A Hybrid Framework Using a QUBO Solver For Permutation-Based Combinatorial Optimization

• URL: http://arxiv.org/abs/2009.12767v2
• Date: Tue, 6 Jul 2021 13:55:43 GMT
• Title: A Hybrid Framework Using a QUBO Solver For Permutation-Based Combinatorial Optimization
• Authors: Siong Thye Goh, Sabrish Gopalakrishnan, Jianyuan Bo, Hoong Chuin Lau
• Abstract summary: We propose a hybrid framework to solve large-scale permutation-based problems using a high-performance quadratic unconstrained binary optimization solver. We propose techniques to overcome the challenges in using a QUBO solver that typically comes with limited numbers of bits.
• Score: 5.460573052311485
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose a hybrid framework to solve large-scale permutation-based combinatorial problems effectively using a high-performance quadratic unconstrained binary optimization (QUBO) solver. To do so, transformations are required to change a constrained optimization model to an unconstrained model that involves parameter tuning. We propose techniques to overcome the challenges in using a QUBO solver that typically comes with limited numbers of bits. First, to smooth the energy landscape, we reduce the magnitudes of the input without compromising optimality. We propose a machine learning approach to tune the parameters for good performance effectively. To handle possible infeasibility, we introduce a polynomial-time projection algorithm. Finally, to solve large-scale problems, we introduce a divide-and-conquer approach that calls the QUBO solver repeatedly on small sub-problems. We tested our approach on provably hard Euclidean Traveling Salesman (E-TSP) instances and Flow Shop Problem (FSP). Optimality gap that is less than $10\%$ and $11\%$ are obtained respectively compared to the best-known approach.

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