Hello wonderful community!
I'm currently writing a small game in my spare time. It takes place in a large galaxy, where the player has control of some number of Stars. On these stars you can construct Buildings, each of which has some number (0..*) of inputs, and produce some number of outputs. These buildings have a maximum capacity/throughput, and scaling down it's inputs scales down it's outputs by an equal amount. I'd like to find a budgeting algorithm that optimizes (or approximates) the throughput of all the buildings. It seems like some kind of max-flow problem, but none of the flow optimization algorithms I've read have differing types of inputs or dependent outputs.
The toy "tech tree" I've been playing with is:
Solar plant - None => 2 energy output.
Extractor - 1 energy => 1 ore output
Refinery - 1 energy, 1 ore => 1 metal
Shipyard - 1 metal, 2 energy => 1 ship
I'm willing to accept sub-optimal algorithms, and I'm willing to make the guarantee that the inputs/outputs have no cycles (they form a DAG from building to building). The idea is to allow reasonable throughput and tech tree complexity, without player intervention, because on the scale of hundreds or thousands of stars, allowing the player to manually define the budgeting strategy isn't fun and gives players who no-life it a distinct advantage.
My current strategy is to build up a DAG, and give the resources a total ordering (Ships are better than Metal is better than Ore is better than energy), then, looping through each of the resources, find the most "descendant" building which produces that resource, allow it to greedily grab from it's inputs recursively (a shipyard would take 2 energy, and 1 metal, and then the refinery would grab 1 energy and 1 ore, etc), then find any "liars" in the graph (the solar plant is providing 4 energy, when it's maximum is 2), scale down their production and propagate the changes forward. Once everything is resolved for the DAG, remove the terminal element (shipyard) from the graph and subtract the "current thruoghput" of each edge from the maximum throughput of the building, and then repeat the process for the next type of resource. I thought I'd ask people far more intelligent than me if there's a better way. :)
Related
I run an infectious disease spread model similar to "VIRUS" model in the model library changing the "infectiousness".
I did 20 runs each for infectiousness values 98% , 95% , 93% and the Maximum infected count was 74.05 , 73 ,78.9 respectively. (peak was at tick 38 for all 3 infectiousness values)
[I took the average of the infected count for each tick and took the maximum of these averages as the "maximum infected".]
I was expecting the maximum infected count to decrease when the infectiousness is reduced, but it didn't. As per what I understood this happens, because I considered the average values of each simulation run. (It is like I am considering a new simulation run with average infected count for each tick ).
I want to say that, I am considering all 20 simulation runs. Is there a way to do that other than the way I used the average?
In the Models Library Virus model with default parameter settings at other values, and those high infectiousness values, what I see when I run the model is a periodic variation in the numbers three classes of person. Look at the plot in the lower left corner, and you'll see this. What is happening, I believe, is this:
When there are many healthy, non-immune people, that means that there are many people who can get infected, so the number of infected people goes up, and the number of healthy people goes down.
Soon after that, the number of sick, infectious people goes down, because they either die or become immune.
Since there are now more immune people, and fewer infectious people, the number of non-immune healthy grows; they are reproducing. (See "How it works" in the Info tab.) But now we have returned to the situation in step 1, ... so the cycle continues.
If your model is sufficiently similar to the Models Library Virus model, I'd bet that this is part of what's happening. If you don't have a plot window like the Virus model, I recommend adding it.
Also, you didn't say how many ticks you are running the model for. If you run it for a short number of ticks, you won't notice the periodic behavior, but that doesn't mean it hasn't begun.
What this all means that increasing infectiousness wouldn't necessarily increase the maximum number infected: a faster rate of infection means that the number of individuals who can infected drops faster. I'm not sure that the maximum number infected over the whole run is an interesting number, with this model and a high infectiousness value. It depends what you are trying to understand.
One of the great things about NetLogo and some other ABM systems is that you can watch the system evolve over time, using various tools such as plots, monitors, etc. as well as just looking at the agents move around or change states over time. This can help you understand what is going on in a way that a single number like an average won't. Then you can use this insight to figure out a more informative way of measuring what is happening.
Another model where you can see a similar kind of periodic pattern is Wolf-Sheep Predation. I recommend looking at that. It may be easier to understand the pattern. (If you are interested in mathematical models of this kind of phenomenon, look up Lotka-Volterra models.)
(Real virus transmission can be more complicated, because a person (or other animal) is a kind of big "island" where viruses can reproduce quickly. If they reproduce too quickly, this can kill the host, and prevent further transmission of the virus. Sometimes a virus that reproduces more slowly can harm more people, because there is time for them to infect others. This blog post by Elliott Sober gives a relatively simple mathematical introduction to some of the issues involved, but his simple mathematical models don't take into account all of the complications involved in real virus transmission.)
EDIT: You added a comment Lawan, saying that you are interested in modeling COVID-19 transmission. This paper, Variation and multilevel selection of SARS‐CoV‐2 by Blackstone, Blackstone, and Berg, suggests that some of the dynamics that I mentioned in the preceding remarks might be characteristic of COVID-19 transmission. That paper is about six months old now, and it offered some speculations based on limited information. There's probably more known now, but this might suggest avenues for further investigation.
If you're interested, you might also consider asking general questions about virus transmission on the Biology Stackexchange site.
Currently I'm building my monitoring services for my e-commerce Server, which mostly focus on CPU/RAM usage. It's likely Anomaly Detection on Timeseries data.
My approach is building LSTM Neural Network to predict next CPU/RAM value on chart trending and compare with STD (standard deviation) value multiply with some number (currently is 10)
But in real life conditions, it depends on many differents conditions, such as:
1- Maintainance Time (in this time "anomaly" is not "anomaly")
2- Sales time in day-off events, holidays, etc., RAM/CPU usages increase is normal, of courses
3- If percentages of CPU/RAM decrement are the same over 3 observations: 5 mins, 10 mins & 15 mins -> Anomaly. But if 5 mins decreased 50%, but 10 mins it didn't decrease too much (-5% ~ +5%) -> Not an "anomaly".
Currently I detect anomaly on formular likes this:
isAlert = (Diff5m >= 10 && Diff10m >= 15 && Diff30m >= 40)
where Diff is Different Percentage in Absolute value.
Unfortunately I don't save my "pure" data for building neural network, for example, when it detects anomaly, I modified that it is not an anomaly anymore.
I would like to add some attributes to my input for model, such as isMaintenance, isPromotion, isHoliday, etc. but sometimes it leads to overfitting.
I also want to my NN can adjust baseline over the time, for example, when my Service is more popular, etc.
There are any hints on these aims?
Thanks
I would say that an anomaly is an unusual outcome, i.e. a outcome that's not expected given the inputs. As you've figured out, there are a few variables that are expected to influence CPU and RAM usage. So why not feed those to the network? That's the whole point of Machine Learning. Your network will make a prediction of CPU usage, taking into account the sales volume, whether there is (or was) a maintenance window, etc.
Note that you probably don't need an isPromotion input if you include actual sales volumes. The former is a discrete input, and only captures a fraction of the information present in the totalSales input
Machine Learning definitely needs data. If you threw that away, you'll have to restart capturing it. As for adjusting the baseline, you can achieve that by overweighting recent input data.
I am making an AI for a zero-sum 4-player board game. It's actually not zero-sum (the 4 players will "die" when they lose all their lives, so there will be a player who died first, second, third and a player who survived. However, I am telling the AI that only surviving counts as a win and anything else is a lose) After some research, I figured I would use a minimax algorithm in combination with a heuristic function. I came across this question and decided to do the same as the OP of that question - write an evolutionary algorithm that gives me the best weights.
However, my heuristic function is different from the one the OP of that question had. Mine takes 9 weights and is a lot slower, so I can't let the agents play 1000 games (takes too much time) or breed them with the crossover method (how do I do a crossover with 9 weights?).
So I decided to come up with my own method of determining fitness and breeding. And this question is only about the fitness function.
Here are my attempts at this.
First Attempt
For each agent A in a randomly generated population of 50 agents, select 3 more agents from the population (with replacement but not the same agent as A itself) and let the 4 agents play a game where A is the first player. Select another 3 and play a game where A is the second player, and so on. For each of these 4 games, if A died first, its fitness does not change. If A died second, its fitness is increased by 1. If it died third, its fitness is increased by 2. If it survived, its fitness is increased by 3. Therefore, I concluded that the highest fitness one can get is 12 (surviving/wining all 4 games -> 3 + 3 + 3 + 3).
I ran this for 7 generations and starting from the first generation, the highest fitness is as high as 10. And I calculated the average fitness of the top 10 agents, but the average didn't increase a bit throughout the 7 generations. It even decreased a little.
I think the reason why this didn't work is because there's gotta be a few agents that got lucky and got some poor performing agents as its opponents.
Second Attempt
The game setups are the same as my first attempt but instead of measuring the results of each game, I decided to measure how many moves did that agent make before it died.
After 7 generations the average fitness of top 10 does increase but still not increasing as much as I think it should.
I think the reason why this failed is that the game is finite, so there is a finite number of moves you can make before you die and the top performing agents pretty much reached that limit. There is no room for growth. Another reason is that the fitness of the player who survived and the fitness of the player who died third differs little.
What I want
From my understanding of EAs (correct me if I'm wrong), the average fitness should increase and the top performing individual's fitness should not decrease over time.
My two attempts failed at both of these. Since the opponents are randomly selected, the top performing agent in generation 1 might get stronger opponents in the next generation, and thus its fitness decreases.
Notes
In my attempts, the agents play 200 games each generation and each generation takes up to 3 hours, so I don't want to let them play too many games.
How can I write a fitness function like this?
Seven generations doesn't seem like nearly enough to get a useful result. Especially for a game, I would expect something like 200+ generations to be more realistic. You could do a number of things:
Implement elitism in order to ensure the survival of the best individual(s).
The strength of evolution stems from repeated mutation and crossover, so I'd recommend letting the agents play only a few games per generation (say, 5 ~ 10), at least at the beginning, and then evolve the population. You might even want to do only one game per generation.
In this regard, you could adopt a continuous evolution strategy. What this means is that as soon as an agent dies, they are subjected to mutation, and as soon as an agent wins, they can produce offspring. Or any combination of the two. The point is that the tournament is ongoing, everyone can play against anyone else. This is a little more "organic" in the sense that it does not have strictly defined generations, but it should speed up the process (especially if you can parallelise the evaluation).
I hope that helps. The accepted answer in the post you referenced has a good suggestion about the way you could implement crossover.
Just starting to play around with Neural Networks for fun after playing with some basic linear regression. I am an English teacher so don't have a math background and trying to read a book on this stuff is way over my head. I thought this would be a better avenue to get some basic questions answered (even though I suspect there is no easy answer). Just looking for some general guidance put in layman's terms. I am using a trial version of an Excel Add-In called NEURO XL. I apologize if these questions are too "elementary."
My first project is related to predicting a student's Verbal score on the SAT based on a number of test scores, GPA, practice exam scores, etc. as well as some qualitative data (gender: M=1, F=0; took SAT prep class: Y=1, N=0; plays varsity sports: Y=1, N=0).
In total, I have 21 variables that I would like to feed into the network, with the output being the actual score (200-800).
I have 9000 records of data spanning many years/students. Here are my questions:
How many records of the 9000 should I use to train the network?
1a. Should I completely randomize the selection of this training data or be more involved and make sure I include a variety of output scores and a wide range of each of the input variables?
If I split the data into an even number, say 9x1000 (or however many) and created a network for each one, then tested the results of each of these 9 on the other 8 sets to see which had the lowest MSE across the samples, would this be a valid way to "choose" the best network if I wanted to predict the scores for my incoming students (not included in this data at all)?
Since the scores on the tests that I am using as inputs vary in scale (some are on 1-100, and others 1-20 for example), should I normalize all of the inputs to their respective z-scores? When is this recommended vs not recommended?
I am predicting the actual score, but in reality, I'm NOT that concerned about the exact score but more of a range. Would my network be more accurate if I grouped the output scores into buckets and then tried to predict this number instead of the actual score?
E.g.
750-800 = 10
700-740 = 9
etc.
Is there any benefit to doing this or should I just go ahead and try to predict the exact score?
What if ALL I cared about was whether or not the score was above or below 600. Would I then just make the output 0(below 600) or 1(above 600)?
5a. I read somewhere that it's not good to use 0 and 1, but instead 0.1 and 0.9 - why is that?
5b. What about -1(below 600), 0(exactly 600), 1(above 600), would this work?
5c. Would the network always output -1, 0, 1 - or would it output fractions that I would then have to roundup or rounddown to finalize the prediction?
Once I have found the "best" network from Question #3, would I then play around with the different parameters (number of epochs, number of neurons in hidden layer, momentum, learning rate, etc.) to optimize this further?
6a. What about the Activation Function? Will Log-sigmoid do the trick or should I try the other options my software has as well (threshold, hyperbolic tangent, zero-based log-sigmoid).
6b. What is the difference between log-sigmoid and zero-based log-sigmoid?
Thanks!
First a little bit of meta content about the question itself (and not about the answers to your questions).
I have to laugh a little that you say 'I apologize if these questions are too "elementary."' and then proceed to ask the single most thorough and well thought out question I've seen as someone's first post on SO.
I wouldn't be too worried that you'll have people looking down their noses at you for asking this stuff.
This is a pretty big question in terms of the depth and range of knowledge required, especially the statistical knowledge needed and familiarity with Neural Networks.
You may want to try breaking this up into several questions distributed across the different StackExchange sites.
Off the top of my head, some of it definitely belongs on the statistics StackExchange, Cross Validated: https://stats.stackexchange.com/
You might also want to try out https://datascience.stackexchange.com/ , a beta site specifically targeting machine learning and related areas.
That said, there is some of this that I think I can help to answer.
Anything I haven't answered is something I don't feel qualified to help you with.
Question 1
How many records of the 9000 should I use to train the network? 1a. Should I completely randomize the selection of this training data or be more involved and make sure I include a variety of output scores and a wide range of each of the input variables?
Randomizing the selection of training data is probably not a good idea.
Keep in mind that truly random data includes clusters.
A random selection of students could happen to consist solely of those who scored above a 30 on the ACT exams, which could potentially result in a bias in your result.
Likewise, if you only select students whose SAT scores were below 700, the classifier you build won't have any capacity to distinguish between a student expected to score 720 and a student expected to score 780 -- they'll look the same to the classifier because it was trained without the relevant information.
You want to ensure a representative sample of your different inputs and your different outputs.
Because you're dealing with input variables that may be correlated, you shouldn't try to do anything too complex in selecting this data, or you could mistakenly introduce another bias in your inputs.
Namely, you don't want to select a training data set that consists largely of outliers.
I would recommend trying to ensure that your inputs cover all possible values for all of the variables you are observing, and all possible results for the output (the SAT scores), without constraining how these requirements are satisfied.
I'm sure there are algorithms out there designed to do exactly this, but I don't know them myself -- possibly a good question in and of itself for Cross Validated.
Question 3
Since the scores on the tests that I am using as inputs vary in scale (some are on 1-100, and others 1-20 for example), should I normalize all of the inputs to their respective z-scores? When is this recommended vs not recommended?
My understanding is that this is not recommended as the input to a Nerual Network, but I may be wrong.
The convergence of the network should handle this for you.
Every node in the network will assign a weight to its inputs, multiply them by their weights, and sum those products as a core part of its computation.
That means that every node in the network is searching for some coefficients for each of their inputs.
To do this, all inputs will be converted to numeric values -- so conditions like gender will be translated into "0=MALE,1=FEMALE" or something similar.
For example, a node's metric might look like this at a given point in time:
2*ACT_SCORE + 0*GENDER + (-5)*VARISTY_SPORTS ...
The coefficients for each values are exactly what the network is searching for as it converges.
If you change the scale of a value, like ACT_SCORE, you just change the scale of the coefficient that will be found by the reciporical of that scaling factor.
The result should still be the same.
There are other concerns in terms of accuracy (computers have limited capacity to represent small fractions) and speed that may enter this, but not being familiar with NEURO XL, I can't say whether or not they apply for this technology.
Question 4
I am predicting the actual score, but in reality, I'm NOT that concerned about the exact score but more of a range. Would my network be more accurate if I grouped the output scores into buckets and then tried to predict this number instead of the actual score?
This will reduce accuracy, although you should converge to a solution much faster with fewer possible outputs (scores).
Neural Networks actually describe very high-dimensional functions in their input variables.
If you reduce the granularity of that function's output space, you essentially state that you don't care about local minima and maxima in that function, especially around the borders between your output scores.
As a result, you are sacrificing information that may be an essential component of the "true" function that you are searching for.
I hope this has been helpful, but you really should break this question down into its many components and ask them separately on different sites -- potentially some of them do belong here on StackOverflow as well.
In an online manager game (like Hattrick), I want to simulate matches between two teams.
A team consists of 11 players. Every player has a strength value between 1 and 100. I take these strength values of the defensive players for each team and calculate the average. That's the defensive quality of a team. Then I take the strengths of the offensive players and I get the offensive quality.
For each attack, I do the following:
$offFactor = ($attackerTeam_offensive-$defenderTeam_defensive)/max($attackerTeam_offensive, $defenderTeam_defensive);
$defFactor = ($defenderTeam_defensive-$attackerTeam_offensive)/max($defenderTeam_defensive, $attackerTeam_offensive);
At the moment, I don't know why I divide it by the higher one of both values. But this formula should give you a factor for the quality of offense and defense which is needed later.
Then I have nested conditional statements for each event which could happen. E.g.: Does the attacking team get a scoring chance?
if ((mt_rand((-10+$offAdditionalFactor-$defAdditionalFactor), 10)/10)+$offFactor >= 0)
{ ... // the attack succeeds
These additional factors could be tactical values for example.
Do you think this is a good way of calculating a game? My users say that they aren't satisfied with the quality of the simulations. How can I improve them? Do you have different approaches which could give better results? Or do you think that my approach is good and I only need to adjust the values in the conditional statements and experiment a bit?
I hope you can help me. Thanks in advance!
Here is a way I would do it.
Offensive/Defensive Quality
First lets work out the average strength of the entire team:
Team.Strength = SUM(Players.Strength) / 11
Now we want to split out side in two, and work out the average for our defensive players, and our offensive players.]
Defense.Strength = SUM(Defensive_Players.Strength)/Defensive_Players.Count
Offense.Strength = SUM(Offense_Players.Strength)/Offense_Players.Count
Now, we have three values. The first, out Team average, is going to be used to calculate our odds of winning. The other two, are going to calculate our odds of defending and our odds of scoring.
A team with a high offensive average is going to have more chances, a team with a high defense is going to have more chance at saving.
Now if we have to teams, lets call them A and B.
Team A, have an average of 80, An offensive score of 85 and a defensive score of 60.
Team B, have an average of 70, An offensive score of 50 and a defensive score of 80.
Now, based on the average. Team A, should have a better chance at winning. But by how much?
Scoring and Saving
Lets work out how many times goals Team A should score:
A.Goals = (A.Offensive / B.Defensive) + RAND()
= (85/80) + 0.8;
= 1.666
I have assumed the random value adds anything between -1 and +1, although you can adjust this.
As we can see, the formula indicates team A should score 1.6 goals. we can either round this up/down. Or give team A 1, and calculate if the other one is allowed (random chance).
Now for Team B
B.Goals = (B.Offensive / A.Defensive) + RAND()
= (50/60) + 0.2;
= 1.03
So we have A scoring 1 and B scoring 1. But remember, we want to weight this in A's favour, because, overall, they are the better team.
So what is the chance A will win?
Chance A Will Win = (A.Average / B.Average)
= 80 / 70
= 1.14
So we can see the odds are 14% (.14) in favor of A winning the match. We can use this value to see if there is any change in the final score:
if Rand() <= 0.14 then Final Score = A 2 - 1 B Otherwise A 1 - 1 B
If our random number was 0.8, then the match is a draw.
Rounding Up and Further Thoughts
You will definitely want to play around with the values. Remember, game mechanics are very hard to get right. Talk to your players, ask them why they are dissatisfied. Are there teams always losing? Are the simulations always stagnant? etc.
The above outline is deeply affected by the randomness of the selection. You will want to normalise it so the chances of a team scoring an extra 5 goals is very very rare. But a little randomness is a great way to add some variety to the game.
There are ways to edit this method as well. For example instead of the number of goals, you could use the Goal figure as the number of scoring chances, and then have another function that worked out the number of goals based on other factors (i.e. choose a random striker, and use that players individual stats, and the goalies, to work out if there is a goal)
I hope this helps.
The most basic tactical decision in football is picking formation, which is a set of three numbers which assigns the 10 outfield players to defence, midfield and attack, respectively, e.g. 4/4/2.
If you use average player strength, you don't merely lose that tactic, you have it going backwards: the strongest defence is one with a single very good player, giving him any help will make it more likely the other team score. If you have one player with a rating of 10, the average is 10. Add another with rating 8, and the average drops (to 9). But assigning more people to defence should make it stronger, not weaker.
So first thing, you want to make everything be based on the total, not the average. The ratio between the totals is a good scale-independent way of determining which teams is stronger and by how much. Ratios tend to be better than differences, because they work in a predictable way with teams of any range of strengths. You can set up a combat results table that says how many goals are scored (per game, per half, per move, or whatever).
The next tactical choice is whether it is better to have one exceptional player, or several good ones. You can make that matter that by setting up scenarios that represent things that happen in game, e.g. a 1 on 1, a corner, or a long ball. The players involved in a scenario are first randomly chosen, then the result of the scenario is rolled for. One result can be that another scenario starts (midfield pass leads to cross leads to header chance).
The final step, which would bring you pretty much up to the level of actual football manager games, is to give players more than one type of strength rating, e.g., heading, passing, shooting, and so on. Then you use the strength rating appropriate to the scenario they are in.
The division in your example is probably a bad idea, because it changes the scale of the output variable depending on which side is better. Generally when comparing two quantities you either want interval data (subtract one from the other) or ratio data (divide one by the other) but not both.
A better approach in this case would be to simply divide the offensive score by the defensive score. If both are equal, the result will be 1. If the attacker is better than the defender, it will be greater than 1, and if the defender is stronger, it will be less than one. These are easy numbers to work with.
Also, instead of averaging the whole team, average parts of the team depending on the formations or tactics used. This will allow teams to choose to play offensively or defensively and see the pros and cons of this.
And write yourself some better random number generation functions. One that returns floating point values between -1 and 1 and one that works from 0 to 1, for starters. Use these in your calculations and you can avoid all those confusing 10s everywhere!
You might also want to ask the users what about the simulation they don't like. It's possible that, rather than seeing the final outcome of the game, they want to know how many times their team had an opportunity to attack but the defense regained control. So instead of
"Your team wins 2-1"
They want to see match highlights:
"Your team wins 2-1:
- scored at minute 15,
- other team took control and went for tried for a goal at minute 30,
but the shoot was intercepted,
- we took control again and $PLAYER1 scored a beautiful goal!
... etc
You can use something like what Jamie suggests for a starting point, choose the times at random, and maybe pick who scored the goal based on a weighted sampling of the offensive players (i.e. a player with a higher score gets a higher chance of being the one who scored). You can have fun and add random low-probability events like a red card on a player, someone injuring themselves, streakers across the field...
The average should be the number of players... using the max means if you have 3 player teams:
[4 4 4]
[7 4 1]
The second one would be considered weaker. Is that what you want? I think you would rather do something like:
(Total Scores / Total Players) + (Max Score / Total Players), so in the above example it would make the second team slightly better.
I guess it depends on how you feel the teams should be balanced.