Shaping and Trimming Branch-and-bound Trees

TL;DR

This paper introduces a novel branch-and-bound search method for mixed integer linear optimization that incorporates shaping and trimming techniques, allowing for more flexible and potentially more efficient exploration of solution spaces.

Contribution

The paper proposes a new branch-and-bound approach based on offshoots, enabling variable order changes and removal of unnecessary branches, extending traditional methods.

Findings

Demonstrates potential efficiency improvements through numerical experiments

Shows flexibility in branching strategies such as top or bottom of offshoots

Provides initial evidence of the method's effectiveness

Abstract

We present a new branch-and-bound type search method for mixed integer linear optimization problems based on the concept of offshoots (introduced in this paper). While similar to a classic branch-and-bound method, it allows for changing the order of the variables in a dive (shaping) and removing unnecessary branching variables from a dive (trimming). The regular branch-and-bound algorithm can be seen as a special case of our new method. We also discuss extensions to our new method such as choosing to branch from the top or the bottom of an offshoot. We present several numerical experiments to give a first impression of the potential of our new method.