Abstract
This paper describes a Diversification-Driven Tabu Search (D2TS) algorithm for solving unconstrained binary quadratic problems. D2TS is distinguished by the introduction of a perturbation-based diversification strategy guided by long-term memory. The performance of the proposed algorithm is assessed on the largest instances from the ORLIB library (up to 2500 variables) as well as still larger instances from the literature (up to 7000 variables). The computational results show that D2TS is highly competitive in terms of both solution quality and computational efficiency relative to some of the best performing heuristics in the literature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alidaee B, Kochenberger GA, Ahmadian A (1994) 0–1 quadratic programming approach for the optimal solution of two scheduling problems. Int J Syst Sci 25: 401–408
Alidaee B, Kochenberger GA, Lewis K, Lewis M, Wang H (2008) A new approach for modeling and solving set packing problems. Eur J Oper Res 86(2): 504–512
Alkhamis TM, Hasan M, Ahmed MA (1998) Simulated annealing for the unconstrained binary quadratic pseudo-boolean function. Eur J Oper Res 108: 641–652
Amini M, Alidaee B, Kochenberger GA (1999) A scatter search approach to unconstrained quadratic binary programs. McGraw-Hill, New York, pp 317–330. New Methods in Optimization
Beasley JE (1996) Obtaining test problems via internet. J Glob Optim 8: 429–433
Beasley JE (1998) Heuristic algorithms for the unconstrained binary quadratic programming problem. Working Paper, The Management School, Imperial College, London, England
Borgulya I (2005) An evolutionary algorithm for the binary quadratic problems. Adv Soft Comput 2: 3–16
Boros E, Hammer PL, Tavares G (2007) Local search heuristics for quadratic unconstrained binary optimization (QUBO). J Heuristics 13: 99–132
Chardaire P, Sutter A (1994) A decomposition method for quadratic zero-one programming. Manage Sci 41(4): 704–712
Gallo G, Hammer P, Simeone B (1980) Quadratic knapsack problems. Math Programm 12: 132–149
Glover F, Hao JK (2009a) Efficient evaluations for solving large 0-1 unconstrained quadratic optimization problems. To appear in Int J Metaheuristics, 1(1)
Glover F, Hao JK (2009b) Fast 2-flip move evaluations for binary unconstrained quadratic optimization problems. To appear in Int J Metaheuristics
Glover F, Laguna M (1997) Tabu search. Kluwer, Boston
Glover F, Kochenberger GA, Alidaee B (1998) Adaptive memory tabu search for binary quadratic programs. Manag Sci 44: 336–345
Harary F (1953) On the notion of balanced of a signed graph. Mich Math J 2: 143–146
Katayama K, Narihisa H (2001) Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem. Eur J Oper Res 134: 103–119
Katayama K, Tani M, Narihisa H (2000) Solving large binary quadratic programming problems by an effective genetic local search algorithm. In: Proceedings of the genetic and evolutionary computation conference (GECCO’00). Morgan Kaufmann, pp 643–650
Kochenberger GA, Glover F, Alidaee B, Rego C (2004) A unified modeling and solution framework for combinatorial optimization problems. OR Spectrum 26: 237–250
Kochenberger GA, Glover F, Alidaee B, Rego C (2005) An unconstrained quadratic binary programming approach to the vertex coloring problem. Ann Oper Res 139: 229–241
Krarup J, Pruzan A (1978) Computer aided layout design. Math Programm Study 9: 75–94
Laughunn DJ (1970) Quadratic binary programming. Oper Res 14: 454–461
Lewis M, Kochenberger GA, Alidaee B (2008) A new modeling and solution approach for the set-partitioning problem. Comput Oper Res 35(3): 807–813
Lodi A, Allemand K, Liebling TM (1999) An evolutionary heuristic for quadratic 0-1 programming. Eur J Oper Res 119(3): 662–670
Lü Z, Hao JK (2009) A critical element-guided perturbation strategy for iterated local search. In: Cotta C, Cowling P (eds) Ninth European conference on evolutionary computation in combinatorial optimization (EvoCop 2009). Springer, LNCS 5482, pp 1–12
McBride RD, Yormark JS (1980) An implicit enumeration algorithm for quadratic integer programming. Manag Sci 26: 282–296
Merz P, Freisleben B (1999) Genetic algorithms for binary quadratic programming. In: Proceedings of the genetic and evolutionary computation conference (GECCO’99). Morgan Kaufmann, pp 417–424
Merz P, Freisleben B (2002) Greedy and local search heuristics for unconstrained binary quadratic programming. J Heuristics 8: 197–213
Merz P, Katayama K (2004) Memetic algorithms for the unconstrained binary quadratic programming problem. BioSystems 78: 99–118
Palubeckis G (2004) Multistart tabu search strategies for the unconstrained binary quadratic optimization problem. Ann Oper Res 131: 259–282
Palubeckis G (2006) Iterated tabu search for the unconstrained binary quadratic optimization problem. Informatica 17(2): 279–296
Pardalos P, Rodgers GP (1990) Computational aspects of a branch and bound algorithm for quadratic zero-one programming. Computing 45: 131–144
Pardalos P, Xue J (1994) The maximum clique problem. J Glob Optim 4: 301–328
Phillips AT, Rosen JB (1994) A quadratic assignment formulation of the molecular conformation problem. J Glob Optim 4: 229–241
Witsgall C (1975) Mathematical methods of site selection for electronic system (ems). NBS Internal Report
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Glover, F., Lü, Z. & Hao, JK. Diversification-driven tabu search for unconstrained binary quadratic problems. 4OR-Q J Oper Res 8, 239–253 (2010). https://doi.org/10.1007/s10288-009-0115-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10288-009-0115-y