Quadratic unconstrained binary optimization problem preprocessing: Theory and empirical analysis

The Quadratic Unconstrained Binary Optimization problem (QUBO) has become a unifying model for representing a wide range of combinatorial optimization problems, and for linking a variety of disciplines that face these problems. A new class of quantum annealing computer that maps QUBO onto a physical...

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Bibliographic Details
Published in:Networks Vol. 70; no. 2; pp. 79 - 97
Main Authors: Lewis, Mark, Glover, Fred
Format: Journal Article
Language:English
Published: New York Wiley Subscription Services, Inc 01.09.2017
Subjects:
binary quadratic optimization
Combinatorial analysis
Empirical analysis
Graph theory
Heuristic methods
Ising model
network reduction
Optimization
Preprocessing
quadratic unconstrained binary optimization
quantum annealing
Reduction
Tabu search
ISSN:0028-3045, 1097-0037
Online Access:Get full text
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Summary:The Quadratic Unconstrained Binary Optimization problem (QUBO) has become a unifying model for representing a wide range of combinatorial optimization problems, and for linking a variety of disciplines that face these problems. A new class of quantum annealing computer that maps QUBO onto a physical qubit network structure with specific size and edge density restrictions is generating a growing interest in ways to transform the underlying QUBO structure into an equivalent graph having fewer nodes and edges. In this article, we present rules for reducing the size of the QUBO matrix by identifying variables whose value at optimality can be predetermined. We verify that the reductions improve both solution quality and time to solution and, in the case of metaheuristic methods where optimal solutions cannot be guaranteed, the quality of solutions obtained within reasonable time limits. We discuss the general QUBO structural characteristics that can take advantage of these reduction techniques and perform careful experimental design and analysis to identify and quantify the specific characteristics most affecting reduction. The rules make it possible to dramatically improve solution times on a new set of problems using both the exact Cplex solver and a tabu search metaheuristic. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(2), 79–97 2017
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ISSN:0028-3045
1097-0037
DOI:10.1002/net.21751