# Local Rapid Learning for Integer Programs

## TL;DR

This paper extends Rapid Learning, a hybrid CP/MIP conflict learning technique, to integer programs by applying it at local search nodes, significantly improving MIP solving efficiency especially on complex problems.

## Contribution

It introduces a novel approach for applying Rapid Learning repeatedly within the MIP search tree for integer programs, with heuristics to predict success.

## Key findings

- Significant speed-up in MIP search times.
- Particularly effective on highly dual degenerate problems.
- Heuristics improve the efficiency of local Rapid Learning.

## Abstract

Conflict learning algorithms are an important component of modern MIP and CP solvers. But strong conflict information is typically gained by depth-first search. While this is the natural mode for CP solving, it is not for MIP solving. Rapid Learning is a hybrid CP/MIP approach where CP search is applied at the root to learn information to support the remaining MIP solve. This has been demonstrated to be beneficial for binary programs. In this paper, we extend the idea of Rapid Learning to integer programs, where not all variables are restricted to the domain {0,1}, and rather than just running a rapid CP search at the root, we will apply it repeatedly at local search nodes within the MIP search tree. To do so efficiently, we present six heuristic criteria to predict the chance for local \rapidlearning to be successful. Our computational experiments indicate that our extended Rapid Learning algorithm significantly speeds up MIP search and is particularly beneficial on highly dual degenerate problems.