
| oclc_num | 1005510727 |
| open_access_boolean | |
| owner | DE-1049 DE-861 DE-1046 DE-355 DE-BY-UBR DE-523 DE-634 DE-2070s DE-862 DE-BY-FWS DE-863 DE-BY-FWS DE-898 DE-BY-UBR DE-92 DE-M347 DE-Aug4 DE-859 DE-706 DE-739 DE-91 DE-BY-TUM DE-824 DE-473 DE-BY-UBG DE-860 DE-1051 DE-1043 DE-20 DE-29 DE-703 DE-573 DE-188 DE-83 |
| owner_facet | DE-1049 DE-861 DE-1046 DE-355 DE-BY-UBR DE-523 DE-634 DE-2070s DE-862 DE-BY-FWS DE-863 DE-BY-FWS DE-898 DE-BY-UBR DE-92 DE-M347 DE-Aug4 DE-859 DE-706 DE-739 DE-91 DE-BY-TUM DE-824 DE-473 DE-BY-UBG DE-860 DE-1051 DE-1043 DE-20 DE-29 DE-703 DE-573 DE-188 DE-83 |
| physical | 1 Online-Ressource (IX, 208 Seiten) 37 Illustrationen |
| psigel | ZDB-2-BUM ZDB-2-BUM_2018 |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Springer |
| record_format | marc |
| series2 | EURO Advanced Tutorials on Operational Research |
| spellingShingle | Lancia, Giuseppe Serafini, Paolo 1947- Compact Extended Linear Programming Models Business Data mining Mathematical models Operations research Management science Business and Management Operations Research/Decision Theory Operations Research, Management Science Mathematical Modeling and Industrial Mathematics Data Mining and Knowledge Discovery Mathematisches Modell Wirtschaft Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)4035816-1 |
| title | Compact Extended Linear Programming Models |
| title_auth | Compact Extended Linear Programming Models |
| title_exact_search | Compact Extended Linear Programming Models |
| title_full | Compact Extended Linear Programming Models by Giuseppe Lancia, Paolo Serafini |
| title_fullStr | Compact Extended Linear Programming Models by Giuseppe Lancia, Paolo Serafini |
| title_full_unstemmed | Compact Extended Linear Programming Models by Giuseppe Lancia, Paolo Serafini |
| title_short | Compact Extended Linear Programming Models |
| title_sort | compact extended linear programming models |
| topic | Business Data mining Mathematical models Operations research Management science Business and Management Operations Research/Decision Theory Operations Research, Management Science Mathematical Modeling and Industrial Mathematics Data Mining and Knowledge Discovery Mathematisches Modell Wirtschaft Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Business Data mining Mathematical models Operations research Management science Business and Management Operations Research/Decision Theory Operations Research, Management Science Mathematical Modeling and Industrial Mathematics Data Mining and Knowledge Discovery Mathematisches Modell Wirtschaft Lineare Optimierung |
| url | https://doi.org/10.1007/978-3-319-63976-5 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029930293&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lanciagiuseppe compactextendedlinearprogrammingmodels AT serafinipaolo compactextendedlinearprogrammingmodels |