Download Othello Tutorial - Artificial Intelligence I | CS 5314 and more Study Guides, Projects, Research Computer Science in PDF only on Docsity!
J. A. A. A.
J. B.
M. V.
M. S.
Project codename: Agent Double O 111
Othello Tutorial
Object of the Game Othello is a 2-player game played on an 8x8 square board with each square holding a disc (white or black). One player chooses white and the other chooses black discs to play The object of the game is to have the majority of your color discs on the board at the end of the game How to start the Game Initially, Black places two black discs and White places two white discs as shown in Fig
- The game always begins with this setup. Figure 1 : Initial setup of the Game How does a player make a move A move consists of " outflanking " your opponent's disc(s), then " flipping " the outflanked disc(s) to your color. To outflank means to place a disc on the board so that your opponent's row (or rows) of disc(s) is bordered at each end by a disc of your color. (A "row" may be made up of one or more discs). Here's one example: White disc A was already in place on the board. The placement of white disc B outflanks the row of three black discs.
White flips the outflanked discs and now the row looks like this: Othello Rules
- Black always moves first.
- If on your turn you cannot outflank and flip at least one opposing disc, your turn is forfeited and your opponent moves again. However, if a move is available to you, you may not forfeit your turn.
- A disc may outflank any number of discs in one or more rows in any number of directions at the same time - horizontally, vertically or diagonally. (A row is defined as one or more discs in a continuous straight line). See Figures 2 and 3. Figure 2 Figure 3
- You may not skip over your own color disc to outflank an opposing disc. (See Figure 4). Figure 4
- Discs may only be outflanked as a direct result of a move and must fall in the direct line of the disc placed down. (See Figures 5 and 6).
The example shows that the values of x and y are not needed because the algorithm will select the lowest value between 2, x, and y, only to then select the highest value from 3, (2, x, or y), and 2, which is 3. So, finding out what x and y are is not necessary for the algorithm to work. Neural Networks Neural Networks basic conception stems from trying to model brain synapses and neurons. The idea is that when you learn, certain paths are reinforced. These reinforced paths contain either new knowledge or make it easier to recall old knowledge. Unfortunately the abstract models currently in existence are pale shadows compared to the makeup of the ones we as humans use. This is not to say these models are not useful; actually the opposite is quite true. They are used in many different systems to develop new answers to difficult problems. Make Up Basically Neural Networks use a series of nodes that are distributed in different layers (mimicking a tree like design), to simulate decision making. A neural network is required to have an input layer and output layer at the very least. There are sometimes layers called hidden layers that are simply just another layer between the input and output layers. Each of the nodes in the system will give a certain output. This is dependent on the input given to the node and the weight you give certain paths out of the node. This, of course, makes the entire structure configurable. Why Use Them? We decided to use them for several reasons. First off the network can output different information depending on the input given to it. This is very applicable with Othello because there are a lot of different board configurations possible in any given game. Secondly, the entire system is configurable due to the weights on any given node. This makes the entire system very flexible. It also allows the system to have certain “learning” qualities. For example, if our Neural Network is given certain input it will generate a move. If this move is a very poor one then we can adjust he weights to give this move lower priority. Genetic Algorithms Introduction Genetic algorithms are a part of evolutionary computing , which is a rapidly growing area of artificial intelligence. Search Space If we are solving a problem, we are usually looking for some solution which will be the best among others. The space of all feasible solutions (the set of solutions among which the desired solution resides) is called search space (also state space). Each point in the
search space represents one possible solution. Each possible solution can be "marked" by its value (or fitness) for the problem. With GA we look for the best solution among a number of possible solutions - represented by one point in the search space. Looking for a solution is then equal to looking for some extreme value (minimum or maximum) in the search space. At times the search space may be well defined, but usually we know only a few points in the search space. In the process of using GA, the process of finding solutions generates other points (possible solutions) as evolution proceeds. Basic Description of Genetic Algorithms Genetic algorithms are inspired by Darwin's theory of evolution. Solution to a problem solved by genetic algorithms uses an evolutionary process (it is evolved). Algorithm begins with a set of solutions (represented by chromosomes ) called population. Solutions from one population are taken and used to form a new population. This is motivated by a hope, that the new population will be better than the old one. Solutions which are then selected to form new solutions (offspring) are selected according to their fitness - the more suitable they are the more chances they have to reproduce. This process of generating successive generations of solutions is repeated until some condition (for example number of populations or improvement of the best solution) is satisfied. Encoding of a Chromosome A chromosome should in some way contain information about solution that it represents. The most used way of encoding is a binary string. A chromosome then could look like this: Chromosome 1 1101100100110110 Chromosome 2 1101111000011110 Each chromosome is represented by a binary string. Each bit in the string can represent some characteristics of the solution. There are many other ways of encoding. The encoding depends mainly on the solved problem. For example, one can encode directly integer or real numbers (which is the case for generating weights of a Neural Network); sometimes it is useful to encode some permutations and so on. Crossover After we have decided what encoding we will use, we can proceed to crossover operation. Crossover operates on selected genes from parent chromosomes and creates
chromosomes and therefore the new chromosomes will be better. However, it is good to leave some part of old population survive to the next generation. Mutation probability : How often parts of chromosome will be mutated. If there is no mutation, offspring are generated immediately after crossover (or directly copied) without any change. If mutation is performed, one or more parts of a chromosome are changed. If mutation probability is 100%, whole chromosome is changed, if it is 0%, nothing is changed. Mutation generally prevents the GA from falling into local extremes. Mutation should not occur very often, because then GA will in fact change to random search. Other Parameters There are also some other parameters of GA. One another particularly important parameter is population size. Population size : How many chromosomes are in population (in one generation). If there are too few chromosomes, GA have few possibilities to perform crossover and only a small part of search space is explored. On the other hand, if there are too many chromosomes, GA slows down. Research shows that after some limit (which depends mainly on encoding and the problem) it is not useful to use very large populations because it does not solve the problem faster than moderate sized populations. Diagram of the system
Timeline
- Research specific components of the agent
- Continue researching
- Requirements and decide on design
- Tutorial completion
- Low level design
- Start coding
- Keep coding
- Don’t stop
- You are almost there
- Prototype ready
- Keep working on prototype
- Celebrate victory over other team References The Othello rules were taken from http://www.rainfall.com/othello/rules/othellorules.asp The genetic algorithms explanation was taken from http://cs.felk.cvut.cz/~xobitko/ga/ Both the rules and the genetic algorithm information were slightly modified to preserve the overall structure of the tutorial. No corrections were made in the grammar of the information to preserve copyright.
