Abstract
The bandwidth minimization problem is a well-known \(\mathcal {NP}\)-hard problem. This paper describes our experience in implementing a biased random-key genetic algorithm for the bandwidth reduction problem. Specifically, this paper compares the results of the new algorithm with the results yielded by four approaches. The results obtained on a set of standard benchmark matrices taken from the SuiteSparse sparse matrix collection indicated that the novel approach did not compare favorably with the state-of-the-art metaheuristic algorithm for bandwidth reduction. The former seems to be faster than the latter. On the other hand, the design of heuristics for bandwidth reduction is a very consolidated research area. Thus, a paradigm shift seems necessary to design a heuristic with better results than the state-of-the-art meta-heuristic algorithm at shorter execution times.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Papadimitriou, C.H.: The NP-completeness of bandwidth minimization problem. Comput. J. 16, 177–192 (1976)
Gonzaga de Oliveira, S.L., Chagas, G.O.: A systematic review of heuristics for symmetric-matrix bandwidth reduction: methods not based on metaheuristics. In: The XLVII Brazilian Symposium of Operational Research (SBPO), Ipojuca-PE, Brazil, Sobrapo, August 2015
George, A., Liu, J.W.: Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall, Englewood Cliffs (1981)
Gonzaga de Oliveira, S.L., Bernardes, J.A.B., Chagas, G.O.: An evaluation of low-cost heuristics for matrix bandwidth and profile reductions. Comput. Appl. Math. 37(2), 1412–1471 (2016). https://doi.org/10.1007/s40314-016-0394-9
Gonzaga de Oliveira, S.L., Abreu, A.A.A.M.: An evaluation of pseudoperipheral vertex finders for the reverse Cuthill-Mckee method for bandwidth and profile reductions of symmetric matrices. In: Proceedings of the 37th International Conference of the Chilean Computer Science Society (SCCC), Santiago, Chile, November 2018, pp. 1–9. IEEE (2018). https://doi.org/10.1109/SCCC.2018.8705263
Gonzaga de Oliveira, S. L., Silva, L.M.: Evolving reordering algorithms using an ant colony hyperheuristic approach for accelerating the convergence of the ICCG method. Eng. Comput. (2019). https://doi.org/10.1007/s00366-019-00801-5)
Gonzaga de Oliveira, S., Silva, L.: An ant colony hyperheuristic approach for matrix bandwidth reduction. Appl. Soft Comput. 94, 106434 (2020)
Gilbert, J.R., Moler, C., Schreiber, R.: Sparse matrices in MATLAB: design and implementation. SIAM J. Matrix Anal. 3(1), 333–356 (1992)
The MathWorks Inc.: MATLAB (1994–2018). http://www.mathworks.com/products/matlab/
Eaton, J.W., Bateman, D., Hauberg, S., Wehbring, R.: GNU Octave version 4.0.0 manual: a high-level interactive language for numerical computations (2015)
Boost: Boost C++ libraries (2017). http://www.boost.org/. Accessed 28 Jun 2017
Chagas, G.O., Gonzaga de Oliveira, S.L.: Metaheuristic-based heuristics for symmetric-matrix bandwidth reduction: a systematic review. Procedia Comput. Sci. 51, 211–220 (2015)
Martí, R., Laguna, M., Glover, F., Campos, V.: Reducing the bandwidth of a sparse matrix with tabu search. Eur. J. Oper. Res. 135(2), 450–459 (2001)
Campos, V., Piñana, E., Martí, R.: Adaptive memory programming for matrix bandwidth minimization. Ann. Oper. Res. 183, 7–23 (2011)
Piñana, E., Plana, I., Campos, V., Martí, R.: GRASP and path relinking for the matrix bandwidth minimization. Eur. J. Oper. Res. 153(1), 200–210 (2004)
Lim, A., Rodrigues, B., Xiao, F.: Heuristics for matrix bandwidth reduction. Eur. J. Oper. Res. 174(1), 69–91 (2006)
Czibula, G., Crişan, G.C., Pintea, C.M., Czibula, I.G.: Soft computing approaches on the bandwidth problem. Informatica 24(2), 169–180 (2013)
Lim, A., Lin, J., Rodrigues, B., Xiao, F.: Ant colony optimization with hill climbing for the bandwidth minimization problem. Appl. Soft Comput. 6(2), 180–188 (2006)
Kaveh, A., Sharafi, P.: Nodal ordering for bandwidth reduction using ant system algorithm. Eng. Comput. 26, 313–323 (2009)
Pintea, C.-M., Crişan, G.-C., Chira, C.: A hybrid ACO approach to the matrix bandwidth minimization problem. In: Graña Romay, M., Corchado, E., Garcia Sebastian, M.T. (eds.) HAIS 2010. LNCS (LNAI), vol. 6076, pp. 405–412. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13769-3_49
Pintea, C.M., Crişan, G.C., Shira, C.: Hybrid ant models with a transition policy for solving a complex problem. Logic J. IGPL 20(3), 560–569 (2012)
Lim, A., Lin, J., Xiao, F.: Particle swarm optimization and hill climbing for the bandwidth minimization problem. Appl. Intell. 3(26), 175–182 (2007)
Rodriguez-Tello, E., Jin-Kao, H., Torres-Jimenez, J.: An improved simulated annealing algorithm for bandwidth minimization. Eur. J. Oper. Res. 185, 1319–1335 (2008)
Torres-Jimenez, J., Izquierdo-Marquez, I., Garcia-Robledo, A., Gonzalez-Gomez, A., Bernal, J., Kacker, R.N.: A dual representation simulated annealing algorithm for the bandwidth minimization problem on graphs. Inf. Sci. 303, 33–49 (2015)
Mladenovic, N., Urosevic, D., Pérez-Brito, D., García-González, C.G.: Variable neighbourhood search for bandwidth reduction. Eur. J. Oper. Res. 1(200), 14–27 (2010)
Koohestani, B., Poli, R.: A hyper-heuristic approach to evolving algorithms for bandwidth reduction based on genetic programming. In: Bramer, M., Petridis, M., Nolle, L. (eds.) Research and Development in Intelligent Systems XXVIII, pp. 93–106. Springer, London (2011). https://doi.org/10.1007/978-1-4471-2318-7_7
Pop, P.C., Matei, O.: An improved heuristic for the bandwidth minimization based on genetic programming. In: Corchado, E., Kurzyński, M., Woźniak, M. (eds.) HAIS 2011. LNCS (LNAI), vol. 6679, pp. 67–74. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21222-2_9
Pop, P., Matei, O., Comes, C.A.: Reducing the bandwidth of a sparse matrix with a genetic algorithm. Optim. J. Math. Prog. Oper. Res. 63(12), 1851–1876 (2013)
Gonzaga de Oliveira, S.L., de Abreu, A.A.A.M., Robaina, D., Kischinhevsky, M.: A new heuristic for bandwidth and profile reductions of matrices using a self-organizing map. In: Gervasi, O., et al. (eds.) ICCSA 2016. LNCS, vol. 9786, pp. 54–70. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-42085-1_5
Gonzaga de Oliveira, S.L., Abreu, A.A.A.M., Robaina, D.T., Kischnhevsky, M.: An evaluation of four reordering algorithms to reduce the computational cost of the Jacobi-preconditioned conjugate gradient method using high-precision arithmetic. Int. J. Bus. Intell. Data Min. 12(2), 190–209 (2017)
Ericsson, M., Resende, M.G.C., Pardalos, P.M.: A genetic algorithm for the weight setting problem in OSPF routing. J. Comb. Optim. 6, 299–333 (2002)
Gonçalves, J.F., Resende, M.G.C.: An evolutionary algorithm for manufacturing cell formation. Comput. Ind. Eng. 47, 247–273 (2004)
Resende, M.G.C.: Biased random-key genetic algorithms with applications in telecommunications. TOP 20, 130–153 (2012)
Gonçalves, J.F., Resende, M.G.C.: Biased random-key genetic algorithms for combinatorial optimization. J. Heuristics 17, 487–525 (2011)
Bean, J.C.: Genetic algorithms and random keys for sequencing and optimization. ORSA J. Comput. 6, 154–160 (1994)
Toso, R.F., Resende, M.G.C.: A C++ application programming interface for biased random-key genetic algorithms. Optim. Methods Softw. 30, 81–93 (2015)
Spears, W.M., De Jong, K.D.: On the virtues of parameterized uniform crossover. Technical report, DTIC Document (1995)
Davis, T.A., Hu, Y.: The University of Florida sparse matrix collection. ACM Trans. Math. Softw. 38(1), 1–25 (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Silva, P.H.G., Brandão, D.N., Morais, I.S., de Oliveira, S.L.G. (2020). A Biased Random-Key Genetic Algorithm for Bandwidth Reduction. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science(), vol 12249. Springer, Cham. https://doi.org/10.1007/978-3-030-58799-4_23
Download citation
DOI: https://doi.org/10.1007/978-3-030-58799-4_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-58798-7
Online ISBN: 978-3-030-58799-4
eBook Packages: Computer ScienceComputer Science (R0)