Improving the LP bound of a MILP by branching concurrently

TL;DR

This paper introduces a novel method for improving the LP relaxation bounds of MILPs by analyzing dual variable differences and strategically branching to tighten the problem's feasible region.

Contribution

It proposes a new technique that leverages dual variable differences to select branches, enhancing LP bounds and enabling cut generation in MILP solving.

Findings

The method improves LP bounds by strategic branching.

It allows for better problem relaxation and tighter bounds.

The approach can generate effective cuts for MILPs.

Abstract

We'll measure the differences of the dual variables and the gain of the objective function when creating new problems, which each has one inequality more than the starting LP-instance. These differences of the dual variables are naturally connected to the branches. Then we'll choose those differences of dual variables, so that for all combinations of choices at the connected branches, all dual inequalities will hold for sure. By adding the gain of each chosen branching, we get a total gain, which gives a better limit of the original problem. By this technique it is also possible to create cuts.