Evolutionary Search for Matrix Multiplication Algorithms

This paperaddresses the problemof algorithm discovery, via evolutionarysearch, in the context of matrix multiplication. Thetraditional multiplicationalgorithm requiresO(n3) multiplicationsfor squarematricesof order n. Strassen(Strassen1969)discovereda re, cursive matrix multiplication algorithm requiring only seven multiplicationsat each level, resulting in a runtimeof O(n/x7), or O(n2"81).Wehave beenable to replicate this discoveryusing evolutionarysearch (Fogel1995). Thepaperpresents the representational schema,evaluation criteria, andevolution mechanismsemployedduring search. The most crucial decision wasremoving the determinationof coefficients used to combinethe producttermsin the final addition steps fromthe search spaceand calculating themdirectly fromthe specified multiplications. Extendingthis methodologyfrom2 x 2 submatricesto algorithmsusing 3

• Type: Conference
• Year: 2001
• Where: FLAIRS
• Authors: John F. Kolen, Phillip Bruce
• Keywords: Artificial Intelligence, FLAIRS 2001, Matrix Multiplication, Matrix Multiplication Algorithm, Problemof Algorithm Discovery