In the code examples from the SAT4J documentation, calling the solver multiple times on the same SAT problem always yields the same solution, even if multiple possible solutions exist - that is, the result is deterministic.
I'm looking for a way to get different solutions on multiple runs, that is, a nondeterministic/random result. For each possible solution, there should be a non-zero probability for the solution to be picked. Ideally, every solution should be picked with the same probability, but that's not a strict requirement.
I'm aware of the possibility to (deterministically) iterate over all solutions and just take a random one, but that's not a feasible solution in my case since there are too many solutions to begin with, and calculating them all takes too long.
Yes, Sat4j is by default deterministic: it will always find the same solution if you run it several times on the same problem from the command line.
The way to add some non determinism in the heuristics is to use the RandomWalkDecorator, as found for instance in the GreedySolver in org.sat4j.minisat.SolverFactory.
Note however that if you several times such solver from the command line :
java -jar org.sat4j.core.jar GreedySolver file.cnf
you will still be deterministic, since the pseudo random numbers generator is seeded by a constant.
Thus you need to ask several models within your Java code.
As mentioned in your question, you can use a ModelIterator decorator with a bound for that:
ISolver solver = SolverFactory.newGreedySolver();
ModelIterator mi = new ModelIterator(solver,10); // look for 10 models
Related
What is the difference between np.random.seed(0), np.random.seed(42), and np.random.seed(..any number). what is the function of the number in parentheses?
python uses the iterative Mersenne Twister algorithm to generate pseudo-random numbers [1]. The seed is simply where we start iterating.
To be clear, most computers do not have a "true" source of randomness. It is kind of an interesting thing that "randomness" is so valuable to so many applications, and is quite hard to come by (you can buy a specialized device devoted to this purpose). Since it is difficult to make random numbers, but they are nevertheless necessary, many, many, many, many algorithms have been developed to generate numbers that are not random, but nevertheless look as though they are. Algorithms that generate numbers that "look randomish" are called pseudo-random number generators (PRNGs). Since PRNGs are actually deterministic, they can't simply create a number from the aether and have it look randomish. They need an input. It turns out that using some complex operations and modular arithmetic, we can take in an input, and get another number that seems to have little or no relation to the input. Using this intuition, we can simply use the previous output of the PRNG as the next input. We then get a sequence of numbers which, if our PRNG is good, will seem to have no relation to each other.
In order to get our iterative PRNG started, we need an initial input. This initial input is called a "seed". Since the PRNG is deterministic, for a given seed, it will generate an identical sequence of numbers. Usually, there is a default seed that is, itself, sort of randomish. The most common one is the current time. However, the current time isn't a very good random number, so this behavior is known to cause problems sometimes. If you want your program to run in an identical manner each time you run it, you can provide a seed (0 is a popular option, but is entirely arbitrary). Then, you get a sequence of randomish numbers, but if you give your code to someone they can actually entirely recreate the runtime of the program as you witnessed it when you ran it.
That would be the starting key of the generator. Typically if you want to get reproducible results you'll use the same seed over and over again throughout your simulations.
You are setting the seed of the random number generator so you can get reproducible results. Example.
np.random.seed(0)
np.random.randint(0,100,10)
Output:
array([44, 47, 64, 67, 67, 9, 83, 21, 36, 87])
Now, if you ran the same code your computer, you should get the same 10 number output from the random integers from 0 to 100.
I am building a pymc model which must evaluate a very cpu expensive function (up to 1 sec per call on a very decent hardware). I am trying to limit the explored parameter space to meaningful solutions by means of a potential (the sum of a list of my variables has to stay within a given range). This works but I noticed that even when my potential returns an infinite value and forbids the parameters choice, this function gets evaluated. Is there a way to prevent that? Can one force the sampler to use a given evaluation sequence (pick up the necessary variables, check if the potential is ok and proceed if allowed)
I thought of using the potential inside the function itself and use it to determine whether it must proceed or immediately return, but is there a better way?
Jean-François
I am not aware of a way of ordering the evaluation of the potentials. This might not be the best way of doing so, but you might be able to check if the parameters are within reasonable at the beginning of the simulation. If the parameters are not within reasonable bounds you can return a value that will create your posterior to be zero.
Another option is to create a function for your likelihood. At the beginning of this function you could check if the parameters are within reasonable limits. If they are not you can return -inf without running your simulation. If they are reasonable you can run your model and calculate the log(p).
This is definitely not an elegant solution but it should work.
Full disclosure - I am not by any means a pymc expert.
I have a model implemented in OPL. I want to use this model to implement a local search in java. I want to initialize solutions with some heuristics and give these initial solutions to cplex find a better solution based on the model, but also I want to limit the search to a specific neighborhood. Any idea about how to do it?
Also, how can I limit the range of all variables? And what's the best: implement these heuristics and local search in own opl or in java or even C++?
Thanks in advance!
Just to add some related observations:
Re Ram's point 3: We have had a lot of success with approach b. In particular it is simple to add constraints to fix the some of the variables to values from a known solution, and then re-solve for the rest of the variables in the problem. More generally, you can add constraints to limit the values to be similar to a previous solution, like:
var >= previousValue - 1
var <= previousValue + 2
This is no use for binary variables of course, but for general integer or continuous variables can work well. This approach can be generalised for collections of variables:
sum(i in indexSet) var[i] >= (sum(i in indexSet) value[i])) - 2
sum(i in indexSet) var[i] <= (sum(i in indexSet) value[i])) + 2
This can work well for sets of binary variables. For an array of 100 binary variables of which maybe 10 had the value 1, we would be looking for a solution where at least 8 have the value 1, but not more than 12. Another variant is to limit something like the Hamming distance (assume that the vars are all binary here):
dvar int changed[indexSet] in 0..1;
forall(i in indexSet)
if (previousValue[i] <= 0.5)
changed[i] == (var[i] >= 0.5) // was zero before
else
changed[i] == (var[i] <= 0.5) // was one before
sum(i in indexSet) changed[i] <= 2;
Here we would be saying that out of an array of e.g. 100 binary variables, only a maximum of two would be allowed to have a different value from the previous solution.
Of course you can combine these ideas. For example, add simple constraints to fix a large part of the problem to previous values, while leaving some other variables to be re-solved, and then add constraints on some of the remaining free variables to limit the new solution to be near to the previous one. You will notice of course that these schemes get more complex to implement and maintain as we try to be more clever.
To make the local search work well you will need to think carefully about how you construct your local neighbourhoods - too small and there will be too little opportunity to make the improvements you seek, while if they are too large they take too long to solve, so you don't get to make so many improvement steps.
A related point is that each neighbourhood needs to be reasonably internally connected. We have done some experiments where we fixed the values of maybe 99% of the variables in a model and solved for the remaining 1%. When the 1% was clustered together in the model (e.g. all the allocation variables for a subset of resources) we got good results, while in comparison we got nowhere by just choosing 1% of the variables at random from anywhere in the model.
An often overlooked idea is to invert these same limits on the model, as a way of forcing some changes into the solution to achieve a degree of diversification. So you could add a constraint to force a specific value to be different from a previous solution, or ensure that at least two out of an array of 100 binary variables have a different value from the previous solution. We have used this approach to get a sort-of tabu search with a hybrid matheuristic model.
Finally, we have mainly done this in C++ and C#, but it would work perfectly well from Java. Not tried it much from OPL, but it should be fine too. The key for us was being able to traverse the problem structure and use problem knowledge to choose the sets of variables we freeze or relax - we just found that easier and faster to code in a language like C#, but then the modelling stuff is more difficult to write and maintain. We are maybe a bit "old-school" and like to have detailed fine-grained control of what we are doing, and find we need to create many more arrays and index sets in OPL to achieve what we want, while we can achieve the same effect with more intelligent loops etc without creating so many data structures in a language like C#.
Those are several questions. So here are some pointers and suggestions:
In Cplex, you give your model an initial solution with the use of IloOplCplexVectors()
Here's a good example in IBM's documentation of how to alter CPLEX's solution.
Within OPL, you can do the same. You basically set a series of values for your variables, and hand those over to CPLEX. (See this example.)
Limiting the search to a specific neighborhood: There is no easy way to respond without knowing the details. But there are two ways that people do this:
a. change the objective to favor that 'neighborhood' and make other areas unattractive.
b. Add constraints that weed out other neighborhoods from the search space.
Regarding limiting the range of variables in OPL, you can do it directly:
dvar int supply in minQty..maxQty;
Or for a whole array of decision variables, you can do something along the lines of:
range CreditsAllowed = 3..12;
dvar int credits[student] in CreditsAllowed;
Hope this helps you move forward.
I'm curious how many test cases others have for a site similar to mine. It's your basic CRUD with business workflow website. 3 user roles, a couple input pages, a couple search pages, a business rule engine, etc. Maybe 50k lines of .NET code (workflow and persistence altogether). DB with about 10 main tables plus about 100 supporting tables (lookups, logs, etc.). The main UI for entering data is quite big, around 100 data fields, multiple grids, about 5 action/submit type buttons.
I know this is vague and I'm only hoping for order of magnitude figures. I'm also thinking of basic test cases, not code coverage type cases. But like if I told you we had 25 test cases I'm sure you'd say way WAY not enough. So I'm just looking for ballpark figures.
TIA
I would have as many test cases as it takes to ensure a high level of confidence in the system.
The number of tables, rules, lines of code, etc is actually immaterial.
You should have the appropriate unit tests to ensure your domain objects and business rules are firing correctly. You should have tests to ensure your queries execute appropriately (this is a harder one).
You might even want to have test cases for paths through the software. In other words, click here, get this page, click there, edit a field, save the page, go back... This type is the most difficult as the tests are usually recorded and have to be rerecorded when the pages change (ie: a field is added or removed).
Generally speaking it's more about coverage than number of tests. You want your tests to cover as much of the applications funcionality as is feasible. Note that I didn't say possible. You can cover an entire application (100%) with test cases, but for every little change, bug fix, etc you'll have to recode those tests. This is more desired for a mature app. For newer apps you don't want to hamstring your developers and QA team that way as they'll spend inordinate amounts of time fixing/changing unit tests...
For any system, you could easily spend as much time developing your automated tests as you do the system itself. In some cases, even more.
As for our group, we tend to have lots of unit tests. However, for testing paths through the system we only record those once a particular area has moved into a "maintenance" type of mode. Meaning we expect little change for quite a while in that area and the path test is simply to ensure no one jacked it up.
UPDATE: the comments here led me to the following:
Going a little further: Let's examine 1 small piece of code:
Int32 AddNumbers(Int32 a, Int32 b) {
return a+b;
}
On the face of it you could get away with a single test:
Int32 result = AddNumbers(1,2);
Assert.Equals(result, 3);
However, that probably isn't enough. What happens if you do this:
Int32 result = AddNumbers(Int32.MaxValue, 1);
Assert.Equals(result, (Int32.MaxValue+1));
Now we have a failure. Here's another one:
Int32 result = AddNumbers(Int32.MinValue, -1);
Assert.Equals(result, (Int32.MinValue-1));
So, we have an extremely simple method that requires at least 3 tests. The initial to see if it can give any result, then 2 for bounds checking. That's 3 tests for essentially 2 lines of code (method definition and the one line computation).
As your code becomes more complex, things get really dicey:
Decimal DivideThis(Decimal a, Decimal b) {
result = Decimal.Divide(a,b);
}
This slight change introduces yet another exception condition beyond bounds: DivideByZero. So now we are up to 4 tests required for 2 lines of code.
Now, let's simplify it a bit:
String AppendData(String data, String toAppend) {
return String.Format("{0}{1}", data, toAppend);
}
Our test case here is:
String result = AppendData("Hello", "World");
Assert.Equals(result, "HelloWorld");
That's just one test case for the code block, with no others really needed.
What does this tell us: For starters 2 lines of code might cause us to need between 1 and 4 test cases. You mentioned 50k lines... Using that logic, you will need between 50,000 and 200,000 test cases...
Of course, life is rarely so simple. In those 50k lines of code you have, there are going to be large blocks of code that have very limited inputs. For example a mortgage interest calculator might take 3 parameters, and return 1 value (the APR). The code itself might run 100 lines or so (been awhile, just work with me). The number of test cases for this is going to be determined by edge cases along the lines of making sure you properly handle rounding.
So, let's say it's 5 cases: which brings us to 20 lines of code = 1 case. Calculating that out your 50k lines might result in 2,500 test cases. Obviously much smaller than what we expected above.
Finally, I'm going to throw another wrinkle into the mix. Some test systems can handle inputs and your assertions coming from a data file. Considering our first one we could have a data file that has a line for each parameter combination we want to test. In this scenario, we only need 1 test case to cover 3 (or more..) possible conditions.
The test case might look like (pseudo code):
read input file.
parse expected result, parameter 1, parameter 2
run method
assert method result = parsed result
repeat for each line of the file
With that capability, we are down to 1 test case per scenario. I would say 1 per method, but the reality is that most methods are rarely standalone and it's entirely possible that numerous methods are implicitly tested through explicit testing of others; therefore not requiring their own individual tests.
This leads me to this: It is impossible to determine the right number of test cases without a full understanding of your code base. 5 cases that are at the UI level might be enough for complete coverage depending on the complexity of the tests; or it might take thousands. Therefore it's much better to base it on code coverage. What percentage of the code, and branching logic, are you testing?
If you ask a car salesman for a rough price of a car and he would give me that price, I wouldn't buy my car there, because he forgot to ask me some important questions. What kind of car do you want? Which extras do you want on the car? etc.
Same for number of test cases .... If a hiring manager would ask me that question I would probably give him the following answer.
#test cases = between #Requirements*2 and #Requirements*infinite (some requirements can lead to bollions of possibilities)
I also would say that based on my experience the number would realistically be #Requirements*5 (is the number I use at the initial phase, for projects with new, changed and omitted functionality)
where the following error margin has to be taken depending on the phase I am making this estimate:
Initiation phase : error margins = 400%
...
Testing phase : error margin = 10%
By the time you start the testing phase, detailed requirements/specs are available, volatillity of requirements is stabilized, creep of requirements is almost zero, etc.
At that time I also will be able to give better estimates ...
Y
I have 6 parameters for which I know maxi and mini values. I have a complex function that includes the 6 parameters and return a 7th value (say Y). I say complex because Y is not directly related to the 6 parameters; there are many embeded functions in between.
I would like to find the combination of the 6 parameters which returns the highest Y value. I first tried to calculate Y for every combination by constructing an hypercube but I have not enough memory in my computer. So I am looking for kinds of markov chains which progress in the delimited parameter space, and are able to overpass local peaks.
when I give one combination of the 6 parameters, I would like to know the highest local Y value. I tried to write a code with an iterative chain like a markov's one, but I am not sure how to process when the chain reach an edge of the parameter space. Obviously, some algorythms should already exist for this.
Question: Does anybody know what are the best functions in R to do these two things? I read that optim() could be appropriate to find the global peak but I am not sure that it can deal with complex functions (I prefer asking before engaging in a long (for me) process of code writing). And fot he local peaks? optim() should not be able to do this
In advance, thank you for any lead
Julien from France
Take a look at the Optimization and Mathematical Programming Task View on CRAN. I've personally found the differential evolution algorithm to be very fast and robust. It's implemented in the DEoptim package. The rgenoud package is another good candidate.
I like to use the Metropolis-Hastings algorithm. Since you are limiting each parameter to a range, the simple thing to do is let your proposal distribution simply be uniform over the range. That way, you won't run off the edges. It won't be fast, but if you let it run long enough, it will do a good job of sampling your space. The samples will congregate at each peak, and will spread out around them in a way that reflects the local curvature.