Progress in Mathematical Programming Solvers from 2001 to 2020

TL;DR

This paper reviews two decades of progress in LP and MILP solvers, highlighting hardware improvements and algorithmic advancements that significantly increased solving efficiency and capability.

Contribution

It provides a comprehensive comparison of solver performance from 2001 to 2020, quantifying hardware and algorithmic improvements over time.

Findings

Hardware speed increased about 20 times.

Algorithmic improvements led to 9-50 times faster solving.

Many problem instances now solved within seconds, unlike in 2001.

Abstract

This study investigates the progress made in LP and MILP solver performance during the last two decades by comparing the solver software from the beginning of the millennium with the codes available today. On average, we found out that for solving LP/MILP, computer hardware got about 20 times faster, and the algorithms improved by a factor of about nine for LP and around 50 for MILP, which gives a total speed-up of about 180 and 1,000 times, respectively. However, these numbers have a very high variance and they considerably underestimate the progress made on the algorithmic side: many problem instances can nowadays be solved within seconds, which the old codes are not able to solve within any reasonable time.