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European Journal of Operational Research

Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem

Kengo Katayama, Hiroyuki Narihisa

Published Oct 1, 2001• 100 citations
Publisher
DOI
10.1016/s0377-2217(00)00242-3

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In this paper we consider the unconstrained binary quadratic programming problem. This is the problem of maximising a quadratic objective by suitable choice of binary (zero-one) variables. We present two heuristic algorithms based upon tabu search and simulated annealing for this problem. Computational results are presented for a number of publically available data sets involving up to 2500 variables. An interesting feature of our results is that whilst for most problems tabu search dominates simulated annealing for the very largest problems we consider the converse is true. This paper typifies a "multiple solution technique, single paper" approach, i.e. an approach that within the same paper presents results for a number of different heuristics applied to the same problem. Issues relating to algorithmic design for such papers are discussed. Keywords: unconstrained binary (zero-one) quadratic programming
Recently, inspired by quantum annealing, many solvers specialized for unconstrained binary quadratic programming problems have been developed. For further improvement and application of these solvers, it is important to clarify the differences in their performance for various types of problems. In this study, the performance of four quadratic unconstrained binary optimization problem solvers, namely D-Wave Hybrid Solver Service (HSS), Toshiba Simulated Bifurcation Machine (SBM), Fujitsu Digital Annealer (DA), and simulated annealing on a personal computer, was benchmarked. The problems used for benchmarking were instances of real problems in MQLib, instances of the SAT-UNSAT phase transition point of random not-all-equal 3-SAT (NAE 3-SAT), and the Ising spin glass Sherrington-Kirkpatrick (SK) model. Concerning MQLib instances, the HSS performance ranked first; for NAE 3-SAT, DA performance ranked first; and regarding the SK model, SBM performance ranked first. These results may help understand the strengths and weaknesses of these solvers.