Abstract
We revisit the analysis of the (\(1\)+\(\lambda \)) EA in a parallel setting when the offspring population size is significantly larger than the number of processors available. If the workload is not balanced across the processors, existing runtime results do not transfer directly. We therefore consider two new scenarios that produce unbalanced processors: (1) when the computation time of the fitness function is variable and depends on the structure of the individual, and (2) when processing is interrupted as soon as a viable offspring is found on one of the machines. We derive parallel execution times for both these models as a function of both the population size and the number of parallel machines. We discuss the potential trade-off between communication overhead and execution time, and we conduct some experiments.
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Notes
- 1.
In this work, we will instead adopt the terminology master-worker.
References
Alba, E., Troya, J.M.: A survey of parallel distributed genetic algorithms. Complex. 4(4), 31–52 (1999)
Cantú-Paz, E.: Master-slave parallel genetic algorithms. In: Efficient and Accurate Parallel Genetic Algorithms, pp. 33–48. Springer, Boston (2001). https://doi.org/10.1007/978-1-4615-4369-5_3
Doerr, B., Künnemann, M.: How the (1+\(\lambda \)) evolutionary algorithm optimizes linear functions. In: Blum, C., Alba, E. (eds.) Genetic and Evolutionary Computation Conference, GECCO ’13, Amsterdam, The Netherlands, 6–10 July 2013, pp. 1589–1596. ACM (2013). https://doi.org/10.1145/2463372.2463569
Doerr, B., Künnemann, M.: Royal road functions and the (1 + \(\lambda \)) evolutionary algorithm: almost no speed-up from larger offspring populations. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC 2013, Cancun, Mexico, 20–23 June 2013, pp. 424–431. IEEE (2013). https://doi.org/10.1109/CEC.2013.6557600
Dubreuil, M., Gagné, C., Parizeau, M.: Analysis of a master-slave architecture for distributed evolutionary computations. IEEE Trans. Syst. Man Cybern. Part B (Cybernetics) 36(1), 229–235 (2006). https://doi.org/10.1109/TSMCB.2005.856724
Gießen, C., Witt, C.: The interplay of population size and mutation probability in the (\(1+\lambda \)) EA on OneMax. Algorithmica 78(2), 587–609 (2016). https://doi.org/10.1007/s00453-016-0214-z
Gießen, C., Witt, C.: Optimal mutation rates for the (1+\(\lambda \)) EA on OneMax through asymptotically tight drift analysis. Algorithmica 80(5), 1710–1731 (2017). https://doi.org/10.1007/s00453-017-0360-y
Grama, A., Gupta, A., Karypis, G., Kumar, V.: Introduction to Parallel Computing. Pearson Education Limited (2003)
Hansen, P., Mladenović, N.: First vs. best improvement: an empirical study. Discr. Appl. Math. 154(5), 802–817 (2006). https://doi.org/10.1016/j.dam.2005.05.020
Jansen, T., De Jong, K.A., Wegener, I.: On the choice of the offspring population size in evolutionary algorithms. Evolution. Comput. 13(4), 413–440 (2005). https://doi.org/10.1162/106365605774666921
Ochoa, G., Verel, S., Tomassini, M.: First-improvement vs. best-improvement local optima networks of NK landscapes. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN 2010. LNCS, vol. 6238, pp. 104–113. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15844-5_11
Roussel-Ragot, P., Dreyfus, G.: A problem independent parallel implementation of simulated annealing: models and experiments. IEEE Trans. Comput. Aided Design Integrat. Circuits Syst. 9(8), 827–835 (1990). https://doi.org/10.1109/43.57790
Sudholt, D.: Parallel evolutionary algorithms. In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 929–959. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-43505-2_46
Verhoeven, M.G.A., Aarts, E.H.L.: Parallel local search. J. Heurist. 1(1), 43–65 (1995). https://doi.org/10.1007/BF02430365
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Aboutaib, B., Sutton, A.M. (2022). Runtime Analysis of Unbalanced Block-Parallel Evolutionary Algorithms. In: Rudolph, G., Kononova, A.V., Aguirre, H., Kerschke, P., Ochoa, G., Tušar, T. (eds) Parallel Problem Solving from Nature – PPSN XVII. PPSN 2022. Lecture Notes in Computer Science, vol 13399. Springer, Cham. https://doi.org/10.1007/978-3-031-14721-0_39
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