Abstract
In this paper we propose an extension to the algebraic differential evolution approach for permutation based problems (DEP). Conversely from classical differential evolution, DEP is fully combinatorial and it is extended in two directions: new generating sets based on exchange and insertion moves are considered, and the case \(F>1\) is now allowed for the differential mutation operator. Moreover, also the crossover and selection operators of the original DEP have been modified in order to address the linear ordering problem with cumulative costs (LOPCC). The new DEP schemes are compared with the state-of-the-art LOPCC algorithms using a widely adopted benchmark suite. The experimental results show that DEP reaches competitive performances and, most remarkably, found 21 new best known solutions on the 50 largest LOPCC instances.
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 subscriptionsNotes
- 1.
The inverting step is not considered in Sect. 3.1 because the exchange generators are self-invertible.
- 2.
For the sake of space, its description is not reported here.
- 3.
Additionally, a run terminates also if its CPU time exceeds one hour. However, this criterion has been sporadically met only on the RND150 instances.
References
Baioletti, M., Milani, A., Santucci, V.: Linear ordering optimization with a combinatorial differential evolution. In: 2015 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 2135–2140 (2015)
Bean, J.C.: Genetic algorithms and random keys for sequencing and optimization. ORSA J. Comput. 6(2), 154–160 (1994)
Bertacco, L., Brunetta, L., Fischetti, M.: The linear ordering problem with cumulative costs. Eur. J. Oper. Res. 189(3), 1345–1357 (2008)
Bespamyatnikh, S., Segal, M.: Enumerating longest increasing subsequences and patience sorting. Inf. Process. Lett. 76(1–2), 7–11 (2000)
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)
Derrac, J., Garca, 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)
Duarte, A., Laguna, M., Martí, R.: Tabu search for the linear ordering problem with cumulative costs. Comput. Optim. Appl. 48(3), 697–715 (2009)
Duarte, A., Martí, R., Álvarez, A., Ángel-Bello, F.: Metaheuristics for the linear ordering problem with cumulative costs. Eur. J. Optim. Res. 216(2), 270–277 (2012)
Herstein, I.N.: Abstract Algebra, 3rd edn. Wiley, New York (1996)
Moraglio, A., Togelius, J., Silva, S.: Geometric differential evolution for combinatorial and programs spaces. Evol. Comput. 21(4), 591–624 (2013)
Righini, G.: A branch-and-bound algorithm for the linear ordering problem with cumulative costs. Eur. J. Oper. Res. 186(3), 965–971 (2008)
Santucci, V., Baioletti, M., Milani, A.: Solving permutation flowshop scheduling problems with a discrete differential evolution algorithm. AI Commun. 29(2), 269–286 (2016)
Santucci, V., Baioletti, M., Milani, A.: Algebraic differential evolution algorithm for the permutation flowshop scheduling problem with total flowtime criterion. IEEE Trans. Evol. Comput. (to be published– preprint online)
Santucci, V., Baioletti, M., Milani, A.: An algebraic differential evolution for the linear ordering problem. In: Proceedings of GECCO 2015, pp. 1479–1480 (2015)
Schiavinotto, T., Stützle, T.: A review of metrics on permutations for search landscape analysis. Comput. Oper. Res. 34(10), 3143–3153 (2007)
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)
Terán-Villanueva, J.D., Fraire Huacuja, H.J., Carpio Valadez, J.M., Pazos Rangel, R., Puga Soberanes, H.J., Martínez Flores, J.A.: A heterogeneous cellular processing algorithm for minimizing the power consumption in wireless communications systems. Comput. Optim. Appl. 62(3), 787–814 (2015)
Thomsen, R.: Multimodal optimization using crowding-based differential evolution. In: Proceedings of CEC 2004, vol. 2, pp. 1382–1389 (2004)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Baioletti, M., Milani, A., Santucci, V. (2016). An Extension of Algebraic Differential Evolution for the Linear Ordering Problem with Cumulative Costs. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-45823-6_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45822-9
Online ISBN: 978-3-319-45823-6
eBook Packages: Computer ScienceComputer Science (R0)