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CPAIOR
2010
Springer

Upper Bounds on the Number of Solutions of Binary Integer Programs

9 years 3 months ago
Upper Bounds on the Number of Solutions of Binary Integer Programs
We present a new method to compute upper bounds of the number of solutions of binary integer programming (BIP) problems. Given a BIP, we create a dynamic programming (DP) table for a redundant knapsack constraint which is obtained by surrogate relaxation. We then consider a Lagrangian relaxation of the original problem to obtain an initial weight bound on the knapsack. This bound is then refined through subgradient optimization. The latter provides a variety of Lagrange multipliers which allow us to filter infeasible edges in the DP table. The number of paths in the final table then provides an upper bound on the number of solutions. Numerical results show the effectiveness of our counting framework on automatic recording and market split problems.
Siddhartha Jain, Serdar Kadioglu, Meinolf Sellmann
Added 19 Jul 2010
Updated 19 Jul 2010
Type Conference
Year 2010
Where CPAIOR
Authors Siddhartha Jain, Serdar Kadioglu, Meinolf Sellmann
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