Generating Multiple Solutions for Mixed Integer Programming Problems
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Approximated consistency for the automatic recording constraint
Computers and Operations Research
Counting CSP solutions using generalized XOR constraints
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
The good old Davis-Putnam procedure helps counting models
Journal of Artificial Intelligence Research
Enhanced Inference for the Market Split Problem
ICTAI '09 Proceedings of the 2009 21st IEEE International Conference on Tools with Artificial Intelligence
Solution counting algorithms for constraint-centered search heuristics
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Leveraging belief propagation, backtrack search, and statistics for model counting
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
| Hi-index | 0.00 |
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.