A Metaheuristic Algorithm for Large Maximum Weight Independent Set Problems

by   Yuanyuan Dong, et al.

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.


page 1

page 2

page 3

page 4


New instances for maximum weight independent set from a vehicle routing application

We present a set of new instances of the maximum weight independent set ...

Exactly Solving the Maximum Weight Independent Set Problem on Large Real-World Graphs

One powerful technique to solve NP-hard optimization problems in practic...

Graph Partitioning for Independent Sets

Computing maximum independent sets in graphs is an important problem in ...

An Adaptive Repeated-Intersection-Reduction Local Search for the Maximum Independent Set Problem

The maximum independent set (MIS) problem, a classical NP-hard problem w...

The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized Search Heuristics

Several important optimization problems in the area of vehicle routing c...

Learn to Design the Heuristics for Vehicle Routing Problem

This paper presents an approach to learn the local-search heuristics tha...

Please sign up or login with your details

Forgot password? Click here to reset