Strength of facets for the set covering and set packing polyhedra on circulant matrices

2009 ◽  
Vol 35 ◽  
pp. 109-114 ◽  
Author(s):  
S. Bianchi ◽  
M.S. Montelar ◽  
M. Escalante
Keyword(s):  
Set Covering ◽  
Circulant Matrices ◽  
Set Packing

scholarly journals On Complexity of Optimal Recombination for Binary Representations of Solutions

2008 ◽  
Vol 16 (1) ◽  
pp. 127-147 ◽  
Author(s):  
Anton V. Eremeev
Keyword(s):  
Optimization Problem ◽  
Minimum Weight ◽  
Packing Problem ◽  
Set Covering ◽  
Set Packing ◽  
Set Partition ◽  
Maximum Weight ◽  
Linear Programming Problems ◽  
Optimal Recombination ◽  
Set Packing Problem

We consider the optimization problem of finding the best possible offspring as a result of a recombination operator in an evolutionary algorithm, given two parent solutions. The optimal recombination is studied in the case where a vector of binary variables is used as a solution encoding. By means of efficient reductions of the optimal recombination problems (ORPs) we show the polynomial solvability of the ORPs for the maximum weight set packing problem, the minimum weight set partition problem, and for linear Boolean programming problems with at most two variables per inequality, and some other problems. We also identify several NP-hard cases of optimal recombination: the Boolean linear programming problems with three variables per inequality, the knapsack, the set covering, the p-median, and some other problems.

scholarly journals Lift-and-project ranks of the set covering polytope of circulant matrices

2012 ◽  
Vol 160 (18) ◽  
pp. 2555-2562
Author(s):  
Silvia M. Bianchi ◽  
Mariana S. Escalante ◽  
M. Susana Montelar
Keyword(s):  
Set Covering ◽  
Circulant Matrices

scholarly journals On the set covering polyhedron of circulant matrices

2009 ◽  
Vol 6 (2) ◽  
pp. 162-173 ◽  
Author(s):  
Gabriela R. Argiroffo ◽  
Silvia M. Bianchi
Keyword(s):  
Set Covering ◽  
Circulant Matrices

scholarly journals The minor inequalities in the description of the set covering polyhedron of circulant matrices

2013 ◽  
Vol 79 (1) ◽  
pp. 69-85 ◽  
Author(s):  
Silvia M. Bianchi ◽  
Graciela L. Nasini ◽  
Paola B. Tolomei
Keyword(s):  
Set Covering ◽  
Circulant Matrices

scholarly journals Some advances on the set covering polyhedron of circulant matrices

2014 ◽  
Vol 166 ◽  
pp. 59-70 ◽  
Author(s):  
S. Bianchi ◽  
G. Nasini ◽  
P. Tolomei
Keyword(s):  
Set Covering ◽  
Circulant Matrices
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