Alexander Hoen – Optimization Online

Analyzing the numerical correctness of branch-and-bound decisions for mixed-integer programming

Published: 2025/03/01

(Mixed) Integer Linear Programming, Integer Programming branch-and-bound methods, exact algorithm, Mixed Integer Programs

Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While the practical success of floating-point MIP solvers bears witness to their overall numerical robustness, it is well-known that numerically challenging input can lead them to produce incorrect results. … Read more

MIP-DD: Delta Debugging for Mixed Integer Programming Solvers

Published: 2025/02/18

Alexander Hoen

Dominik Kamp

Ambros Gleixner

(Mixed) Integer Linear Programming, Integer Programming debugging, mixed integer problem

The recent performance improvements in mixed-integer programming (MIP) have been accompanied by a significantly increased complexity of the codes of MIP solvers, which poses challenges in fixing implementation errors. In this paper, we introduce MIP-DD, a solver-independent tool, which to the best of our knowledge is the first open-source delta debugger for MIP. Delta debugging … Read more

A diving heuristic for mixed-integer problems with unbounded semi-continuous variables

Published: 2024/03/29, Updated: 2024/10/16

Integer Programming diving heuristic, indicator constraints, integer programming, semi-continuous variables, supply chain management

Semi-continuous decision variables arise naturally in many real-world applications. They are defined to take either value zero or any value within a specified range, and occur mainly to prevent small nonzero values in the solution. One particular challenge that can come with semi-continuous variables in practical models is that their upper bound may be large … Read more

The SCIP Optimization Suite 9.0

Published: 2024/02/26

Jasper van Doornmalen

Integer Programming, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems branch-and-cut algorithm, Branch-and-price algorithm, column generation, constraint integer programming, linear programming, Mixed-integer Linear Programming (MILP), Mixed-integer nonlinear programming (MINLP), mixed-integer semidefinite programming, optimization solver, parallelization

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a … Read more

PaPILO: A Parallel Presolving Library for Integer and Linear Optimization with Multiprecision Support

Published: 2023/08/04, Updated: 2025/02/23

Alexander Hoen

Ambros Gleixner

Leona Gottwald

(Mixed) Integer Linear Programming, Integer Programming, Linear Programming linear programming, mixed-integer programming, multi-precision computation, parallel computing, presolving

Presolving has become an essential component of modern MIP solvers both in terms of computational performance and numerical robustness. In this paper we present PaPILO (https://github.com/scipopt/papilo), a new C++ header-only library that provides a large set of presolving routines for MIP and LP problems from the literature. The creation of \papilo was motivated by the … Read more

The SCIP Optimization Suite 8.0

Published: 2021/12/16, Updated: 2022/01/31

Jasper van Doornmalen

Branch and Cut Algorithms, Integer Programming, Optimization Software and Modeling Systems branch-and-cut, branch-and-price, column generation, constraint integer programming, linear programming, mixed-integer linear programming, mixed-integer nonlinear programming, mixed-integer semidefinite programming, optimization solver, parallelization

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type … Read more