Tricks from the Trade for Large-Scale Markdown Pricing: Heuristic Cut Generation for Lagrangian Decomposition

In automated decision making processes in the online fashion industry, the ‘predict-then-optimize’ paradigm is frequently applied, particularly for markdown pricing strategies. This typically involves a mixed-integer optimization step, which is crucial for maximizing profit and merchandise volume. In practice, the size and complexity of the optimization problem is prohibitive for using off-the-shelf solvers for mixed … Read more

The MIP Workshop 2023 Computational Competition on Reoptimization

This paper describes the computational challenge developed for a computational competition held in 2023 for the 20th anniversary of the Mixed Integer Programming Workshop. The topic of this competition was reoptimization, also known as warm starting, of mixed integer linear optimization problems after slight changes to the input data for a common formulation. The challenge … Read more

Improving Conflict Analysis in MIP Solvers by Pseudo-Boolean Reasoning

Conflict analysis has been successfully generalized from Boolean satisfiability (SAT) solving to mixed integer programming (MIP) solvers, but although MIP solvers operate with general linear inequalities, the conflict analysis in MIP has been limited to reasoning with the more restricted class of clausal constraint. This is in contrast to how conflict analysis is performed in … Read more

Using Multiple Reference Vectors and Objective Scaling in the Feasibility Pump

The Feasibility Pump (FP) is one of the best-known primal heuristics for mixed-integer programming (MIP): more than 15 papers suggested various modifications of all of its steps. So far, no variant considered information across multiple iterations, but all instead maintained the principle to optimize towards a single reference integer point. In this paper, we evaluate … Read more

Learning to Use Local Cuts

An essential component in modern solvers for mixed-integer (linear) programs (MIPs) is the separation of additional inequalities (cutting planes) to tighten the linear programming relaxation. Various algorithmic decisions are necessary when integrating cutting plane methods into a branch-and-bound (B&B) solver as there is always the trade-off between the efficiency of the cuts and their costs, … Read more

Learning To Scale Mixed-Integer Programs

Many practical applications require the solution of numerically challenging linear programs (LPs) and mixed-integer programs (MIPs). Scaling is a widely used preconditioning technique that aims at reducing the error propagation of the involved linear systems, thereby improving the numerical behavior of the dual simplex algorithm and, consequently, LP-based branch-and-bound. A reliable scaling method often makes … Read more

The confined primal integral

It is a challenging task to fairly compare local solvers and heuristics against each other and against global solvers. How does one weigh a faster termination time against a better quality of the found solution? In this paper, we introduce the confined primal integral, a new performance measure that rewards a balance of speed and … Read more

Conflict Analysis for MINLP

The generalization of MIP techniques to deal with nonlinear, potentially non-convex, constraints have been a fruitful direction of research for computational MINLP in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers towards the case of nonlinear optimization: the analysis of infeasible subproblems … Read more

Solving Previously Unsolved MIP Instances with ParaSCIP on Supercomputers by using up to 80,000 Cores

Mixed-integer programming (MIP) problem is arguably among the hardest classes of optimization problems. This paper describes how we solved 21 previously unsolved MIP instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in … Read more

Computational Aspects of Infeasibility Analysis in Mixed Integer Programming

The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems. The first is to analyze the sequence of implications, obtained by domain propagation, that led to infeasibility. The … Read more