Evolving Pre-Sort Algorithms

1. Evolving Pre-Sort Algorithms Joe Barker

2. Why Sorting? • Sorting is used everywhere • Classical methods for developing new algorithms has been pretty much mined out • Genetic Programming (GP) will allow us to find new improvements

3. Why Pre-Sorting? • When evolving programs, the question of generality arises • How do we know the solution works for all possible inputs? • Solution: Provide a method for graceful failure • GP creates pre-sort algorithms and classic sorts are used to “clean up”

4. Previously • John Koza did major work on GP • Kenneth Kinnear did some work evolving sort algorithms • No obvious work with pre-sort algorithms

5. (2) Previously • Kinnear’s work was mostly examining the types(and generality) • Action nodes: • Non-terminal: dobl, if, if-lt • Terminal: order, swap • Expression nodes: • Non-terminal: e-, e1-, e1+, wismaller, wislarger, less • Terminal: *len*, index

6. (3) Previously • Genetic Operators • Single Crossover • Mutation • Non-Fitness Single Crossover • Hoist • Create

7. Design - Individual • Actions • Non-Terminals: LOOP, DUAL • Terminals: ORDER,SWAP • Expressions • Non-Terminals: +,-,*,/,%,LARGER,SMALLER • Terminals: SIZE, I(0-3), CONST(0-10)

8. Design - Fitness • Every individual • All individuals use same input • Individual execution is terminated if the number of operations exceeds a limit • Weighted sum of: • Compares in individual and “cleanup” sort • Swaps • Arithmetic operation executed

9. (2) Design - Fitness • Input • Array of random size n, 64-1024 • Initially either in-order or reverse-order • c*n random swaps performed

10. Design - Evolution • Selection: Blocked-rank selection, only mature • Crossover • Make a list of sub-trees of each parent within a [min,max] “expected” depth • Choose a tree uniformly from each list to swap • Mutation • Create a sub-tree with max. depth of tree to be replaced • N-F Crossover, Hoist

11. Design - Population • Initialization • Random trees • Size of action and expression different • Maturity: >=30 steps • Competition • Elitist (except immature ind.)

12. Design - Other • No termination • Signal causes program state and summary to be dumped to file • State can be reloaded to continue run

13. Experiment • Bubble sort (in-order best) • Data distributions • Nearly sorted • Nearly reversed-sorted • Very random

14. Future Work • Different sorts • Node types to match sorts • Run-time compilation of trees to speed execution

15. Questions?