Instance Generation for Maximum Independent Set using Graph Generative Networks

Iker Pérez, Josu Ceberio, Iñigo Urteaga

Keywords: deep learning, maximum independent set, combinatorial optimization, generative model

TL;DR: An initial exploration of generating instances of combinatorial optimization problems (COPs), specifically Maximum Independent Set (MIS), using graph generative models.

Abstract:

In the field of combinatorial optimization, having problem instances is essential for the design, development, and evaluation of algorithms and models. However, their availability is usually limited and, in general, existing benchmark repositories are used to carry out the above-mentioned tasks along with current combinatorial optimization problem (COP) instance generators. The problem is that those instances are usually artificially generated and do not always succeed in reflecting real problem properties, such as a the solutions achieved by a given algorithm. In this paper, we approach the COP instance generation development using graph generative models. Specifically, given a reference sample of instances of a given problem, the aim is to implement a model that is able to generate (i.e., sample) new instances from the probability distribution on the COP instance space that mimics the original examples. In this particular case, we assume that the instances of optimization problems we are interested in can be represented as undirected unweighted graphs. Because of that, we will focus on the maximum independent set problem. Conducted experiments show that although we are capable of creating graphs similar to the original ones, their properties do not coincide with the expected ones, making room for other models and approaches.

Submission Number: 18