BEHIND THE BRAINBALLTeam Leader : Conor RYAN

Problem Leader : Michael HERDY

Offspring :

Andrea TONIOLO STAGGEMEIER

Anne AUGER

Nicolas GODZIK

Jerôme JEAN-CHARLES

THE BRAINBALL PUZZLE

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

BRAINBALL AS A SUBGROUP OF G13x(G2)13

• The symmetric group Gn (1,2, …, n)• The G5 example : (1,2,3,4,5)

• a 3-cycle : (1,2,4,5,3)• a 2-cycle : (2,1,3,4,5)

• The group G13x(G2)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)

THE MAIN STEPS

• Produce good operators• Use conjugation (ABA-1) , commutators (ABA-1B-1)

• Typical generic sets : {ABA-1, ABiA-1, (AB)i , Bi}

• Select operators having max fixed points

• Use this set of operators as ES ’s mutations

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

MINIMIZING THE FITNESS

• Fit = α.FitN + β. FitC

• Using heuristics for representation• Splitting along the product G13x(G2)13

• Balancing α/β using size of G13 and (G2)13

• Fit = α.Σ|xi-x’i|+β. Σ (nb colour changes)

• The colour blind subproblem (β=0)• An easier problem for the E.S.• Justification G13 >> (G2)13

COLOR VERSUS NUMBER• Fit = α.FitN + FitC

• α=1 : no weighting

• α<1 : numbers matters less

• α>1 : colour matters less

• α=3 : best ratio

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