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Journal of Heuristics

Data structures for speeding up Tabu Search when solving sparse quadratic unconstrained binary optimization problems

Ricardo Nantes Liang, Eduardo A.J. Anacleto, Cláudio N. Meneses

Published Apr 27, 2022• 4 citations
Publisher
DOI
10.1007/s10732-022-09498-0

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Abstract Tabu Search is a promising approach for solving quadratic unconstrained binary optimization (QUBO) problems. A key parameter in Tabu Search is tabu tenure, which governs the balance between intensification and diversification in the search process. In this work, we aim to develop a systematic method for determining the effective tabu tenure tailored to each QUBO instance, thereby enhancing overall solver performance. To achieve this, we focus on the statistics obtained during the search, which we term “trajectory metrics.” We consolidate existing trajectory metrics from the literature with newly proposed ones and analyze their responses to variations in tabu tenure using three criteria: suitability for tuning, noise robustness, and classification potential. Based on this analysis, we introduce a method for determining the effective tabu tenure and evaluate its performance across several problem instances. Experimental results demonstrate that the proposed approach improves solving performance compared to a well-known standard Tabu Search-based method.
Tabu search is one of the promising solving methods for quadratic unconstrained binary problem (QUBO). A critical parameter of tabu search is tabu tenure, which balances the behavior of the solver between greedy and exploratory. Our goal is to establish a way to find out tabu tenure suitable for each problem instance in QUBO formulation and utilize it to enhance solver performance. In order to achieve the goal, we proposed a new metric unique move, which is a number of unique decision variables changed, and studied its behavior in several problem instances in QUBO formulation. Based on the study, our proposed method named A3TUM was designed to take a suitable sub-method for each problem instance by classifying problems into typical patterns based on the behavior of unique move. Experimental result shows the effectiveness of the method both in estimation accuracy of tabu tenure and in solving performance compared to a robust tabu search based method as a baseline.