Annals of Operations Research

, Volume 130, Issue 1, pp 41–56

Constraint Programming and Hybrid Formulations for Three Life Designs

  • Robert Bosch
  • Michael Trick

DOI: 10.1023/B:ANOR.0000032569.86938.2f

Cite this article as:
Bosch, R. & Trick, M. Annals of Operations Research (2004) 130: 41. doi:10.1023/B:ANOR.0000032569.86938.2f


Conway's game of Life provides an interesting testbed for exploring issues in formulation, symmetry, and optimization with constraint programming and hybrid constraint programming/integer programming methods. We consider three Life pattern-creation problems: finding maximum density still-Lifes, finding smallest immediate predecessor patterns, and finding period-2 oscillators. For the first two problems, integrating integer programming and constraint programming approaches provides a much better solution procedure than either individually. For the final problem, the constraint programming formulation provides the better approach.

integer programmingconstraint programminghybrid formulationcellular automatagame of Life

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Robert Bosch
    • 1
  • Michael Trick
    • 2
  1. 1.Department of MathematicsOberlin CollegeOberlinUSA
  2. 2.Graduate School of Industrial AdministrationCarnegie Mellon UniversityPittsburghUSA