Update README.md

Author: lagodiuk

README.md

@@ -1,8 +1,60 @@
 genetic-programming
 ===================
 
-Symbolic regression solver, based on genetic programming methodology.
-More info in this [article](http://habrahabr.ru/post/163195/)
+[Symbolic regression](http://en.wikipedia.org/wiki/Symbolic_regression) solver, based on [genetic programming](http://en.wikipedia.org/wiki/Genetic_programming) methodology.
+
+## Description ##
+
+Each mathematical expression can be represented in form of syntax tree: <br/>
+![Syntax Tree Example](https://raw.githubusercontent.com/lagodiuk/genetic-programming/master/img/syntax_tree.png)
+
+Actually, it worth to keep in mind, that there exists infinite number of different syntax trees, which corresponds to semantically equivalent expressions. For example: <br/>
+![Equivalent Syntax Trees](https://raw.githubusercontent.com/lagodiuk/genetic-programming/master/img/equiv_syntax_trees.png)
+
+In practice, on of the most generic problems - is reconstruction of original function, having the information about its values in some specific points. 
+
+It is possible to apply [genetic algorithm](http://en.wikipedia.org/wiki/Genetic_algorithm) - for solving of given problem:
+
+1. In terms of Genetic Algorithm - each syntax tree can be treated as a "chromosome" (an entity, which can "mutate" and change by "crossover" with other "chromosome")
+
+2. It is needed to define [fitness function](http://en.wikipedia.org/wiki/Fitness_function): the function, which will calculate, how good each formula (which was encoded by syntax tree) - can represent existing data (e.g.: using [mean squared error](http://en.wikipedia.org/wiki/Mean_squared_error) value).
+
+### Crossover ###
+During "crossover" - syntax tree is modified by substituion of its subtree, with some subtree from other syntax tree.
+
+Following image explains implementation of "crossover" operation over syntax trees: <br/>
+![Crossover](https://raw.githubusercontent.com/lagodiuk/genetic-programming/master/img/crossover.png)
+
+### Mutation ###
+Currently implemented following "mutation" operations:
+
+1. Substituion of some node of syntax tree - with node, which corresponds to different arithmetical operation: <br/>
+![Mutation - by substitution of arithmetical operation](https://raw.githubusercontent.com/lagodiuk/genetic-programming/master/img/mutation_1.png)
+
+2. Substituion of some subtree with randomly generated subtree: <br/>
+![Mutation - by substituion of some subtree with randomly generated subtree](https://raw.githubusercontent.com/lagodiuk/genetic-programming/master/img/mutation_2.png)
+
+3. Removing of some intermediate node from syntax tree: <br/>
+![Mutation - by removing of some intermediate node](https://raw.githubusercontent.com/lagodiuk/genetic-programming/master/img/mutation_3.png)
+
+4. Expanding tree from root: <br/>
+![Mutation - by expanding tree from root](https://raw.githubusercontent.com/lagodiuk/genetic-programming/master/img/mutation_4.png)
+
+5. Swapping subtrees for non-commutative oparations: <br/>
+![](https://raw.githubusercontent.com/lagodiuk/genetic-programming/master/img/mutation_5.png)
+
+### Optimization of coefficients ###
+Actually, some syntax tree might represent correct structure of searchable function, but due to some non-optimal values of coefficients - given syntax tree can be considered as non-optimal by fitness function. 
+
+For example, following image displays target values of searchable function (red crosses) - and two functions-candidates (green and blue): <br/>
+![Why optimization of coefficients is needed](https://raw.githubusercontent.com/lagodiuk/genetic-programming/master/img/why_should_optimize_coefficients.png)
+
+Blue line has smaller value of mean squared error, but, actually - green parabola - would be a better candidate for the final solution.
+
+By this reason, current implementation of Symbolic Regression Solver - uses second pass of Genetic Algorithm - for optimizing of coefficients of each syntax tree. On the picture below - represented the way, how coefficients of each syntax tree - could be transformed to "chromosome": <br/>
+![Encoding coefficients of syntax tree into chromosome](https://raw.githubusercontent.com/lagodiuk/genetic-programming/master/img/optimize_coefficients_ga.png)
+
+More info in this [article](http://habrahabr.ru/post/163195/) (article is in Russian language).
 
 This project depends on [Generic Genetic Algorithm project](https://github.com/lagodiuk/genetic-algorithm) (has a maven dependency)
 
@@ -122,4 +174,4 @@ public class HelloSymbolicRegression {
 		return list;
 	}
 }
-```
+```