Publication Type

Working Paper

Version

publishedVersion

Publication Date

9-2020

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.

Keywords

Machine learning, quadratic unconstrained binary optimization solver, large-scale permutation-based combinatorial problems, MITB student

Discipline

Numerical Analysis and Scientific Computing | Operations Research, Systems Engineering and Industrial Engineering | Theory and Algorithms

Research Areas

Intelligent Systems and Optimization

First Page

1

Last Page

28

Embargo Period

6-2-2021

Copyright Owner and License

Authors

Additional URL

https://arxiv.org/abs/2009.12767

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