Estimation of Distribution Algorithm and Genetic Programming Structure Complexity Lab,Seoul National University KIM KANGIL

Index What is EDA? EDA with GP Grammar Model based Program Evolution  How it works Conclusion

Conventional GA,GP vs EDA Stochastic Model Conventional GPEDA

What is EDA Stochastic Model  Components to construct individuals  Keep the probability distribution of these components Similar cycle and strategy with traditional evolutionary computation No crossover & mutation Best Individuals Population Model Comp type1 Comp type2. Generate Update Model Selection EDA process

EDA with GP Use Tree representation for individuals More complex and structured model How to get the distribution in complex structure?  Dependency  maintain structure  How to keep meaningful building blocks Grammar is good to give an explanation of internal structure

Grammar Model-based Program Evolution (GMPE) Use Stochastic Context Free Grammar to make a model  A -> B 0.5  -> C 0.5 Tree representation for each individual Doesn ’ t have fixed components to record the probability Probability learning with Structural learning every generation Use Minimum Message Length to give a boundary of generalization

Model Implementation Merging Converting Best Individuals Grammar : The same language with Best individuals Grammar : Expanded language

Converting Exp Y OpExp Individual 1 Individual 2 X X+ N1 N2 N3N4N5 S-> N11 -> N21 N1 -> Y1 N2 -> N3 N4 N51 N3 -> X1 N4 -> +1 N5 -> X1 SCFG Give unique ID to each node Each parent and child relation is production Model is constructed by Stochastic CFG Give 1 count to each created production

Converting - detail Giving 1 count for each production is useful to calculate probabilities on total structure  Even if some nonterminals is merged, we can know how many this production is used in best individuals This grammar can only generate the best individuals selected in last generation  If there is no generalization step, It can’t search solution space

Merging S-> N11 -> N21 N1 -> Y1 N2 -> N3 N4 N51 N3 -> X1 N4 -> +1 N5 -> X1 SCFG Merge (N1, N2) To N6 Select two Nonterminals and merge them Every Production using these Nonterminals should change them to new Nonterminal If some productions become equivalent, compact them to one production with summing their count S-> N61 -> N61 N6 -> Y1 N6 -> N3 N4 N51 N3 -> X1 N4 -> +1 N5 -> X1 SCFG S-> N62 N6 -> Y1 -> N3 N4 N51 N3 -> X1 N4 -> +1 N5 -> X1 SCFG Simplify

Merging - detail Select Nonterminals  Keeping consistency with original grammar  Recording Original Type in each Nonterminal  Select nonterminals which has the same original Type  How many Nonterminals should be merged?  Use Minimum Message Length – give boundary of generalization No crossover – contain all possible combinations with probability

Minimum message length Similar with Minimum Description length Used to describe the model size Based on entropy Lower MML, simpler model  Merge nonterminals who can reduce this cost keep model to be not so complicated or not so simple Calculate the cost in all possible ways

Current issues How much model should be generalized or specialized to make the evolutionary process more efficient? How can we know which sub part of the model should be changed?  Considering the distribution and variable measures to describe some properties of model ( like similarity )  Efficient learning with collecting more important information

Conclusion GMPE is one of EDA with GP approach Update structure with probability at every generation Useful to collect frequently used productions with flexible grammar Easy to give some constraints like GGGP reducing search space Good to get information of best solution set It can give an explanation of model internally about which part is important Too much cost to maintain model, over-generalization problem. Using MML for giving Generalization step