Integer Programming: Optimization and Evaluation Are Equivalent

Abstract We show that if one can find the optimal value of an integer programming problem min{cx : Ax ≥ b, x ∈ Zn +} in polynomial time, then one can find an optimal solution in polynomial time. We also present a proper generalization to general integer programs and to local search problems of the well-known result that optimization and augmentation are equivalent for 0/1-integer programs. Our results imply that, among other things, PLS-complete problems cannot have “near-exact” neighborhoods, unless PLS = P.

• Type: Conference
• Year: 2009
• Where: WADS
• Authors: James B. Orlin, Abraham P. Punnen, Andreas S. Schulz
• Keywords: Algorithms, General Integer Programs, Integer Programming Problem, Polynomial Time, WADS 2009