Progress in mathematical programming solvers from 2001 to 2020

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.(c) 2022 The Authors. Published by Elsevier Ltd on behalf of Association of European Operational Research Societies (EURO). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Automated summary

This study investigates the progress made in LP and MILP solver performance during the last two decades, comparing the solver software from the beginning of the millennium with the codes available today. On average, computer hardware speed for solving LP/MILP increased by about 20 times, and the algorithms improved by a factor of approximately nine for LP and 50 for MILP, resulting in a total speed-up of around 180 and 1,000 times, respectively. However, these numbers vary greatly and significantly underestimate the progress made on the algorithmic side.