Using relaxations in maximum density still life

Authors:
Geoffrey Chu;Peter J. Stuckey;Maria Garcia De La Banda
Affiliations:
NICTA Victoria Laboratory, Department of Computer Science and Software Engineering, University of Melbourne, Australia;NICTA Victoria Laboratory, Department of Computer Science and Software Engineering, University of Melbourne, Australia;Faculty of Information Technology, Monash University, Australia
Venue:
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Year:
2009

Citing 4
Cited 3

Integer Programming and Conway's Game of Life

SIAM Review
Constraint Processing

Constraint Processing
Boosting Search with Variable Elimination in Constraint Optimization and Constraint Satisfaction Problems

Constraints
On the practical use of variable elimination in constraint optimization problems: 'still-life' as a case study

Journal of Artificial Intelligence Research

Generating special-purpose stateless propagators for arbitrary constraints

CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
A complete solution to the Maximum Density Still Life Problem

Artificial Intelligence
Improving combinatorial optimization: extended abstract

IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence

Quantified Score

Hi-index	0.00

Visualization

Abstract

The Maximum Density Sill-Life Problem is to fill an n × n board of cells with the maximum number of live cells so that the board is stable under the rules of Conway's Game of Life. We reformulate the problem into one of minimising "wastage" rather than maximising the number of live cells. This reformulation allows us to compute strong upper bounds on the number of live cells. By combining this reformulation with several relaxation techniques, as well as exploiting symmetries via caching, we are able to find close to optimal solutions up to size n = 100, and optimal solutions for instances as large as n = 69. The best previous method could only find optimal solutions up to n = 20.