What is a Disjunction? - IEOR @IIT Bombay

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Comparison over 30 instances (MIPLIB and Mittleman) 1 Fraction of Instances 0.8 0.6 0.4 0.2 0 Variable Branching General Disj., k=5 General Disj., k=15 1 2 4 8 16 32 64 128 Times size of branch-and-bound tree than the smallest
Computational Complexity The problem of finding the “best” disjunction is: ◮ N P−complete in general (Reduction from Number Partitioning Problem) ◮ N P−complete when π ∈ {0, 1} n ◮ N P−complete when π ∈ {−1, 0, 1} n ◮ N P−complete when (π, π 0 ) ∈ {0, 1} n+1 ◮ N P−complete when x ∈ {0, 1} n and either of above four conditions hold (Reduction from 1-IN-3SAT) . . . lead to similar results for some problems of generating split inequalities
Page 1 and 2: In Search of Optimal Disjunctions i
Page 3 and 4: What is a Disjunction? Given a MIP
Page 5 and 6: Formulation Technique LP 2 DUAL 2 M
Page 7: Examples * * * * * * * * * * * * *
Page 11 and 12: Using Formulations for “best” C
Page 13: Conclusions and Future Work ◮ Sel

What is a Disjunction? - IEOR @IIT Bombay

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