# Genetic Algorithms Yohai Trabelsi. Outline Evolution in the nature Genetic Algorithms and Genetic Programming A simple example for Genetic Algorithms.

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Genetic Algorithms Yohai Trabelsi

Outline Evolution in the nature Genetic Algorithms and Genetic Programming A simple example for Genetic Algorithms An example for Genetic programming

Evolution in the nature Genetic Algorithms and Genetic Programming A simple example for Genetic Algorithms An example for Genetic programming

Evolution in the nature A Chromosome: o A string of DNA. o Each living cell has some. Image by Magnus Manske

Each chromosome contains a set of genes. A gene is a block of DNA. Each gene determines some aspect of the organism (e.g., eye colour).

Reproduction in the nature Reproduction involves: 1. Recombination of genes from parents. 2. Small amounts of mutation (errors) in copying. One type of recombination is crossover.

Reproduction involves: 1. Recombination of genes from parents. 2. Small amounts of mutation (errors) in copying. Right image by Jerry Friedman.

In the nature, fitness describes the ability to survive and reproduce. Images by ShwSie

The evolution cycle Upper left image by 慕尼黑啤酒 Parent selection Recombination Mutation Survivor selection Initialization

Evolution in the nature Genetic Algorithms and Genetic Programming A simple example for Genetic Algorithms An example for Genetic programming

Some history First work of computer simulation of evolution- Nils Aall Barricelli(1954) In the 1950s and 1960s several researchers began independently studying evolutionary systems. The field has experienced impressive growth over the past two decades.

Genetic Algorithms The research on Genetic Algorithms focuses on imitating the evolution cycle in Algorithms. That method is applicable for many hard search and optimization problems.

Initialization Initialization is the process of making the first generation. During the algorithm our goal will be to improve them by imitating the nature.

Termination. In the nature we don’t have (yet) a point that the process stops. In many cases an algorithm that runs forever is useless. We should try to find the correct time for terminating the whole process. o That time may be after the results are good and/or before the running time is too long.

The modified evolution cycle Upper left image by 慕尼黑啤酒 Parent selection Recombination Mutation Survivor selection Initialization termination

GA-Some definitions In any generation there is a group of individuals that belongs to that generation. We call that group population. Fitness will be a function from individuals to real numbers. The product of the recombination process is an offspring.

Genetic Programming Genetic Programming is Genetic Algorithm wherein the population contains programs rather than bitstrings.

Evolution in the nature Genetic Algorithms and Genetic Programming A simple example for Genetic Algorithms An example for Genetic programming

A simple example Problem: “Find” the binary number 11010010.

Initialization We start with 5 random binary numbers with 8 digits each. 1.01001010 2. 10011011 3.01100001 4.10100110 5.01010011

The fitness function

The target: 11010010 1.fitness(01001010)=-3 2.fitness(10011011)=-3 3.fitness(01100001)=-5 4.fitness(10100110)=-4 5.fitness(01010011)=-2

Parent Selection In each generation, some constant number of parents, say, 4 are chosen. Higher is the fitness, greater is the probability of choosing the individual.

Recombination

Mutation

The process and it’s termination We repeat the cycle until one of the numbers that we get would have fitness 0 (that is would be identical to the desired one). We expect that it will not be too long in comparison to checking the fitness of all the numbers in the range. Our hope is based on choosing parents with higher fitness and on producing next generations similarly to the nature.

Some Results

Evolution in the nature Genetic Algorithms and Genetic Programming A simple example for Genetic Algorithms An example for Genetic programming

American Checkers Michel32Nl

Lose Checkers The rules are the same as in the original game. The goal is opposite to the goal in the original game: Each player tries to lose all of his pieces. Player wins if he doesn’t have any pieces or if he can’t do any move.

The complexity

Previous work There are few recent results on Lose checkers. They concentrate either on search or on finding a good evaluation function. They can help to improve good players but they can’t produce good players. Improvements on a random player don’t worth much.

The algorithm The individuals will be trees. Each tree will behave like evaluation function for the board states (more details later). A tree represents a chromosome. Each tree contains nodes. A node represents a gene. There are three kinds of nodes: o Basic Terminal Nodes. o Basic Function Nodes. o Domain-Specific Terminal Nodes.

Basic terminal nodes Return value Return typeNode name Ephemeral Random Constant Floating point ERC Boolean false value BooleanFalse Boolean true value BooleanTrue 1Floating point One 0Floating point Zero

Basic function nodes Return value Node name Logical AND of parameters True iff F1 ≤ F2 Logical NAND of parameters Logical NOR of parameters Logical NOT of B1 Logical OR of parameters F1 if B1 is true and F2 otherwise F1 − F2 F1 multiplied by preset random number F1F1 F1 + F2

Domain-specific nodes EnemyKingCount EnemyManCount EnemyPieceCount FriendlyKingCount FriendlyManCount FriendlyPieceCount FriendlyKingCount − EnemyKingCountKingCount FriendlyManCount − EnemyManCountManCount FriendlyPieceCount −EnemyPieceCountPieceCount King factor valueKingFactor The number of plies available to the playerMobility

Domain specific- details of a square True iff square emptyIsEmptySquare(X,Y) True iff square occupied by friendly pieceIsFriendlyPiece(X,Y) True iff square occupied by kingIsKingPiece(X,Y) True iff square occupied by manIsManPiece(X,Y)

An example for board evaluation tree

The algorithm Make initial population While the termination condition didn’t reached: o Select the best candidates for being parents. o Make the new generation by crossover and mutation o Evaluate the fitness of the new generation.

Make initial population While the termination condition didn’t reached: o Select the best candidates for being parents. o Make the new generation by crossover and mutation o Evaluate the fitness of the new generation.

The initial population The size of the population is one of the running parameters. We select the trees randomly. Their maximum allowed depth is also a running parameter. We omit the details of the random selection.

Make initial population While the termination condition didn’t reached: o Select the best candidates for being parents. o Make the new generation by crossover and mutation o Evaluate the fitness of the new generation.

Selection

Fitness evaluation We define GuideArr to be an array of guide players. Some of them are random players which are useful for evaluating initial runs. Others, alpha-beta players, are based on search up to some level and random behavior since that level. CoPlayNum is the number of players which are selected randomly from the current population for playing with the individual under evaluation. Image by Jon Sullivan

Fitness evaluation back

Make initial population While the termination condition didn’t reached: o Select the best candidates for being parents. o Make the new generation by crossover and mutation o Check whether the termination condition reached

Crossover

Two way crossover Randomly select an internal node in each of the two individuals. Swap the subtrees rooted at these nodes.

One way crossover Randomly select an internal node in each of the two individuals as a root of selected subtree. One individual (donor) inserts a copy of its selected sub-tree into another individual(receiver), in place of its selected sub-tree, while the donor itself remains unchanged. Similar to gene transfer in bacteria, image by Y tambe

Using the one way crossover gives the fitter individuals an additional survival advantage. They still can change due to the standard two-way crossover.

Mutation We randomly choose a node in the tree for mutation. We do probabilistic decision whether to use the traditional tree building mutation method or the Local mutation method. The probability for each method is given as a parameter to our algorithm.

Traditional mutation Traditional tree building mutation: o Done by replacing the selected node with a new subtree. The drawback of using only the traditional mutation is that a mutation can change dramatically the fitness of an individual.

Local mutation Each node that returns a floating-point value has a floating-point variable attached with it (initialized to 1). The returned value of the node was the normal value multiplied by the variable. The mutation is a small change in the variable.

Make initial population While the termination condition didn’t reached: o Select the best candidates for being parents. o Make the new generation by crossover and mutation o Check whether the termination condition reached

Termination The number of Generations until the termination will be a parameter of our program.

The Players Use alpha-beta search algorithm. Evaluate non-terminal states using the individual The depth of the search is 3. There are more methods.

Some Results 1000 games were played against some alpha-beta players. The Score: 1 point was given for win and 0.5 For drawn.

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