A Feasibility-Preserving Crossover and Mutation Operator for Constrained Combinatorial Problems

  • Martin Lukasiewycz
  • Michael Glaß
  • Jürgen Teich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)


This paper presents a feasibility-preserving crossover and mutation operator for evolutionary algorithms for constrained combinatorial problems. This novel operator is driven by an adapted Pseudo-Boolean solver that guarantees feasible offspring solutions. Hence, this allows the evolutionary algorithm to focus on the optimization of the objectives instead of searching for feasible solutions. Based on a proposed scalable testsuite, six specific testcases are introduced that allow a sound comparison of the feasibility-preserving operator to known methods. The experimental results show that the introduced approach is superior to common methods and competitive to a recent state-of-the-art decoding technique.


Feasible Solution Evolutionary Algorithm Mutation Operator Combinatorial Problem Infeasible Solution 
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  1. 1.
    Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press (1972)Google Scholar
  2. 2.
    Lukasiewycz, M., Glaß, M., Haubelt, C., Teich, J.: SAT-Decoding in Evolutionary Algorithms for Discrete Constrained Optimization Problems. In: Proceedings of CEC 2007, pp. 935–942 (2007)Google Scholar
  3. 3.
    Coello, C.: Theoretical and numerical constraint handling techniques used with evolutionary algorithms: A survey of the state of the art. Art. Computer Methods in Applied Mechanics and Engineering 191(11-12), 1245–1287 (2002)CrossRefzbMATHGoogle Scholar
  4. 4.
    Michalewicz, Z., Schoenauer, M.: Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation 4(1), 1–32 (1996)CrossRefGoogle Scholar
  5. 5.
    Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)CrossRefGoogle Scholar
  6. 6.
    Koziel, S., Michalewicz, Z.: A decoder-based evolutionary algorithm for constrained parameter optimization problems. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 231–240. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  7. 7.
    Chai, D., Kuehlmann, A.: A fast pseudo-boolean constraint solver. In: Proceedings of DAC 2003, pp. 830–835 (2003)Google Scholar
  8. 8.
    Lukasiewycz, M., Glaß, M., Haubelt, C., Teich, J.: Efficient symbolic multi-objective design space exploration. In: Proceedings of the ASP-DAC 2008, pp. 691–696 (2008)Google Scholar
  9. 9.
    Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Solving difficult SAT instances in the presence of symmetry. In: Proceedings of DAC 2002, pp. 731–736 (2002)Google Scholar
  10. 10.
    Prasad, M.R., Chong, P., Keutzer, K.: Why is ATPG easy? In: Proceedings of DAC 1999, pp. 22–28 (1999)Google Scholar
  11. 11.
    Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Generic ILP versus specialized 0-1 ILP: an update. In: Proceedings of ICCAD 2002, pp. 450–457 (2002)Google Scholar
  12. 12.
    Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Stoer, M., Wagner, F.: A simple min-cut algorithm. J. ACM 44(4), 585–591 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Opt4J (Java Optimization Framework),

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Martin Lukasiewycz
    • 1
  • Michael Glaß
    • 1
  • Jürgen Teich
    • 1
  1. 1.Hardware-Software-Co-Design, Department of Computer Science 12University of Erlangen-NurembergGermany

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