Improving Optimization Bounds using Machine Learning: Decision Diagrams meet Deep Reinforcement Learning

09/10/2018
by   Quentin Cappart, et al.
0

Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower bounds that can be significantly better than classical bounding mechanisms, such as linear relaxations. It is well known that the quality of the bound achieved through this flexible bounding method is highly reliant on the ordering of variables chosen for building the diagram, and finding an ordering that optimizes standard metrics, or even improving one, is an NP-hard problem. In this paper, we propose an innovative and generic approach based on deep reinforcement learning for obtaining an ordering for tightening the bounds obtained with relaxed and restricted DDs. We apply the approach to both the Maximum Independent Set Problem and the Maximum Cut Problem. Experimental results on synthetic instances show that the deep reinforcement learning approach, by achieving tighter objective function bounds, generally outperforms ordering methods commonly used in the literature when the distribution of instances is known. To the best knowledge of the authors, this is the first paper to apply machine learning to directly improve relaxation bounds obtained by general-purpose bounding mechanisms for combinatorial optimization problems.

READ FULL TEXT
research
03/15/2022

A Differentiable Approach to Combinatorial Optimization using Dataless Neural Networks

The success of machine learning solutions for reasoning about discrete s...
research
08/19/2019

Improved Job sequencing Bounds from Decision Diagrams

We introduce a general method for relaxing decision diagrams that allows...
research
07/06/2023

LEO: Learning Efficient Orderings for Multiobjective Binary Decision Diagrams

Approaches based on Binary decision diagrams (BDDs) have recently achiev...
research
01/10/2023

Strong SDP based bounds on the cutwidth of a graph

Given a linear ordering of the vertices of a graph, the cutwidth of a ve...
research
11/09/2020

Geometric Deep Reinforcement Learning for Dynamic DAG Scheduling

In practice, it is quite common to face combinatorial optimization probl...
research
12/16/2020

Deep Reinforcement Learning of Graph Matching

Graph matching under node and pairwise constraints has been a building b...
research
09/27/2019

Quantum Algorithm for Finding the Optimal Variable Ordering for Binary Decision Diagrams

An ordered binary decision diagram (OBDD) is a directed acyclic graph th...

Please sign up or login with your details

Forgot password? Click here to reset