Abstract
This paper introduces MADEB, a Memetic Algebraic Differential Evolution algorithm for the Binary search space. MADEB has been applied to the Multidimensional Two-Way Number Partitioning Problem (MDTWNPP) and its main components are the binary differential mutation operator and a variable neighborhood descent procedure. The binary differential mutation is a concrete application of the abstract algebraic framework for the binary search space. The variable neighborhood descent is a local search procedure specifically designed for MDTWNPP. Experiments have been held on a widely accepted benchmark suite and MADEB is experimentally compared with respect to the current state-of-the-art algorithms for MDTWNPP. The experimental results clearly show that MADEB is the new state-of-the-art algorithm in the problem here investigated.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
For this reason, \(|F \odot x|\) cannot be larger than n, thus we truncate F to \(F^{(x)}_\mathrm {max} = \frac{n}{|x|}\) whenever \(F>F^{(x)}_\mathrm {max}\).
References
Santucci, V., Baioletti, M., Milani, A.: Algebraic differential evolution algorithm for the permutation flowshop scheduling problem with total flowtime criterion. IEEE Trans. Evol. Comput. 20(5), 682–694 (2016). https://doi.org/10.1109/TEVC.2015.2507785
Kojić, J.: Integer linear programming model for multidimensional two-waynumber partitioning problem. Comput. Math. Appl. 60(8), 2302–2308 (2010). http://www.sciencedirect.com/science/article/pii/S0898122110005882
Mertens, S.: The easiest hard problem: number partitioning. Comput. Complex. Stat. Phys. 125(2), 125–139 (2006)
Corus, D., Oliveto, P.S., Yazdani, D.: Artificial immune systems can find arbitrarily good approximations for the NP-hard partition problem. In: Proceedings of 15th International Conference on Parallel Problem Solving from Nature-PPSN XV - Part II, pp. 16–28 (2018)
Rodriguez, F.J., Glover, F., García-Martínez, C., Martí, R., Lozano, M.: Grasp with exterior path-relinking and restricted local search for the multidimensional two-way number partitioning problem. Comput. Oper. Res. 78, 243–254 (2017). http://www.sciencedirect.com/science/article/pii/S0305054816302209
Pop, P.C., Matei, O.: A memetic algorithm approach for solving the multidimensional multi-way number partitioning problem. Appl. Math. Model. 37(22), 9191–9202 (2013). http://www.sciencedirect.com/science/article/pii/S0307904X13002692
Kratica, J., Kojić, J., Savić, A.: Two metaheuristic approaches for solving multidimensional two-way number partitioning problem. Comput. Oper. Res. 46, 59–68 (2014). http://www.sciencedirect.com/science/article/pii/S0305054814000045
Santucci, V., Baioletti, M., Milani, A.: A differential evolution algorithm for the permutation flowshop scheduling problem with total flow time criterion. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds.) PPSN 2014. LNCS, vol. 8672, pp. 161–170. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10762-2_16
Santucci, V., Baioletti, M., Milani, A.: Solving permutation flowshop scheduling problems with a discrete differential evolution algorithm. AI Commun. 29(2), 269–286 (2016). https://doi.org/10.3233/AIC-150695
Santucci, V., Baioletti, M., Milani, A.: An algebraic differential evolution for the linear ordering problem. In: Companion Material Proceedings of Genetic and Evolutionary Computation Conference, GECCO 2015, pp. 1479–1480 (2015). https://doi.org/10.1145/2739482.2764693
Baioletti, M., Milani, A., Santucci, V.: Linear ordering optimization with a combinatorial differential evolution. In: Proceedings of 2015 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2015, pp. 2135–2140 (2015). https://doi.org/10.1109/SMC.2015.373
Baioletti, M., Milani, A., Santucci, V.: An extension of algebraic differential evolution for the linear ordering problem with cumulative costs. In: Handl, J., Hart, E., Lewis, P.R., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds.) PPSN 2016. LNCS, vol. 9921, pp. 123–133. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45823-6_12
Baioletti, M., Milani, A., Santucci, V.: MOEA/DEP: an algebraic decomposition-based evolutionary algorithm for the multiobjective permutation flowshop scheduling problem. In: Liefooghe, A., López-Ibáñez, M. (eds.) EvoCOP 2018. LNCS, vol. 10782, pp. 132–145. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-77449-7_9
Baioletti, M., Milani, A., Santucci, V.: Learning Bayesian networks with algebraic differential evolution. In: Auger, A., Fonseca, C.M., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds.) PPSN 2018. LNCS, vol. 11102, pp. 436–448. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99259-4_35
Wang, L., Fu, X., Mao, Y., Menhas, M.I., Fei, M.: A novel modified binary differential evolution algorithm and its applications. Neurocomputing 98, 55–75 (2012). http://www.sciencedirect.com/science/article/pii/S0925231212004316
Pampara, G., Engelbrecht, A.P., Franken, N.: Binary differential evolution. In: 2006 IEEE International Conference on Evolutionary Computation, pp. 1873–1879, July 2006
Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341–359 (1997). https://doi.org/10.1023/A:1008202821328
Milani, A., Santucci, V.: Asynchronous differential evolution. In: 2010 IEEE Congress on Evolutionary Computation (CEC 2010), pp. 1–7 (2010). https://doi.org/10.1109/CEC.2010.5586107
Price, K., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-31306-0
Das, S., Suganthan, P.N.: Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evol. Comput. 15(1), 4–31 (2011)
Das, S., Mullick, S.S., Suganthan, P.: Recent advances in differential evolution-an updated survey. Swarm Evol. Comput. 27, 1–30 (2016). http://www.sciencedirect.com/science/article/pii/S2210650216000146
Brest, J., Greiner, S., Boskovic, B., Mernik, M., Zumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10(6), 646–657 (2006)
Pavai, G., Geetha, T.V.: A survey on crossover operators. ACM Comput. Surv. 49(4), 1–43 (2016). http://doi.acm.org/10.1145/3009966
Derrac, J., García, S., Molina, D., Herrera, F.: A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol. Comput. 1(1), 3–18 (2011). http://www.sciencedirect.com/science/article/pii/S2210650211000034
Ceberio, J., Irurozki, E., Mendiburu, A., Lozano, J.A.: A distance-based ranking model estimation of distribution algorithm for the flowshop scheduling problem. IEEE Trans. Evol. Comput. 18(2), 286–300 (2014)
Baioletti, M., Milani, A., Santucci, V.: Algebraic particle swarm optimization for the permutations search space. In: Proceedings of 2017 IEEE Congress on Evolutionary Computation (CEC 2017), pp. 1587–1594 (2017). https://doi.org/10.1109/CEC.2017.7969492
Baioletti, M., Milani, A., Santucci, V.: Automatic algebraic evolutionary algorithms. In: Pelillo, M., Poli, I., Roli, A., Serra, R., Slanzi, D., Villani, M. (eds.) WIVACE 2017. CCIS, vol. 830, pp. 271–283. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78658-2_20
Baioletti, M., Milani, A., Santucci, V.: Algebraic crossover operators for permutations. In: 2018 IEEE Congress on Evolutionary Computation (CEC 2018), pp. 1–8 (2018). https://doi.org/10.1109/CEC.2018.8477867
Santucci, V., Milani, A.: Particle swarm optimization in the EDAs framework. In: Gaspar-Cunha, A., Takahashi, R., Schaefer, G., Costa, L. (eds.) Soft Computing in Industrial Applications. Advances in Intelligent and Soft Computing, vol. 96, pp. 87–96. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20505-7_7
Acknowledgement
The research described in this work has been partially supported by: the research grant “Fondi per i progetti di ricerca scientifica di Ateneo 2019” of the University for Foreigners of Perugia under the project “Algoritmi evolutivi per problemi di ottimizzazione e modelli di apprendimento automatico con applicazioni al Natural Language Processing”; and by RCB-2015 Project “Algoritmi Randomizzati per l’Ottimizzazione e la Navigazione di Reti Semantiche” and RCB-2015 Project “Algoritmi evolutivi per problemi di ottimizzazione combinatorica” of Department of Mathematics and Computer Science of University of Perugia.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Santucci, V., Baioletti, M., Di Bari, G., Milani, A. (2019). A Binary Algebraic Differential Evolution for the MultiDimensional Two-Way Number Partitioning Problem. In: Liefooghe, A., Paquete, L. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2019. Lecture Notes in Computer Science(), vol 11452. Springer, Cham. https://doi.org/10.1007/978-3-030-16711-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-16711-0_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-16710-3
Online ISBN: 978-3-030-16711-0
eBook Packages: Computer ScienceComputer Science (R0)