A hybrid framework using a QUBO solver for permutation-based combinatorial optimization

• Main Authors: GOH, Siong Thye, GOPALAKRISHNAN, Sabrish, BO, Jianyuan, LAU, Hoong Chuin
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2020
• Subjects: Machine learning; quadratic unconstrained binary optimization solver; large-scale permutation-based combinatorial problems; MITB student; Numerical Analysis and Scientific Computing; Operations Research, Systems Engineering and Industrial Engineering; Theory and Algorithms
• Online Access: https://ink.library.smu.edu.sg/sis_research/5978; https://ink.library.smu.edu.sg/context/sis_research/article/6981/viewcontent/Goh__S._T.__Gopalakrishnan__S.__Bo__J.____Lau__H._C.__2020_._A_Hybrid_Framework_Using_a_QUBO_Solver_For_Permutation_Based_Combinatorial_Optimization.pdf
• Institution: Singapore Management University

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.