Advertisement

A Hybrid Genetic Algorithm for the One-Dimensional Minimax Bin-Packing Problem with Assignment Constraints

  • Mariona Vilà
  • Jordi Pereira
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 682)

Abstract

In this paper, the one-dimensional minimax bin-packing problem with assignment constraints is studied. Among other applications, this problem is used in test-splitting, which consists in assigning several sets of questions into different questionnaires so that every one of these questionnaires contains one question from each one of the original sets. Questions have a weight associated, which typically corresponds to a measure of their difficulty, and the objective is to split the questions among the questionnaires in such a way that the weights are distributed as evenly as possible. We propose a hybrid genetic algorithm for solving this problem, which is then tested on a benchmark set of practically-sized instances. The results show its efficiency in solving large size instances from the literature.

Keywords

Genetic Algorithm Simulated Annealing Hybrid Genetic Algorithm Simulated Annealing Procedure Assignment Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Brusco, M.J., Köhn, H.F., Steinley, D.: Exact and approximate methods for a one-dimensional minimax bin-packing problem. Ann. Oper. Res. 206, 611–626 (2013)CrossRefGoogle Scholar
  2. 2.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)Google Scholar
  3. 3.
    Holland, J.H.: Adaptation in Natural and Artificial Systems: an introductory analysis with applications to biology, control, and artificial intelligence. The University of Michigan Press, Oxford (1975)Google Scholar
  4. 4.
    Johnson, D.S., Garey, M.R., Graham, R.L., Demers, A., Ullman, D.: Worst-case performance bounds for simple one dimensional packing algorithms. SIAM. J. Comput. 3, 299–325 (1974)CrossRefGoogle Scholar
  5. 5.
    Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. Wiley, Chichester (1990)Google Scholar
  6. 6.
    Talbi, E.G.: A taxonomy of hybrid metaheuristics. J. Heuristics 8, 541–564 (2002)CrossRefGoogle Scholar
  7. 7.
    Van der Linden, W.J.: Linear Models for Optimal Test Design. Springer, New York (2005)CrossRefGoogle Scholar
  8. 8.
    Pereira, J., Vilà, M.: Variable neighborhood search heuristics for a test assembly design problem. Expert Syst. Appl. 42(10), 4805–4817 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Escola Universitària d’Enginyeria Tècnica IndustrialUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Departamento de Ingeniería IndustrialUniversidad Católica del NorteAntofagastaChile

Personalised recommendations