Jo Devriendt †, Jan Elffers †, Ambros Gleixner ‡, Jakob Nordström *
† KTH Royal Institute of Technology, Sweden
‡ Zuse Institut Berlin, Germany
* University of Copenhagen, Denmark
jhmde@kth.se
For CNF, deciding rational infeasibility is trivial
Goal of our work:
use LP solver to check rational feasibility during PB search
Propagation
Conflict?
Learn PB constraint
Backjump
Decide unassigned variable
yes
no
with LP solver call
Propagation
Conflict?
Backjump
Decide unassigned variable
no
Rational infeasibility?
Query LP solver
yes
no
Learn PB constraint
Extract Farkas multipliers
yes
Learn Farkas constraint
[K1979] A polynomial algorithm for linear programming - 1979 - Khachiyan
[CCT87] On the Complexity of Cutting-Plane Proofs - Cook, Coullard, Turán
[F1902] Über die Theorie der Einfachen Ungleichungen - 1902 - Farkas
[EGNV18] Using combinatorial benchmarks to probe the reasoning power of pseudo-Boolean solvers - 2018 - Elffers, Giráldez-Cru, Nordström, Vinyals
[EN18] Divide and conquer: Towards faster pseudo-boolean solving - 2018 - Elffers, Nordström
[ZIB] SoPlex - soplex.zib.de