So I was assigned the problem of writing a 5x5x5 tic-tac-toe player using a genetic algorithm. My approach was to start off with 3x3, get that working, and then extend to 5x5, and then to 5x5x5.
The way it works is this:
Simulate a whole bunch of games, and during each turn of each game, lookup in a corresponding table (X table or O table implemented as a c++ stdlib maps) for a response. If the board was not there, add the board to the table. Otherwise, make a random response.
After I have complete tables, I initialize a bunch of players (each with a copy of the board table, initialized with random responses), and let them play against each other.
Using their wins/losses to evaluate fitness, I keep a certain % of the best, and they move on. Rinse and repeat for X generations, and an optimal player should emerge.
For 3x3, discounting boards that were reflections/rotations of other boards, and boards where the move is either 'take the win' or 'block the win', the total number of boards I would encounter were either 53 or 38, depending on whether you go first or second. Fantastic! An optimal player was generated in under an hour. Very cool!
Using the same strategy for 5x5, I knew the size of the table would increase, but did not realize it would increase so drastically. Even discounting rotations/reflections and mandatory moves, my table is ~3.6 million entries, with no end in sight.
Okay, so that's clearly not going to work, I need a new plan. What if I don't enumerate all the boards, but just some boards. Well, it seems like this won't work either, because if each player has just a fraction of possible boards they might see, then they are going to be making a lot of random moves, clearly steering in the opposite direction of optimality.
What is a realistic way of going about this? Am I going to be stuck using board features? The goal is to hard-code as little game functionality as possible.
I've been doing research, but everything I read leads to min/max with A-B pruning as the only viable option. I can certainly do it that way, but the GA is really cool, my current method is just exceeding reality a bit here.
EDIT Problem has been pretty much solved:
Using a similarity function that combines hamming distance of open spaces, the possible win conditions, and a few other measures has brought the table down to a very manageable 2500 possibilities, which a std::map handles in a fraction of a second.
My knowledge of GA is pretty limited, but in modeling board configurations, aren't you asking the wrong question? Your task isn't to enumerate all the possible winning configurations -- what you're trying to do is to find a sequence of moves that leads to a winning configuration. Maybe the population you should be looking at isn't a set of boards, but a set of move sequences.
Edit: I wasn't thinking so much of starting from a particular board as starting from an empty board. It's obvious on a 3x3 board that move sequences starting with (1,1) work out best for X. The important thing isn't that the final board has an X in the middle, it's that the X was placed in the middle first. If there's one or more best first moves for X, maybe there's also a best second, third, or fourth move for X, too? After several rounds of fitness testing and recombining, will we find that X's second move is usually the same, or is one of a small set of values? And what about the third move?
This isn't minimax because you're not looking for the best moves one at a time based on the previous state of the board, you're looking for all the best moves at the same time, hoping to converge on a winning strategy.
I know this doesn't solve your problem, but if the idea is to evolve a winning strategy then it seems natural that you'd want to look at sequences of moves rather than board states.
This seems to be a very old conversation but attracted my attention. Thinking it might serve the public discussion, here is my input.
I think the aim in your assigned task needs to be defined more clearly:
Are you trying to find a set of winning boards? I don’t think so, because this is very straigtforward for a 3x3 board which can even be solved by hand, and it can be extrapolated to larger boards. GA could be utilized for larger boards, but it would only be a GA exercise.
Are you trying to utilize GA to train TicTacToe to AI players? I think this should be the case. In that case, your GA strings/chromosomes should not represent winning boards, but rather, they should represent ordered move sequences of players, for winning games. This is really a bit trickier to model though, as expected, and it would be a real AI training programming exercise.
I hope this perspective helps.
Related
I cannot realy say why, but once YouTube suggested a video about an Genetic Alogirthm to me, well it really flashed me, someone made the google chrome no internet jump&run play alone by an learning AI.
Well since i'm programing plugins for Minecraft i got an idea to make an PvE Based Gamemode with an self learning AI (The Genetic Alogrithm), but right now i'm confused where to start, i can make the Fitness depended on the Kills of the Zombie, or on the damage dealt, but i dont know how i can reproduce this again, somehow i have to control the movement, the shots and so on with the AI, and i got no clue how to do that, i hope someone can help me, and you understand my question.
I think what you're trying to do is far more complex than you might think.
If you really want to train autonomous AI for zombies, you're going to need neural networks. But I think this is far too complex for a PvE game.
If you don't want to use neural networks, you have to set up a handful of parameters that define how the zombie acts, like:
Damage
Speed
Health
But it's illogical to use a genetic algorithm for this - you already know that maxing out these values will return the best zombie, so you might need to create more distinct parameters like:
Speed after hitting a player
Potion effect after hitting a player
If you want to stay to the 3 points named above, then you should create a maximum value - and make the genetic algorithm find the optimal distribution of this value.
That's the main part sorted out, then you want to get started on the genetic algorithm
Generation, generate zombies with random properties
Evaluation, let the zombies play a game, determine their fitness on: damage dealt, kills made, distance travelled
Selection, select the individuals ripe for crossover
Crossover, create offspring
Mutation, modify some values with a chance of x
I'm quite interested in your project. I advise you to start training some zombies on a local server, and then use these trained zombies as a base for the online version - so the first waves of zombies aren't too easy :)
With regards to your comment:
Actually i want to improve the movement and fight skills ov Zombies, meqans that they go back when they attack delay is colding down when enemys are really defensive and so on, and the zombies try to catch some single players when they play aggressive etc, but not sure how to do something like this, i dont know how to control movement with an AI, and when to attack etc, I know its a lot to do, but i'm realy interested in this.
This definitely requires a neural network. A neural network can have x inputs, these must all be environment variables, like:
distance nearest player
speed nearest player
health nearest player
etc. nearest player
its own health
And will compute outputs, which could be:
movement direction
movement speed
hit (true/false)
And you have to evolve the neural network through neuroevolution. You can definitely do this, but heads up; it's hard. Especially with a lot of environment variables.
But read some articles on neural networks, then read some articles on genetic algorithms. Then implement neuroevolution, for example through NeuroEvolution of Augmenting Topologies
I suggest you do some research on genetic algorithms, it looks like you're trying to run before you've learned to walk.
Ideally, if you want the AI to learn how to move, shoot, and other activities, you need to create a fitness function that can score based on all of these things. You then need to figure out at what point you're going to evolve/mutate/mate your AI/s, the product of this should start with the initial score of 0, as you will need to rescore the AI, as there is a possibility it could have taken a step backwards, rather than forwards.
So basically, I have to write a Battleships AI, which follows all of the conventional rules, apart from the fact that you are not notified whether or not your shot has sunk a ship - just whether or not it was a hit or miss
At the moment I have a working AI, but it suffers from the problem that it has to fire shots all the way around each enemy ship, as it doesn't know if the ship is sunk - this video may explain it better (for those who are wondering, there are some custom ship shapes, and the board is an L-shape): https://www.youtube.com/watch?v=SzLspp4JzNE
Any suggestions on how to go about reducing the number of shots required?
Many thanks :)
What information the computer can have? Number of ships, number of blocks for each ship, the shape of each ship. The algorithm has to check for the shapes of all remaining ships and pick next field such that the chance of hit is largest. Maybe there is a better long term strategy than "greatest hit chance", but solve the shape recognition part before delving into strategies.
If shapes of the ships are not known in advance then there's not much the algorithm can do. All it can is to check if the block being hit is the part of the largest remaining ship. The advanced strategy here would be to determine if largest ship cannot be anywhere else. If there are other ships remaining then use turns to search for them, but in such a search pattern that you also eliminate the possibility of the largest ship being somewhere else.
However, if there is a rule of number of attacks per turn being in proportion with number of your remaining ships, then you have to eliminate every ship as soon as possible, and so the "advanced" strategy above should not be used.
The most basic idea is to keep information regarding sunked ships as well as remaining ones (I assume that you know, that there are a_i ships with i pieces), and ones you sunk all the 4-pieces, and hit some connected 3-piece ship you will know, that there is no need to shoot around it anymore. So in general you shoot around hitted ship as long, as amount of hitted pieces is smaller that the number of pieces in the biggest non-empty class of ships. And once you sunk some - you decrease the respective ship class counter.
Some interesting alternative would be to learn some statistics of ships positions and shapes based on played games - if you play against human player it is most probable, that he won't place any ship anywhere - there are some psychological aspects that "bias" your decisions towards placements that you consider as "hard to find" - your program could learn such conditional probabilities and use it to assume its confidency in sunking some ship without shooting around it. Unfortunately this would not work with well designed - uniformly placing ships - algorithms.
I think I understand the basic concept of simulated annealing. It's basically adding random solutions to cover a better area of the search space at the beginning then slowly reducing the randomness as the algorithm continues running.
I'm a little confused on how I would implement this into my genetic algorithm.
Can anyone give me a simple explanation of what I need to do and clarify that my understand of how simulated annealing works is correct?
When constructing a new generation of individuals in a genetic algorithm, there are three random aspects to it:
Matching parent individuals to parent individuals, with preference according to their proportional fitness,
Choosing the crossover point, and,
Mutating the offspring.
There's not much you can do about the second one, since that's typically a uniform random distribution. You could conceivably try to add some random factor to the roulette wheel as you're selecting your parent individuals, and then slowly decrease that random function. But that goes against the spirit of the genetic algorithm and (more importantly) I don't think it will do much good. I think it would hurt, actually.
That leaves the third factor-- change the mutation rate from high mutation to low mutation as the generations go by.
It's really not any more complicated than that.
For my bachelor's thesis I want to write a genetic algorithm that learns to play the game of Stratego (if you don't know this game, it's probably safe to assume I said chess). I haven't ever before done actual AI projects, so it's an eye-opener to see how little I actually know of implementing things.
The thing I'm stuck with is coming up with a good representation for an actual strategy. I'm probably making some thinking error, but some problems I encounter:
I don't assume you would have a representation containing a lot of
transitions between board positions, since that would just be
bruteforcing it, right?
What could branches of a decision tree look
like? Any representation I come up with don't have interchangeable
branches... If I were to use a bit string, which is apparently also
common, what would the bits represent?
Do I assign scores to the distance between certain pieces? How would I represent that?
I think I ought to know these things after three+ years of study, so I feel pretty stupid - this must look likeI have no clue at all. Still, any help or tips on what to Google would be appreciated!
I think, you could define a decision model and then try to optimize the parameters of that model. You can create multi-stage decision models also. I once did something similar for solving a dynamic dial-a-ride problem (paper here) by modeling it as a two stage linear decision problem. To give you an example, you could:
For each of your figures decide which one is to move next. Each figure is characterized by certain features derived from its position on the board, e.g. ability to make a score, danger, protecting x other figures, and so on. Each of these features can be combined (e.g. in a linear model, through a neural network, through a symbolic expression tree, a decision tree, ...) and give you a rank on which figure to act next with.
Acting with the figure you selected. Again there are a certain number of actions that can be taken, each has certain features. Again you can combine and rank them and one action will have the highest priority. This is the one you choose to perform.
The features you extract can be very simple or insanely complex, it's up to what you think will work best vs what takes how long to compute.
To evaluate and improve the quality of your decision model you can then simulate these decisions in several games against opponents and train the parameters of the model that combines these features to rank the moves (e.g. using a GA). This way you tune the model to win as many games as possible against the specified opponents. You can test the generality of that model by playing against opponents it has not seen before.
As Mathew Hall just said, you can use GP for this (if your model is a complex rule), but this is just one kind of model. In my case a linear combination of the weights did very well.
Btw, if you're interested we've also got a software on heuristic optimization which provides you with GA, GP and that stuff. It's called HeuristicLab. It's GPL and open source, but comes with a GUI (Windows). We've some Howto on how to evaluate the fitness function in an external program (data exchange using protocol buffers), so you can work on your simulation and your decision model and let the algorithms present in HeuristicLab optimize your parameters.
Vincent,
First, don't feel stupid. You've been (I infer) studying basic computer science for three years; now you're applying those basic techniques to something pretty specialized-- a particular application (Stratego) in a narrow field (artificial intelligence.)
Second, make sure your advisor fully understands the rules of Stratego. Stratego is played on a larger board, with more pieces (and more types of pieces) than chess. This gives it a vastly larger space of legal positions, and a vastly larger space of legal moves. It is also a game of hidden information, increasing the difficulty yet again. Your advisor may want to limit the scope of the project, e.g., concentrate on a variant with full observation. I don't know why you think this is simpler, except that the moves of the pieces are a little simpler.
Third, I think the right thing to do at first is to take a look at how games in general are handled in the field of AI. Russell and Norvig, chapters 3 (for general background) and 5 (for two player games) are pretty accessible and well-written. You'll see two basic ideas: One, that you're basically performing a huge search in a tree looking for a win, and two, that for any non-trivial game, the trees are too large, so you search to a certain depth and then cop out with a "board evaluation function" and look for one of those. I think your third bullet point is in this vein.
The board evaluation function is the magic, and probably a good candidate for using either a genetic algorithm, or a genetic program, either of which might be used in conjunction with a neural network. The basic idea is that you are trying to design (or evolve, actually) a function that takes as input a board position, and outputs a single number. Large numbers correspond to strong positions, and small numbers to weak positions. There is a famous paper by Chellapilla and Fogel showing how to do this for a game of Checkers:
http://library.natural-selection.com/Library/1999/Evolving_NN_Checkers.pdf
I think that's a great paper, tying three great strands of AI together: Adversarial search, genetic algorithms, and neural networks. It should give you some inspiration about how to represent your board, how to think about board evaluations, etc.
Be warned, though, that what you're trying to do is substantially more complex than Chellapilla and Fogel's work. That's okay-- it's 13 years later, after all, and you'll be at this for a while. You're still going to have a problem representing the board, because the AI player has imperfect knowledge of its opponent's state; initially, nothing is known but positions, but eventually as pieces are eliminated in conflict, one can start using First Order Logic or related techniques to start narrowing down individual pieces, and possibly even probabilistic methods to infer information about the whole set. (Some of these may be beyond the scope of an undergrad project.)
The fact you are having problems coming up with a representation for an actual strategy is not that surprising. In fact I would argue that it is the most challenging part of what you are attempting. Unfortunately, I haven't heard of Stratego so being a bit lazy I am going to assume you said chess.
The trouble is that a chess strategy is rather a complex thing. You suggest in your answer containing lots of transitions between board positions in the GA, but a chess board has more possible positions than the number of atoms in the universe this is clearly not going to work very well. What you will likely need to do is encode in the GA a series of weights/parameters that are attached to something that takes in the board position and fires out a move, I believe this is what you are hinting at in your second suggestion.
Probably the simplest suggestion would be to use some sort of generic function approximation like a neural network; Perceptrons or Radial Basis Functions are two possibilities. You can encode weights for the various nodes into the GA, although there are other fairly sound ways to train a neural network, see Backpropagation. You could perhaps encode the network structure instead/as well, this also has the advantage that I am pretty sure a fair amount of research has been done into developing neural networks with a genetic algorithm so you wouldn't be starting completely from scratch.
You still need to come up with how you are going to present the board to the neural network and interpret the result from it. Especially, with chess you would have to take note that a lot of moves will be illegal. It would be very beneficial if you could encode the board and interpret the result such that only legal moves are presented. I would suggest implementing the mechanics of the system and then playing around with different board representations to see what gives good results. A few ideas top of the head ideas to get you started could be, although I am not really convinced any of them are especially great ways to do this:
A bit string with all 64 squares one after another with a number presenting what is present in each square. Most obvious, but probably a rather bad representation as a lot of work will be required to filter out illegal moves.
A bit string with all 64 squares one after another with a number presenting what can move to each square. This has the advantage of embodying the covering concept of chess where you what to gain as much coverage of the board with your pieces as possible, but still has problems with illegal moves and dealing with friendly/enemy pieces.
A bit string with all 32 pieces one after another with a number presenting the location of that piece in each square.
In general though I would suggest that chess is rather a complex game to start with, I think it will be rather hard to get something playing to standard which is noticeably better than random. I don't know if Stratego is any simpler, but I would strongly suggest you opt for a fairly simple game. This will let you focus on getting the mechanics of the implementation correct and the representation of the game state.
Anyway hope that is of some help to you.
EDIT: As a quick addition it is worth looking into how standard chess AI's work, I believe most use some sort of Minimax system.
When you say "tactic", do you mean you want the GA to give you a general algorithm to play the game (i.e. evolve an AI) or do you want the game to use a GA to search the space of possible moves to generate a move at each turn?
If you want to do the former, then look into using Genetic programming (GP). You could try to use it to produce the best AI you can for a fixed tree size. JGAP already comes with support for GP as well. See the JGAP Robocode example for an instance of this. This approach does mean you need a domain specific language for a Stratego AI, so you'll need to think carefully how you expose the board and pieces to it.
Using GP means your fitness function can just be how well the AI does at a fixed number of pre-programmed games, but that requires a good AI player to start with (or a very patient human).
#DonAndre's answer is absolutely correct for movement. In general, problems involving state-based decisions are hard to model with GAs, requiring some form of GP (either explicit or, as #DonAndre suggested, trees that are essentially declarative programs).
A general Stratego player seems to me quite challenging, but if you have a reasonable Stratego playing program, "Setting up your Stratego board" would be an excellent GA problem. The initial positions of your pieces would be the phenotype and the outcome of the external Stratego-playing code would be the fitness. It is intuitively likely that random setups would be disadvantaged versus setups that have a few "good ideas" and that small "good ideas" could be combined into fitter-and-fitter setups.
...
On the general problem of what a decision tree, even trying to come up with a simple example, I kept finding it hard to come up with a small enough example, but maybe in the case where you are evaluation whether to attack a same-ranked piece (which, IIRC destroys both you and the other piece?):
double locationNeed = aVeryComplexDecisionTree();
if(thatRank == thisRank){
double sacrificeWillingness = SACRIFICE_GENETIC_BASE; //Assume range 0.0 - 1.0
double sacrificeNeed = anotherComplexTree(); //0.0 - 1.0
double sacrificeInContext = sacrificeNeed * SACRIFICE_NEED_GENETIC_DISCOUNT; //0.0 - 1.0
if(sacrificeInContext > sacrificeNeed){
...OK, this piece is "willing" to sacrifice itself
One way or the other, the basic idea is that you'd still have a lot of coding of Stratego-play, you'd just be seeking places where you could insert parameters that would change the outcome. Here I had the idea of a "base" disposition to sacrifice itself (presumably higher in common pieces) and a "discount" genetically-determined parameter that would weight whether the piece would "accept or reject" the need for a sacrifice.
I would just like to know the various AI algorithms or logics used in arcade/strategy games for finding/selecting best target to attack for individual unit.
Because, I had to write an small AI logic, where their will be group of unit were attacked by an various tankers, so i am stuck in getting the better logic or algorithm for selecting an best target for unit to attack onto the tankers.
Data available are:
Tanker position, range, hitpoints, damage.
please anybody know the best suitable algorithm/logic for solving this problem, respond early.
Thanks in advance,
Ramanand.
I'm going to express this in a perspective similar to RPG gamers:
What character would you bring down first in order to strike a crippling blow to the rest of your enemies? It would be common sense to bring down the healers of the party, as they can heal the rest of the team. Once the healers are gone, the team needs to use medicine - which is limited in supply - and once medicine is exhausted, the party is screwed.
Similar logic would apply to the tank program. In your AI, you need to figure out which tanks provide the most strength and support to the user's fleet, and eliminate them first. Don't focus on any other tanks unless they become critical in achieving their goal: Kill the strongest, most useful members of the group first.
So I'm going to break down what I feel is most likely pertains to the attributes of your tanks.
RANGE: Far range tanks can hit from a distance but have weak STRENGTH in their attacks.
TANKER POSITION: Closer tanks are faster tanks, but have less STRENGTH in their attacks. Also low HITPOINTS because they're meant for SPEED, and not for DAMAGE.
TANKER HP: Higher HP means a slower-moving tank, as they're stronger. But they won't be close to the front lines.
DAMAGE: Higher DAMAGE means a STRONGER tank with lots of HP, but SLOWER as well to move.
So if I were you, I'd focus first on the tanks that have the highest HP/strongest attacks, followed by the closest ones, and then worry about the ranged tanks - you can't do anything to them anyway until they move into your attack radius :P
And the algorithm would be pretty simple. if you have a list of tanks in a party, create a custom sort for them (using CompareTo) and sort the tanks by class with the highest possible HP to the top of the list, followed by tanks with their focus being speed, and then range.
And then go through each item in the list. If it is possible to attack Tank(0), attack. If not, go to Tank(1).
The goal is to attack only one opponent at a time and receive fire from at most one enemy at a time (though, preferably, none).
Ideally, you would attack the tanks by remaining behind cover and flanking them with surprise attacks. This allows you to destroy the tanks one at a time, while receiving no or little fire.
If you don't have cover, then you should use the enemy as cover. Move into a position that puts the enemy behind the enemy. This also improves your chance to hit.
You can also use range to reduce fire from multiple enemies. Retreat until you are only within range of one enemy.
If the enemies can all fire on you, you want to attack one target until it is no longer a threat, then move on to the next target. The goal is to reduce the amount of fire that you receive as quickly as possible.
If more than one enemy can fire on you at the same time, and you can choose your target, you should fire at the one that allows you to reduce the most amount of damage for the least cost. Simply divide the hit points by the damage, and attack the one with the smallest result. You should also figure in any other relevant stats. Range probably affects you and the enemy equally, but considering the ability to maneuver out of the way of fire, closer enemies are more harmful and should be given some weight in the calculation.
If moving decreases the likelihood of being hit, then you should keep moving, typically by circling your opponent to stay at their flank.
Team tactics would mostly include flanking and diversions.
What's the ammo situation, and is it possible to miss a stationary target?
Based on your comments it sounds like you already have some adhoc set of rules or heuristics to give you something around 70% success based on your own measures, and you want to optimize this further to get a higher win rate.
As a general solution method I would use a hill-climbing algorithm. Since I don't know the details of your current algorithm that is responsible for the 70% success rate, I can only describe in abstract terms how to adapt hill-climbing to optimize your algorithm.
The general principle of hill-climbing is as follows. Hopefully, a small change in some numeric parameter of your current algorithm would be responsible for a small (hopefully linear) change in the resulting success rate. If this is true then you would first parameterize your current set of rules -- meaning you must decide in your current algorithm which numeric parameters may be tweaked and optimized to achieve a higher success rate. Once you've decided what they are, the learning process is straight-forward. Start with your current algorithm. Generate a variety of new algorithms with slightly tweaked parameters than before, and run your simulations to evaluate the performance of this new set of algorithms. Pick the best one as your next starting point. Repeat this process until the algorithm can't get any better.
If your algorithm is a set of if-then rules (this includes rule-matching systems), and improving the performance involves reordering or restructuring those rules, then you may want to consider genetic algorithms, which is a little more complex. To apply genetic algorithms, it is essential that you define the mutation and crossover operators such that a single application of mutation or crossover results in a small change in the overall performance while a many applications of mutation and crossover results in a large change in the overall performance of your algorithm. I'm not an expert in this field but there should be much that comes up when you google for "genetic algorithms on decision trees". The pitfall to avoid is that if you simply consider swapping branches in a decision tree for the mutation operator, a single application might modify the root of your decision tree, generating a huge performance difference. This typically adds too much noise for a genetic algorithm, so my advice in this approach is to be very careful about the encoding of your operators.
Note that these two methods are very popular AI methods for learning or improving your current algorithm. You would do all of these simulations and learning offline. Then you would simply deploy the resulting, learned algorithm.