1. BEHIND THE BRAINBALL Team Leader : Conor RYAN Problem Leader : Michael HERDY Offspring : Andrea TONIOLO STAGGEMEIER Anne AUGER Nicolas GODZIK Jerôme JEAN-CHARLES

2. THE BRAINBALL PUZZLE

3. WORKING FORMALISM An operator is an ordered sequence of basic actions Swap - Turn - Swap - Turn An operator acts on a position The set of operator is a group structure Neutral element : do nothing Inversable element : you can inverse an operator Stability : chain 2 operators gives a new one

4. BRAINBALL AS A SUBGROUP OF G 13 x(G 2 ) 13 The symmetric group G n (1,2, …, n) The G 5 example : (1,2,3,4,5) a 3-cycle : (1,2,4,5,3) a 2-cycle : (2,1,3,4,5) The group G 13 x(G 2 ) 13 Identity (1,2,3,4,5,6,7,8,9,10,11,12,13)(0,0,0,0,0,0,0,0,0,0,0,0,0) By turn (13,1,2,3,4,5,6,7,8,9,10,11,12)(0,0,0,0,0,0,0,0,0,0,0,0,0) By swap (1,2,11,10,9,6,7,8,5,4,3,12,13)(0,0,1,1,1,0,0,0,1,1,1,0,0)

5. THE MAIN STEPS Produce good operators Use conjugation (ABA -1 ), commutators (ABA -1 B -1 ) Typical generic sets : {ABA -1, AB i A -1, (AB) i, B i } Select operators having max fixed points Use this set of operators as ES ’s mutations

6. USING EVOLUTION STRATEGIES (E.S.) Standard E.S. : practice Operators are not always available The step size is not adaptative E.S. in combinatorial problems (1,λ) Adaptative size works well weighting operators Rubix ’s cube : an example of success

7. MINIMIZING THE FITNESS Fit = α.Fit N + β. Fit C Using heuristics for representation Splitting along the product G 13 x(G 2 ) 13 Balancing α/β using size of G 13 and (G 2 ) 13 Fit = α.Σ|x i -x’ i |+β. Σ (nb colour changes) The colour blind subproblem (β=0) An easier problem for the E.S. Justification G 13 >> (G 2 ) 13

8. COLOR VERSUS NUMBER Fit = α.Fit N + Fit C α=1 : no weighting α<1 : numbers matters less α>1 : colour matters less α=3 : best ratio

9. CONCLUSION THE ATTRACTION OF PUZZLES Seducing the business world A challenge for the EA community DON’T BE EA-CENTRIC Domain matters Fitness is your window of the world USE EXPERTS’ KNOWLEDGE