• Corpus ID: 17124850

Chapter 16 Mixed Integer Programming Computation

  title={Chapter 16 Mixed Integer Programming Computation},
  author={Andrea Lodi},
The first 50 years of Integer and Mixed-Integer Programming have taken us to a very stable paradigm for solving problems in a reliable and effective way. We run over these 50 exciting years by showing some crucial milestones and we highlight the building blocks that are making nowadays solvers effective from both a performance and an application viewpoint. Finally, we show that a lot of work must still be done for improving the solvers and extending their modeling capability. In memory of my… 

Figures and Tables from this paper



A Computational Study of Search Strategies for Mixed Integer Programming

The goal of this article is to survey many of the results regarding branch-and-bound search strategies and evaluate them again in light of the other advances that have taken place over the years.

Strong formulations for mixed integer programs: valid inequalities and extended formulations

Examining progress over the last fifteen years in finding strong valid inequalities and tight extended formulations for simple mixed integer sets lying both on the ``easy'' and ``hard'' sides of the complexity frontier concludes by citing briefly some of the more intriguing new avenues of research.

Computing with multi-row Gomory cuts

Preprocessing and Probing Techniques for Mixed Integer Programming Problems

This work presents a framework for describing basic techniques to improve the representation of a mixed integer programming problem, and discusses recent extensions to these basic techniques.

Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework

We investigate the computational issues that need to be addressed when incorporating general cutting planes for mixed 0-1 programs into a branch-and-cut framework. The cuts we use are of the

Conflict analysis in mixed integer programming

Solving Mixed Integer Programming Problems Using Automatic Reformulation

The solution to optimality of 18 medium-to large-size problems, including production planning problems with setup costs and capacity constraints, multilevel distribution planning problems, drainage and heating system design problems, and electricity generator scheduling problems is reported on.

Generating Multiple Solutions for Mixed Integer Programming Problems

This paper introduces the one-tree algorithm, a modification of the standard branch-and-bound algorithm, and presents three different algorithms to solve the problem of effectively generating multiple solutions for the same model, concentrating on optimal and near-optimal solutions.

Improved strategies for branching on general disjunctions

Within the context of solving Mixed-Integer Linear Programs by a Branch-and-Cut algorithm, a new strategy for branching is proposed that enumerates fewer nodes than traditional branching on instances that contain both integer and continuous variables.

Testing cut generators for mixed-integer linear programming

  • F. Margot
  • Mathematics
    Math. Program. Comput.
  • 2009
A methodology for testing the accuracy and strength of cut generators for mixed-integer linear programming is presented and the problem of constructing benchmark instances for which feasible solutions can be obtained is addressed.