Gradient descent procedure for solving linear programming relaxations of combinatorial optimization problems in parallel mode on extra large scale
Abstract
Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO problems. The algorithm can be run in parallel mode and was implemented as CUDA C/C++ program to be executed on GPU. We exemplify efficiency of the algorithm by solving a fractional 2-matching problem. Our results demonstrate that a fractional 2-matching problem with 100,000 nodes is solved by our algorithm on a modern GPU on a scale of a second while solving the problem with simplex method would take more than an hour. The algorithm can be modified to solve more complicated LP relaxations derived from CO problems.
Cite
@article{arxiv.2011.08170,
title = {Gradient descent procedure for solving linear programming relaxations of combinatorial optimization problems in parallel mode on extra large scale},
author = {Alexey Antonov},
journal= {arXiv preprint arXiv:2011.08170},
year = {2020}
}