Blocks World Problem

The CS Terminal Specifies the block at the top of the stack. Example CS evaluates to E Note: Evaluates to nil if the stack is empty.

The TB Terminal Indicates which block on the stack is at the top of a number of correctly ordered blocks. Example: TB evaluates to R Note: Evaluates to nil if the stack is empty or there are no correctly ordered blocks on the stack.

The NN Terminal Indicates the next block from the table that must be placed on TB on the stack. Example NN evaluates to E Note: Evaluates to nil if the table is empty or TB is nil and the stack is not empty.

The MB Operator Takes a block label, X, as input. If the block is on the table the block is moved to the top of the stack and a value of true is returned else a value of false is returned. A value false is returned if: The table is empty X is already on the stack X is nil

MB Example MB N

The MT Operator Takes a block label, X, as an argument. If X is on the stack the first element of the stack is moved to the table and a value of true is returned else a value of false is returned. A value of false is returned if The stack is empty. If X is already on the table. If X is nil.

MT Example MT S

The DU Operator This function takes two arguments. The first represents the code that must be executed for a number of iterations. The second is a condition specifying when the iteration must stop. Maximum number of iterations per individual: 100 Maximum number of iterations per DU instance: 25 This function returns a value of true if the entire loop is performed and is not terminated due to either of the limits being exceeded otherwise it returns a value of false.

Other Operators NOT Takes a single argument and performs the function of the logical not. If its argument is a block label returns a value of true if the label is nil. EQ Takes two arguments and performs the function of the logical equal.

Fitness cases Ten cases consisting of 0 to nine blocks already in the correct order. Eight fitness cases where there is exactly one block in the wrong order on top of the remaining correctly ordered blocks on the stack. A hundred and forty eight cases where blocks are correctly ordered in the stack and the a random number in the interval 2-8 blocks out- of-order on the stack.

Summary of GP Parameters Function to generate: Induce program that implements a plan to add blocks to a stack so that it spells UNIVERSAL. Terminal set:T = {CS, TB, NN } Function set:F = {MS, MT, DU, NOT, EQ} Number of generations: 51 Population size: 500 Raw fitness:The number of fitness cases for which the stack is correctly constructed.

Summary of GP Parameters Hits criterion:Same as raw fitness Method of selection:Fitness proportionate selection. Initial population generator:The ramped half- and-half method with an initial tree depth of six and a depth limit of seventeen on the size of trees created by the genetic operators. Genetic Operators Crossover - 90% Reproduction - 10%

An Evolved Solution