Quadratic Unconstrained Binary Optimization Problem Preprocessing: Theory and Empirical Analysis
This work addresses preprocessing for QUBO problems, which is crucial for quantum annealing and classical solvers, but it is incremental as it builds on existing reduction techniques.
The paper tackles the problem of reducing the size of Quadratic Unconstrained Binary Optimization (QUBO) matrices by identifying variables that can be predetermined at optimality, resulting in improved solution quality and time, with dramatic improvements in solution times using exact and metaheuristic methods.
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 paper 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.