scholarly journals Lifting Linear Extension Complexity Bounds to the Mixed-Integer Setting

2018 ◽  
pp. 788-807 ◽  
Author(s):  
Alfonso Cevallos ◽  
Stefan Weltge ◽  
Rico Zenklusen
Keyword(s):  
Linear Extension ◽  
Mixed Integer ◽  
Complexity Bounds ◽  
Extension Complexity

scholarly journals On the linear extension complexity of regular n-gons

2017 ◽  
Vol 521 ◽  
pp. 217-239 ◽  
Author(s):  
Arnaud Vandaele ◽  
Nicolas Gillis ◽  
François Glineur
Keyword(s):  
Linear Extension ◽  
Extension Complexity

scholarly journals Maximum semidefinite and linear extension complexity of families of polytopes

2017 ◽  
Vol 167 (2) ◽  
pp. 381-394 ◽  
Author(s):  
Gennadiy Averkov ◽  
Volker Kaibel ◽  
Stefan Weltge
Keyword(s):  
Linear Extension ◽  
Extension Complexity

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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