A Graph Neural Network-Based QUBO-Formulated Hamiltonian-Inspired Loss Function for Combinatorial Optimization using Reinforcement Learning

• URL: http://arxiv.org/abs/2311.16277v1
• Date: Mon, 27 Nov 2023 19:33:14 GMT
• Title: A Graph Neural Network-Based QUBO-Formulated Hamiltonian-Inspired Loss Function for Combinatorial Optimization using Reinforcement Learning
• Authors: Redwan Ahmed Rizvee, Raheeb Hasan and Md. Mosaddek Khan
• Abstract summary: We introduce a novel Monty Carlo Tree Search-based strategy with Graph Neural Network (GNN) We identify a behavioral pattern related to PI-GNN and devise strategies to improve its performance. We also focus on creating a bridge between the RL-based solutions and the QUBO-formulated Hamiltonian.
• Score: 1.325953054381901
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quadratic Unconstrained Binary Optimization (QUBO) is a generic technique to model various NP-hard Combinatorial Optimization problems (CO) in the form of binary variables. Ising Hamiltonian is used to model the energy function of a system. QUBO to Ising Hamiltonian is regarded as a technique to solve various canonical optimization problems through quantum optimization algorithms. Recently, PI-GNN, a generic framework, has been proposed to address CO problems over graphs based on Graph Neural Network (GNN) architecture. They introduced a generic QUBO-formulated Hamiltonian-inspired loss function that was directly optimized using GNN. PI-GNN is highly scalable but there lies a noticeable decrease in the number of satisfied constraints when compared to problem-specific algorithms and becomes more pronounced with increased graph densities. Here, We identify a behavioral pattern related to it and devise strategies to improve its performance. Another group of literature uses Reinforcement learning (RL) to solve the aforementioned NP-hard problems using problem-specific reward functions. In this work, we also focus on creating a bridge between the RL-based solutions and the QUBO-formulated Hamiltonian. We formulate and empirically evaluate the compatibility of the QUBO-formulated Hamiltonian as the generic reward function in the RL-based paradigm in the form of rewards. Furthermore, we also introduce a novel Monty Carlo Tree Search-based strategy with GNN where we apply a guided search through manual perturbation of node labels during training. We empirically evaluated our methods and observed up to 44% improvement in the number of constraint violations compared to the PI-GNN.

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