Reinforcement Learning-Based Formulations With Hamiltonian-Inspired Loss Functions for Combinatorial Optimization Over Graphs

Quadratic Unconstrained Binary Optimization (QUBO) is a versatile approach used to represent a wide range of NP-hard Combinatorial Optimization (CO) problems through binary variables. The transformation of QUBO to an Ising Hamiltonian is recognized as an effective method for solving key optimization...

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Main Authors: Redwan Ahmed Rizvee, Raheeb Hassan, Md. Mosaddek Khan
Format: Article
Language:English
Published: IEEE 2024-01-01
Series:IEEE Access
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Online Access:https://ieeexplore.ieee.org/document/10752916/
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author Redwan Ahmed Rizvee
Raheeb Hassan
Md. Mosaddek Khan
author_facet Redwan Ahmed Rizvee
Raheeb Hassan
Md. Mosaddek Khan
author_sort Redwan Ahmed Rizvee
collection DOAJ
description Quadratic Unconstrained Binary Optimization (QUBO) is a versatile approach used to represent a wide range of NP-hard Combinatorial Optimization (CO) problems through binary variables. The transformation of QUBO to an Ising Hamiltonian is recognized as an effective method for solving key optimization problems using quantum algorithms. Recently, PI-GNN, a generic framework, has been proposed to address CO problems over graphs based on QUBO with Hamiltonian loss function to train the underlying GNN architecture. Though PI-GNN is highly scalable, it exhibits a noticeable decrease in terms of the number of satisfied constraints with higher graph densities. In this paper, firstly, we identify the limitations and empirically present our strategy to improve PI-GNN&#x2019;s performance. Secondly, we formulate and evaluate two strategies to integrate QUBO-Hamiltonian as the generic loss function in Reinforcement learning-based (RL) frameworks. The major contribution of our work lies in understanding the feasibility and quality of the QUBO-based generic reward function in an unsupervised RL setup in addressing graph-based CO problems. Empirically, through our empirical evaluation (Our implementation can be found in <uri>https://tinyurl.com/5apnymz7</uri>), we have observed up to 44% improvement in terms of the number of satisfied constraints over PI-GNN in a representative Max-Cut problem.
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spelling doaj-art-4a5f6a7a3da242a5b01c397b21975fe72025-08-20T02:01:57ZengIEEEIEEE Access2169-35362024-01-011217105517106510.1109/ACCESS.2024.349795510752916Reinforcement Learning-Based Formulations With Hamiltonian-Inspired Loss Functions for Combinatorial Optimization Over GraphsRedwan Ahmed Rizvee0https://orcid.org/0000-0001-5056-1701Raheeb Hassan1https://orcid.org/0009-0003-2074-1113Md. Mosaddek Khan2https://orcid.org/0000-0002-7871-7111Department of Computer Science and Engineering, University of Dhaka, Dhaka, BangladeshDepartment of Computer Science and Engineering, University of Dhaka, Dhaka, BangladeshDepartment of Computer Science and Engineering, University of Dhaka, Dhaka, BangladeshQuadratic Unconstrained Binary Optimization (QUBO) is a versatile approach used to represent a wide range of NP-hard Combinatorial Optimization (CO) problems through binary variables. The transformation of QUBO to an Ising Hamiltonian is recognized as an effective method for solving key optimization problems using quantum algorithms. Recently, PI-GNN, a generic framework, has been proposed to address CO problems over graphs based on QUBO with Hamiltonian loss function to train the underlying GNN architecture. Though PI-GNN is highly scalable, it exhibits a noticeable decrease in terms of the number of satisfied constraints with higher graph densities. In this paper, firstly, we identify the limitations and empirically present our strategy to improve PI-GNN&#x2019;s performance. Secondly, we formulate and evaluate two strategies to integrate QUBO-Hamiltonian as the generic loss function in Reinforcement learning-based (RL) frameworks. The major contribution of our work lies in understanding the feasibility and quality of the QUBO-based generic reward function in an unsupervised RL setup in addressing graph-based CO problems. Empirically, through our empirical evaluation (Our implementation can be found in <uri>https://tinyurl.com/5apnymz7</uri>), we have observed up to 44% improvement in terms of the number of satisfied constraints over PI-GNN in a representative Max-Cut problem.https://ieeexplore.ieee.org/document/10752916/Deep reinforcement learninggraph neural networkHamiltonian functionMonte Carlo tree search
spellingShingle Redwan Ahmed Rizvee
Raheeb Hassan
Md. Mosaddek Khan
Reinforcement Learning-Based Formulations With Hamiltonian-Inspired Loss Functions for Combinatorial Optimization Over Graphs
IEEE Access
Deep reinforcement learning
graph neural network
Hamiltonian function
Monte Carlo tree search
title Reinforcement Learning-Based Formulations With Hamiltonian-Inspired Loss Functions for Combinatorial Optimization Over Graphs
title_full Reinforcement Learning-Based Formulations With Hamiltonian-Inspired Loss Functions for Combinatorial Optimization Over Graphs
title_fullStr Reinforcement Learning-Based Formulations With Hamiltonian-Inspired Loss Functions for Combinatorial Optimization Over Graphs
title_full_unstemmed Reinforcement Learning-Based Formulations With Hamiltonian-Inspired Loss Functions for Combinatorial Optimization Over Graphs
title_short Reinforcement Learning-Based Formulations With Hamiltonian-Inspired Loss Functions for Combinatorial Optimization Over Graphs
title_sort reinforcement learning based formulations with hamiltonian inspired loss functions for combinatorial optimization over graphs
topic Deep reinforcement learning
graph neural network
Hamiltonian function
Monte Carlo tree search
url https://ieeexplore.ieee.org/document/10752916/
work_keys_str_mv AT redwanahmedrizvee reinforcementlearningbasedformulationswithhamiltonianinspiredlossfunctionsforcombinatorialoptimizationovergraphs
AT raheebhassan reinforcementlearningbasedformulationswithhamiltonianinspiredlossfunctionsforcombinatorialoptimizationovergraphs
AT mdmosaddekkhan reinforcementlearningbasedformulationswithhamiltonianinspiredlossfunctionsforcombinatorialoptimizationovergraphs