Binary-Integer-Linear-Programming

We provide simple R-functions to approximately solve many large binary integer programs (BILPs). We follow the primal-dual approach of D. P. Williamson: LP relaxation of the primal BILP, solution of the dual LP, complementary slackness to assign primal binaries, and comparison of resulting objective function value to the relaxed dual LP bound to gauge precision. More specifically, we approximately solve a collapsed version of the dual LP using a simple nonlinear solver followed by a simple shadow price sort to assign primal binaries. For large problems, the resulting binary solution value is very close to the relaxed dual bound. Using this approach, we were able to approximately solve a maximization BILP with 100 constraints and 50,000 variables in about four minutes on a beefy Dell PC. The resulting BILP value was within 99.9% of the dual upper bound. Results for a minimization BILP were similar.