A Metaheuristic Algorithm for Large Maximum Weight Independent Set Problems

TL;DR

This paper presents METAMIS, a novel metaheuristic algorithm within the GRASP framework, designed to efficiently solve large maximum-weight independent set problems arising from real-world vehicle routing applications, outperforming existing methods on large benchmarks.

Contribution

Introduction of METAMIS, a new local search metaheuristic with innovative data structures and path-relinking techniques for large MWIS problems, especially in vehicle routing contexts.

Findings

METAMIS outperforms existing open-source algorithms on large benchmark instances.

The algorithm efficiently handles graphs with hundreds of millions of edges.

New local search moves improve solution quality and escape local optima.

Abstract

Motivated by a real-world vehicle routing application, we consider the maximum-weight independent set problem: Given a node-weighted graph, find a set of independent (mutually nonadjacent) nodes whose node-weight sum is maximum. Some of the graphs airsing in this application are large, having hundreds of thousands of nodes and hundreds of millions of edges. To solve instances of this size, we develop a new local search algorithm, which is a metaheuristic in the greedy randomized adaptive search (GRASP) framework. This algorithm, which we call METAMIS, uses a wider range of simple local search operations than previously described in the literature. We introduce data structures that make these operations efficient. A new variant of path-relinking is introduced to escape local optima and so is a new alternating augmenting-path local search move that improves algorithm performance. We compare an implementation of our algorithm with a state-of-the-art openly available code on public benchmark sets, including some large instances with hundreds of millions of vertices. Our algorithm is, in general, competitive and outperforms this openly available code on large vehicle routing instances. We hope that our results will lead to even better MWIS algorithms.