Constraint Programming and Hybrid Formulations for Three Life Designs
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.
Bosch, Robert, and Michael Trick. 2004. "Constraint Programming and Hybrid Formulations for Three Life Designs." Annals of Operations Research 130(1): 41-56.
Annals of Operations Research
Theory of computation, Combinatorics, Operation Research/Decision Theory