Annals of Operations Research

, Volume 199, Issue 1, pp 269–284 | Cite as

Parallel hybrid heuristics for the permutation flow shop problem

  • Martín Gómez RavettiEmail author
  • Carlos Riveros
  • Alexandre Mendes
  • Mauricio G. C. Resende
  • Panos M. Pardalos


This paper addresses the Permutation Flowshop Problem with minimization of makespan, which is denoted by Fm|prmu|C max. In the permutational scenario, the sequence of jobs has to remain the same in all machines. The Flowshop Problem (FSP) is known to be NP-hard when more than three machines are considered. Thus, for medium and large scale instances, high-quality heuristics are needed to find good solutions in reasonable time. We propose and analyse parallel hybrid search methods that fully use the computational power of current multi-core machines. The parallel methods combine a memetic algorithm (MA) and several iterated greedy algorithms (IG) running concurrently. Two test scenarios were included, with short and long CPU times. The tests were conducted on the set of benchmark instances introduced by Taillard (Eur. J. Oper. Res. 64:278–285, 1993), commonly used to assess the performance of new methods. Results indicate that the use of the MA to manage a pool of solutions is highly effective, allowing the improvement of the best known upper bound for one of the instances.


Metaheuristics Memetic algorithms Flowshop problem Combinatorial optimization Scheduling 


  1. Agarwal, A., Colak, S., & Eryarsoy, E. (2006). Improvement heuristic for the flow-shop scheduling problem: an adaptive-learning approach. European Journal of Operational Research, 169, 801–815. CrossRefGoogle Scholar
  2. Baker, K. R. (1993). Handbooks in operations research and management science: Vol. 4. Requirements planning (pp. 571–627). New York: Elsevier. Google Scholar
  3. Ben-Daya, M., & Al-Fawzan, M. (1998). A tabu search approach for the flow shop scheduling problem. European Journal of Operational Research, 109, 88–95. CrossRefGoogle Scholar
  4. Buriol, L., Franca, P., & Moscato, P. (2004). A new memetic algorithm for the asymmetric traveling salesman problem. Journal of Heuristics, 10, 483–506. CrossRefGoogle Scholar
  5. Coffman, E. (1976). Computer and job-shop scheduling theory. New York: Wiley. Google Scholar
  6. Dannenbring, D. G. (1977). An evaluation of flow shop sequencing heuristics. Management Science, 23, 1174–1182. CrossRefGoogle Scholar
  7. Glover, F., & Kochenberger, G. (2003). Handbook of metaheuristics. New York: Springer. Google Scholar
  8. Goldberg, D., & Sastry, K. (2010). Genetic algorithms: the design of innovation (2nd ed.). New York: Springer. Google Scholar
  9. Johnson, S. M. (1954). Optimal two- and three-stage production schedules with setup times included. Naval Research Logistics Quarterly, 1, 61–68. CrossRefGoogle Scholar
  10. Moscato, P., Mendes, A., & Berretta, R. (2007). Benchmarking a memetic algorithm for ordering microarray data. Biosystems, 88, 56–75. CrossRefGoogle Scholar
  11. Nagano, M. S., & Moccellin, J. V. (2002). A high quality solution constructive heuristic for flow shop sequencing. The Journal of the Operational Research Society, 53, 1374–1379. CrossRefGoogle Scholar
  12. Nawaz, M., Enscore, E. E., & Ham, I. (1983). A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega, 11, 91–95. CrossRefGoogle Scholar
  13. Ogbu, F. A., & Smith, D. K. (1990). The application of the simulated annealing to the solution of the n/m/c max flow shop problem. Computers & Operations Research, 17, 243–253. CrossRefGoogle Scholar
  14. Reeves, C. R. (1995). A genetic algorithm for flowshop sequencing. Computers & Operations Research, 22, 5–13. CrossRefGoogle Scholar
  15. Rinnooy Kan, A. H. G. (1976). Machine scheduling problems: classification, complexity, and computations. The Hagues: Nijhoff. Google Scholar
  16. Ruiz, R., & Maroto, C. (2005). A comprehensive review and evaluation of permutation flowshop heuristics. European Journal of Operational Research, 165, 479–494. CrossRefGoogle Scholar
  17. Ruiz, R., & Stützle, T. (2006). A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. European Journal of Operational Research, 77, 2033–2049. Google Scholar
  18. Ruiz, R., Maroto, C., & Alcaraz, J. (2003). New genetic algorithms for the permutational flowshop scheduling problem. In MIC2003: The fifth metaheuristics international conference (pp. 63.1–63.8). Google Scholar
  19. Ruiz, R., Maroto, C., & Alcaraz, J. (2006). Two new robust genetic algorithms for the flowshop scheduling problem. Omega, 34, 461–476. CrossRefGoogle Scholar
  20. Stützle, T. (1998). Applying iterated local search to the permutation flow shop problem. Technical report, TU Darmstadt, AIDA-98-04, FG Intellektik. Google Scholar
  21. Taillard, É. (1990). Some efficient heuristic methods for the flow shop sequencing problem. European Journal of Operational Research, 47, 65–74. CrossRefGoogle Scholar
  22. Taillard, É. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64, 278–285. CrossRefGoogle Scholar
  23. Vallada, E., & Ruiz, R. (2009). Cooperative metaheuristics for the permutation flowshop scheduling problem. European Journal of Operational Research, 192, 365–376. CrossRefGoogle Scholar

Copyright information

© Springer Science & Business Media, LLC 2012

Authors and Affiliations

  • Martín Gómez Ravetti
    • 1
    Email author
  • Carlos Riveros
    • 2
  • Alexandre Mendes
    • 2
  • Mauricio G. C. Resende
    • 3
  • Panos M. Pardalos
    • 4
    • 5
  1. 1.Departamento de Engenharia de ProduçãoUniversidade Federal de Minas Gerais (UFMG)Belo HorizonteBrazil
  2. 2.School of Electrical Engineering and Computer ScienceThe University of NewcastleNewcastleAustralia
  3. 3.AT&T Labs ResearchFlorham ParkUSA
  4. 4.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  5. 5.Laboratory of Algorithms and Technologies for Networks Analysis (LATNA), Higher School of EconomicsNational Research UniversityMoscowRussia

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