Presolving Mixed–Integer Linear Programs

Abstract

We survey the techniques used for presolving Mixed-integer linear programs (MILPs). Presolving is an important component of all modern MILP solvers. It is used for simplifying a given instance, for detecting any obvious problems or errors, and for identifying structures and characteristics that are useful for solving an instance.

CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

“…The first part f obj at the beginning is zero and is updated all the time as we reduce the problem (remove some c k from c); the terms in the summation in the second part are continuously reduced and c k are updated as necessary when we reduce the problem. The first 6 pre-process methods presented below were reported in various literatures, such as [1,17,25,26,27]; the rest of them, to the best of our knowledge, are not reported anywhere. …”

A wide neighborhood infeasible-interior-point method with arc-search for linear programming

“…Pre-process or pre-solver is a major factor that can significantly affect the numerical stability and computational efficiency. Many literatures have been focused on this topic, for example, [1,7,25,26,27]. As we will test all linear programming problems in standard form in Netlib, we focus on the strategies only for the standard linear programming problems in the form of (1) and solved in normal equations 2 .…”

“…The first part f obj at the beginning is zero and is updated all the time as we reduce the problem (remove some c k from c); the terms in the summation in the second part are continuously reduced and c k are updated as necessary when we reduce the problem. The first 6 pre-process methods presented below were reported in various literatures, such as [1,17,25,26,27]; the rest of them, to the best of our knowledge, are not reported anywhere.…”

Progress in presolving for mixed integer programming

“…Williams [28] developed a projection method for the elimination of integer variables and Savelsbergh [25] investigated preprocessing and probing techniques for mixed integer programming problems. An overview of different presolving techniques can be found in the books of Nemhauser [24] and Wolsey [29], in Fügenschuh and Martin [17] and in Mahajan [23]. Details on implementing presolving techniques effectively within a mixed integer linear programming solver are presented in Suhl and Szymanski [26], Atamtürk and Savelsbergh [7], and Achterberg [2].…”