A Branch-and-Bound Algorithm for Zero-One Mixed Integer Programming Problems

1971 ◽  
Vol 19 (4) ◽  
pp. 1036-1044 ◽  
Author(s):  
Ronald E. Davis ◽  
David A. Kendrick ◽  
Martin Weitzman
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Branch And Bound ◽  
Branch And Bound Algorithm ◽  
Mixed Integer ◽  
Integer Programming Problems

scholarly journals Estimating the size of search trees by sampling with domain knowledge

2017 ◽  
Author(s):  
Gleb Belov ◽  
Samuel Esler ◽  
Dylan Fernando ◽  
Pierre Le Bodic ◽  
George L. Nemhauser
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Branch And Bound ◽  
Domain Knowledge ◽  
Estimation Error ◽  
Search Tree ◽  
Branch And Bound Algorithm ◽  
Mixed Integer ◽  
Search Trees ◽  
Sampling Algorithm

We show how recently-defined abstract models of the Branch-and-Bound algorithm can be used to obtain information on how the nodes are distributed in B&B search trees. This can be directly exploited in the form of probabilities in a sampling algorithm given by Knuth that estimates the size of a search tree. This method reduces the offline estimation error by a factor of two on search trees from Mixed-Integer Programming instances.

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