Progress in presolving for mixed integer programming

Abstract

This paper describes three presolving techniques for solving mixed integer programming problems (MIPs) that were implemented in the academic MIP solver SCIP. The task of presolving is to reduce the problem size and strengthen the formulation, mainly by eliminating redundant information and exploiting problem structures. The first method fixes continuous singleton columns and extends results known from duality fixing. The second analyzes and exploits pairwise dominance relations between variables, whereas the third detects isolated subproblems and solves them independently. The performance of the presented techniques is demonstrated on two MIP test sets. One contains all benchmark instances from the last three MIPLIB versions, while the other consists of real-world supply chain management problems. The computational results show that the combination of all three presolving techniques almost halves the solving time for the considered supply chain management problems. For the MIPLIB instances we obtain a speedup of 20 % on affected instances while not degrading the performance on the remaining problems.

MIPLIB 2017: data-driven compilation of the 6th mixed-integer programming library

“…The justification for distributing the instances in their original submitted form is simply that this allows the most complete and realistic testing of the ability of each solver to deal with real-world instances, including all of the idiosyncratic artifacts that may arise in the modeling process. In particular, algorithms for presolving instances are actively developed and have a high impact on the performance of a solver (see [2,20]). They not only strengthen the original formulation, but also simplify and remove unnecessary artifacts.…”

Optimal decision trees for the algorithm selection problem: integer programming based approaches

“…The model proposed in Section 2 can be optimized by stand‐alone MIP solvers and in finite time the optimal solution for the ASP will be produced. Despite the continuous evolution of MIP solvers (Johnson et al., 2000; Gamrath et al., 2015), the optimization of large MIP models in restricted times, in the general case, is still challenging. Thus, we performed some scalability tests (Section 4.2) to check how practical it is the use of the our complete model to create optimal decision trees for the ASP in datasets of different sizes in limited times.…”

Extended formulation for hop constrained distribution network configuration problems

“…In Figure 8, we observe that LF is globally better than LFR. This can be explained by the powerful preprocessing and cutting techniques that have been developed for models using integer and binary variables, from Gomory's cuts end of the 50's [10] to recent work [8,15], that are integrated in state-of-the-art MIP solvers. On average, the preprocessing of CPLEX eliminates 32% more variables in LF compared to LFR.…”