### Abstract

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. In recent work, we have introduced the important notion of product geometric crossover that enables the construction of new geometric crossovers combining preexisting geometric crossovers in a simple way. In this paper, we use it to design an evolutionary algorithm to solve the Sudoku puzzle. The different types of constraints make Sudoku an interesting study case for crossover design. We conducted extensive experimental testing and found that, on medium and hard problems, the new geometric crossovers perform significantly better than hill-climbers and mutations alone.

Original language | English (US) |
---|---|

Title of host publication | 2006 IEEE Congress on Evolutionary Computation, CEC 2006 |

Pages | 470-476 |

Number of pages | 7 |

State | Published - 2006 |

Event | 2006 IEEE Congress on Evolutionary Computation, CEC 2006 - Vancouver, BC, Canada Duration: Jul 16 2006 → Jul 21 2006 |

### Other

Other | 2006 IEEE Congress on Evolutionary Computation, CEC 2006 |
---|---|

Country | Canada |

City | Vancouver, BC |

Period | 7/16/06 → 7/21/06 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence
- Software
- Theoretical Computer Science

### Cite this

*2006 IEEE Congress on Evolutionary Computation, CEC 2006*(pp. 470-476). [1688347]

**Product geometric crossover for the Sudoku puzzle.** / Moraglio, Alberto; Togelius, Julian; Lucas, Simon.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2006 IEEE Congress on Evolutionary Computation, CEC 2006.*, 1688347, pp. 470-476, 2006 IEEE Congress on Evolutionary Computation, CEC 2006, Vancouver, BC, Canada, 7/16/06.

}

TY - GEN

T1 - Product geometric crossover for the Sudoku puzzle

AU - Moraglio, Alberto

AU - Togelius, Julian

AU - Lucas, Simon

PY - 2006

Y1 - 2006

N2 - Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. In recent work, we have introduced the important notion of product geometric crossover that enables the construction of new geometric crossovers combining preexisting geometric crossovers in a simple way. In this paper, we use it to design an evolutionary algorithm to solve the Sudoku puzzle. The different types of constraints make Sudoku an interesting study case for crossover design. We conducted extensive experimental testing and found that, on medium and hard problems, the new geometric crossovers perform significantly better than hill-climbers and mutations alone.

AB - Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. In recent work, we have introduced the important notion of product geometric crossover that enables the construction of new geometric crossovers combining preexisting geometric crossovers in a simple way. In this paper, we use it to design an evolutionary algorithm to solve the Sudoku puzzle. The different types of constraints make Sudoku an interesting study case for crossover design. We conducted extensive experimental testing and found that, on medium and hard problems, the new geometric crossovers perform significantly better than hill-climbers and mutations alone.

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M3 - Conference contribution

AN - SCOPUS:34547282598

SN - 0780394879

SN - 9780780394872

SP - 470

EP - 476

BT - 2006 IEEE Congress on Evolutionary Computation, CEC 2006

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