A GPU-Based Genetic Algorithm for the P-Median Problem

TL;DR

This paper introduces a GPU-accelerated genetic algorithm for the NP-hard p-median problem, leveraging parallel computing to efficiently find near-optimal solutions on large benchmark instances.

Contribution

It presents a novel CUDA-based genetic algorithm using a Pseudo Boolean formulation, demonstrating high effectiveness on diverse benchmark problems.

Findings

Successfully solved most benchmark instances to optimality.

Achieved over 99.9% approximation for difficult instances.

Proved the efficiency of GPU parallelization for combinatorial optimization.

Abstract

The p-median problem is a well-known NP-hard problem. Many heuristics have been proposed in the literature for this problem. In this paper, we exploit a GPGPU parallel computing platform to present a new genetic algorithm implemented in Cuda and based on a Pseudo Boolean formulation of the p-median problem. We have tested the effectiveness of our algorithm using a Tesla K40 (2880 Cuda cores) on 290 different benchmark instances obtained from OR-Library, discrete location problems benchmark library, and benchmarks introduced in recent publications. The algorithm succeeded in finding optimal solutions for all instances except for two OR-library instances, namely pmed30 and pmed40, where better than 99.9\% approximations were obtained.