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 Initialization Upper left image by 慕尼黑啤酒 Parent selection Recombination Mutation • • • • 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 Initialization Upper left image by 慕尼黑啤酒 Parent selection Recombination Mutation 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 • We define the fitness of a number to be the sum of the distances of its digits from these in the target, with the sign minus. • The target: 11010010 • fitness(01001010)= 1−0 + 1−1 + 0−0 + 1−0 + 0−1 − + 0 − 0 + 1 − 1 + |0 − 0| = −3 The target: 11010010 1. 2. 3. 4. 5. fitness(01001010)=-3 fitness(10011011)=-3 fitness(01100001)=-5 fitness(10100110)=-4 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. • • • • {01001010,10011011,01100001,10100110,01010011} {-3,-3, -5,-4,-2} Assume we select 10011011, 10100110. fitness(10011011) > fitness(10100110) 10011011 selected. … • We get {01001010,10011011,10100110,01010011} Recombination • Two selected parents will be coupled with probability 0.5. • (01001010,10011011) , (01001010, 10100110), (10100110 ,01010011) • 3 is selected as a random number from 1…8 • Then we do a crossover: From (01001010,10011011) we get (01011011,10001010) • We repeat that for each selected couple. Mutation • For each digit in each of the offsprings , we make the bit flip with probability 0.05. • For 10001010 we have 10011010. 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 • Similar example, where the target was “Hello world” achieved the score in generation 65. (population size=400 , 2611 options) • In our simple case there are 28 = 256 options in total. • • • • 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 • There are roughly 1020 legal positions. • In chess there are 1043 − 1050 . 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 Node name Return type Return value ERC Floating point Ephemeral Random Constant False Boolean Boolean false value True Boolean Boolean true value One Floating point 1 Zero Floating point 0 Basic function nodes Node name 𝐴𝑁𝐷(𝐵1, 𝐵2) Return value Logical AND of parameters 𝐿𝑜𝑤𝑒𝑟𝐸𝑞𝑢𝑎𝑙(𝐹1, 𝐹2) True iff F1 ≤ F2 𝑁𝐴𝑁𝐷(𝐵1, 𝐵2) 𝑁𝑂𝑅(𝐵1, 𝐵2) 𝑵𝑶𝑻𝑮(𝑩𝟏, 𝑩𝟐) 𝑂𝑅(𝐵1, 𝐵2) 𝑰𝑭𝑻(𝑩𝟏, 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 𝑀𝑖𝑛𝑢𝑠(𝐹1, 𝐹2) F1 − F2 𝑴𝒖𝒍𝒕𝑬𝑹𝑪(𝑭𝟏) F1 multiplied by preset random number 𝑁𝑢𝑙𝑙𝐽(𝐹1, 𝐹2) F1 𝑃𝑙𝑢𝑠(𝐹1, 𝐹2) F1 + F2 Domain-specific nodes EnemyKingCount EnemyManCount EnemyPieceCount FriendlyKingCount FriendlyManCount FriendlyPieceCount KingCount FriendlyKingCount − EnemyKingCount ManCount FriendlyManCount − EnemyManCount PieceCount FriendlyPieceCount −EnemyPieceCount KingFactor King factor value Mobility The number of plies available to the player Domain specific- details of a square IsEmptySquare(X,Y) True iff square empty IsFriendlyPiece(X,Y) True iff square occupied by friendly piece IsKingPiece(X,Y) True iff square occupied by king IsManPiece(X,Y) True iff square occupied by man 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 • Randomly choose two different previously unselected individuals from the population. • If 𝐼1. 𝑓𝑖𝑡𝑛𝑒𝑠𝑠 ≥ 𝐼2. 𝑓𝑖𝑡𝑛𝑒𝑠𝑠 then o Perform one-way crossover with I1 as donor and I2 as receiver • Else o Perform two-way crossover with I1 and I2 • End if. 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.