METAHEURISTIC OPTIMISATIONS FOR METAHEURISTIC OPTIMISATIONS FOR SUDOKU PUZZLESSUDOKU PUZZLES

http://en.wikipedia.org/wiki/Sudoku (2009.03.15)

ITEC809 - Sean McGerty 89214617 - Supervisor Mehmet Orgun

AGENDA

•Introduce Sudoku, Heuristics and Constraints

•Introduce the Three Heuristics and the Rag Doll Framework

•Show some results on the Test Bed

•Explain Results

•Take lots of Questions

ITEC809 - Sean McGerty 89214617 - Supervisor Mehmet Orgun

Sudoku puzzles are complex problem spaces •6,670x1018 unique boards possible!

•NPComplete – worst case exponential time order.

Heuristics spread out and look for good solutions,•They learn by experience.

•Can they find the best solution?

Two main types:•Evolutionary(eg. Genetic) or

•Swarming(our focus).

ITEC809 - Sean McGerty 89214617 - Supervisor Mehmet Orgun

•Heuristics learn their idea of the puzzle as they go along.•They randomly change, learn from each other and measure success

with a fitness function.•They find good solutions, but perhaps not the best.

•Our challenge is to find the best without checking everything.

ITEC809 - Sean McGerty 89214617 - Supervisor Mehmet Orgun

• The fitness Function is the heuristic’s guide to comparing solutions. • They are very solution specific.

• I suggest that the fitness function should be tied to constraints, not the board.• Instead of a maximum of 81, my fitness function goes to 9x9x3x9 = 2187

ITEC809 - Sean McGerty 89214617 - Supervisor Mehmet Orgun

•I wrote a program to help test my ideas.•I organised the program with Object Orientation.

•I built a text based screen interface and each of the Heuristics in it.•I found the hardest 4 problems known to test with.

ITEC809 - Sean McGerty 89214617 - Supervisor Mehmet Orgun

• This is a screen shot of the Genetic Algorithm Succeeding on an Impossible!

ITEC809 - Sean McGerty 89214617 - Supervisor Mehmet Orgun

• This is a screen shot of Particle Swarming Succeeding at an Impossible!

ITEC809 - Sean McGerty 89214617 - Supervisor Mehmet Orgun

• This is a screen shot of Simulated Annealing Succeeding at an Impossible!

ITEC809 - Sean McGerty 89214617 - Supervisor Mehmet Orgun

• All the Heuristics worked, even examples with impossibles! • Not predicted by the research.

•Most problems solved within 100 iterations, hard ones as little as 1000.•Came from optimisations from the Rag Doll framework, the Constraints

based Fitness Function and the Greedy Random. •Even better, the Rag Doll worked on Impossibles without the Heuristics!!!

ITEC809 - Sean McGerty 89214617 - Supervisor Mehmet Orgun

Questions?ITEC809 - Sean McGerty 89214617 - Supervisor Mehmet Orgun

Thanks!ITEC809 - Sean McGerty 89214617 - Supervisor Mehmet Orgun