# Optimality gap integer programming

*2020-02-19 06:17*

How to measure the difficulty of a MixedLinear Integer Programming (MILP) problem? The intuitive answer is the number of binary variables, when solving the MILP through the branchandcut algorithm.Optimality gap in a mathematical model solver. (For details see any book on Integer Programming). This is a very unique property of a MIP solver that practitioners (like me) use a lot: instead of looking for proven optimal solutions that take a long time to compute we are happy with a solution guaranteed not worse than x from the optimal solution. optimality gap integer programming

Generally the difference between a best known solution, e. g. the incumbent solution in mixed integer programming, and a value that bounds the best possible solution. One such measure is the duality gap. The term is often qualified as the absolute gap, which is the magnitude of the difference between the best known solution and the best bound, or as the relative gap, which is the absolute gap divided by the

Interpretation of GAP in CPLEX. The optimality is proven if the upper bound and the lower bound evaluate the same value, i. e. CPLEX could prove an optimality gap of 0. Since CPLEX stops with a solution that has a gap of 0. 57, I would assume that you configured an MIPgap 1. If you are interested in a solution with proven optimal, In each step of those algorithms, the parametric subproblem needs to be solved to the global optimality, i. e. 0 gap. Mixedinteger programming problems are usually NPhard and the solution to 0 optimality gap might require significant computational effort when the problem size is large. **optimality gap integer programming**