A precise correspondence between lift-and-project cuts, simple disjunctive cuts, and mixed integer gomory cuts for 0-1 programming

2003 ◽  
Vol 94 (2-3) ◽  
pp. 221-245 ◽  
Author(s):  
Egon Balas ◽  
Michael Perregaard
Keyword(s):  
Mixed Integer ◽  
Disjunctive Cuts ◽  
Gomory Cuts

scholarly journals Projected Chvátal–Gomory cuts for mixed integer linear programs

2006 ◽  
Vol 113 (2) ◽  
pp. 241-257 ◽  
Author(s):  
Pierre Bonami ◽  
Gérard Cornuéjols ◽  
Sanjeeb Dash ◽  
Matteo Fischetti ◽  
Andrea Lodi
Keyword(s):  
Mixed Integer ◽  
Linear Programs ◽  
Gomory Cuts ◽  
Integer Linear Programs

scholarly journals Reduce-and-Split Cuts: Improving the Performance of Mixed-Integer Gomory Cuts

2005 ◽  
Vol 51 (11) ◽  
pp. 1720-1732 ◽  
Author(s):  
Kent Andersen ◽  
Gérard Cornuéjols ◽  
Yanjun Li
Keyword(s):  
Mixed Integer ◽  
Gomory Cuts ◽  
Split Cuts

Optimal Test Assembly in Practice

2013 ◽  
Vol 221 (3) ◽  
pp. 190-200 ◽  
Author(s):  
Jörg-Tobias Kuhn ◽  
Thomas Kiefer
Keyword(s):  
Particle Physics ◽  
Large Scale ◽  
Block Design ◽  
Linear Optimization ◽  
Mixed Integer ◽  
Optimal Test ◽  
Automated Test Assembly ◽  
Test Assembly ◽  
Block Level ◽  
Mixed Integer Linear Optimization

Several techniques have been developed in recent years to generate optimal large-scale assessments (LSAs) of student achievement. These techniques often represent a blend of procedures from such diverse fields as experimental design, combinatorial optimization, particle physics, or neural networks. However, despite the theoretical advances in the field, there still exists a surprising scarcity of well-documented test designs in which all factors that have guided design decisions are explicitly and clearly communicated. This paper therefore has two goals. First, a brief summary of relevant key terms, as well as experimental designs and automated test assembly routines in LSA, is given. Second, conceptual and methodological steps in designing the assessment of the Austrian educational standards in mathematics are described in detail. The test design was generated using a two-step procedure, starting at the item block level and continuing at the item level. Initially, a partially balanced incomplete item block design was generated using simulated annealing, whereas in a second step, items were assigned to the item blocks using mixed-integer linear optimization in combination with a shadow-test approach.

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