so I'm experimenting with boolector and I have reached the point where I have N number of BoolectorNode representing N different formula. I'd like to have a function that ensures that a minimum of 0 and a maximum of N-1 formula are true at the same time. I imagine that with some loops I can achieve that but I was wondering if using some pre-existing function available in boolector I could achieve that easily.
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I need to calculate a pseudo random number in a given range (e.g. 0-150) based on another, strictly increasing number. Is there a mathematical way to solve this?
I am given one number x, which increases by 1 every day. Based on this number, I need to - somehow - calculate a number in a given range, which seems to be random.
I have a feeling that there is an easy mathematical solution for this, but sadly I am not able to find it. So any help would be appreciated. Thanks!
One sound way to do that is to hash the number x (either its binary representation or in text form) and then to use the hash to produce the 'random' number in the desired range (say by taking the first 32 bits of the hash and extracting by any known method the desired value). A cryptographic hash can be used like Sha256, but this is not necessary, MurmurHash is possibly a good one for your application.
Normally when you generate a random number, a seed value is used so that the same sequence of psuedorandom numbers isn't repeated. When a seed isn't explicitly given, many systems will use the time as a seed value.
Perhaps you could use x as a seed.
Here's an article explaining seeding: https://www.statisticshowto.com/random-seed-definition/
The problem I'm trying to solve is about the best allocation for electric vehicles (EVs) in the electrical power grid. My grid has 20 possible positions (busbar) allowed to receive one EV each. Each chromosome has length 20 and its genes can be 0 or 1, where 0 means no EV and 1 means there´s an EV at that position (busbar).
I start my population (100 individuals) with a fixed number of EVs (5, for instance) allocated randomly. And let them evolve through my GA. The GA utilizes tournament selection, 2-points crossover and flip-bit mutation. Each chromosome/individual is evaluated through a fitness function that calculate the power losses between bars (sum of RI^2). The best chromosome is the one with the lowest power losses.
The problem is that utilizing 2-points crossover and flip-bit mutation changes the fixed number of EVs that must be in the grid. I would like to know what are the best techniques for my GA operations. Besides this, I get this weird looking graphic of the most fitness chromosome throughout generations 1
I would appreciate any help/suggestions. Thanks.
You want to define your state space in such a way where the mutations you've chosen can't create an illegal configuration.
This is probably not a great fit for a genetic algorithm. If you want to pick 5 from 20, there are ~15k possibilities. Testing a population of 100 over 50 generations already gives you enough computations to have done 1/3 of the brute force work.
If you have N EV to assign on your grid, you can use chromosomes of size N, each gene being an integer representing the position of an EV. For the crossover, you first need to separate the values that are the same in both parents from the rest and apply a classic (1 or 2 points) crossover on the parts that differ, and mutate a gene randomly picking a valid available position.
I have a huge list of bit vectors (BV) that I want to group in clusters.
The idea behind this clusters is to be able to choose later BVs from each cluster and combine them for generate a BV with (almost) all-ones (which must be maximized).
For example, imagine the 1 means an app is Up and 0 is down in node X in a specific moment in time. We want to find the min list of nodes for having the app Up:
App BV for node X in cluster 1: 1 0 0 1 0 0
App BV for node Y in cluster 2: 0 1 1 0 1 0
Combined BV for App (X+Y): 1 1 1 1 1 0
I have been checking the different cluster algorithms but I did found one that takes into account this "complemental" behavior because in this case each column of the BV is not referred to a feature (only means up or down in an specific timeframe).
Regarding other algorithms like k-means or hierarchical clustering, I do not have clear if I can include in the clustering algorithm this consideration for the later grouping.
Finally, I am using the hamming distance to determine the intra-cluster and the inter-cluster distances given that it seems to be the most appropiated metric for binary data but results show me that clusters are not closely grouped and separated among them so I wonder if I am applying the most suitable group/approximation method or even if I should filter the input data previously grouping.
Any clue or idea regarding grouping/clustering method or filtering data is welcomed.
This does not at all sound like a clustering problem.
None of these algorithms will help you.
Instead, I would rather call this a match making algorithm. But I'd assume it is at least NP-hard (it resembles set cover) to find the true optimum, so you'll need to come up with a fast approximation. Best something specific to your use case.
Also you haven't specified (you wrote + but that likely isn't what you want) how to combine two 1s. Is it xor or or? Nor if it is possible to combine more than two, and what the cost is when doing so. A strategy would be to find the nearest neighbor of the inverse bitvector for each and always combine the best pair.
This question combines math and programming. I will first describe the general problem and then give an example that is (hopefully) simpler to understand.
General Question: Consider a Markov-chain process of N-states with transition matrix Π. Each state is associated with a value x_n (n in {1,…,n}). Our goal is to find the unconditional average of the first two moments (mean and var) along T-period paths conditional on (i) the path starts in a subset of states, N_0, (ii) it ends in a subset of states, N_T, and (iii) it is not going through a subset of states, N_not, in any of the periods between 1 to T-1. By saying we are interested in the unconditional average of these two moments, I basically mean what would be the average of these two moments in the stationary distribution. To be more concrete, let me illustrate the goal of the exercise in a simple case.
Simple Example: Consider a 3-state Markov-chain process with transition matrix Π, and let the three state be denoted by A, B, and C. Each of these states are associated with some value (x_A, x_B, and x_C), respectively. We are interested in what happens along paths that satisfy the following condition. The path starts at point A, after 3 periods are in either points B or C, and between periods 1 to 3 never go again through point A. Denote this condition by (#). So, for example, a path which we are interested in would be {A,B,B,C} with the associated values {x_A, x_B, x_B, x_C}. We are interested in the average and standard deviation along such paths. In particular, we would like to find the unconditional average of these first two moments in paths that satisfy (#).
Let me now propose a solution based on simulating the process. Since both T and N are quite large, this solution is too slow for my purpose.
Simulation Solution: Starting from some initial point simulate the process for a very long time period, and drop the first τ periods. Extract all paths along the simulation that satisfy condition (#) and compute the mean and std along each of these paths. Finally, simply take the average across these paths.
I’m hoping there is a better and more efficient way to achieve the goal. Since I want the solution to be accurate and the size of T and N the simulation takes a long time.
I would love to hear your thoughts and if you know of efficient methods to achieve this goal. Please let me know if something is not clear and I'll try to clarify it.
Thank you!!!
I think I know how to do this if N_0 consists of one state, let's call that state A.
The long run probability of being in A is pi(A) and can be obtained by solving pi = pi*P, with P the transition matrix.
The other thing you need to calculate is the probability of those transient paths. You probably need to introduce a modified P, where all states i in the set N_not are absorbing (i.e. P[i,i]=1 and P[i,j]=0 for j is not i). Then starting from a vector p(0) which has a 1 in the element corresponding to state A and 0 otherwise, you can keep calculating p(n) = p(n-1)*P to get the probabilities of your transient paths.
Multiply the result of that by pi(A) to get the unconditional probability.
You can probably do something like this as well when N_0 is a set, but I don't know how you should select p(0) in that case.
I have an AB PLC where I am trying to read analog values to see if the values vary more than 1V in 5 minutes? I have 10 sets of values I need to read. What would the easiest way to implement this? I can think of creating arrays to save the values each time I read them but the part I am having trouble with is, how to keep a running average of the values and compare against each time I read them.
Any help with this would be greatly appreciated!!
If I understand correctly all you want to do is see if your analog input is more or less than 1V from your set value? Just check if your value is greater than (set value + 1V) or less than (set value - 1V) every plc scan then set a bool value to true. That should be it.
I think finding an average of the analog input is not the way to go for this. But if you did want to find an average of an analog input over time you would need 3 things. Sample time, interval time, and total intervals. You would set up a sample time of, lets say 12 seconds. You will get the analog value every 12 seconds. After 60 seconds you would take the total and divide by (60/12 == 5). You would then add that value to the previous value average value that you totaled up and divide by the total number of intervals times (total intervals) you have accumulated. Hope I didn't make that to complicated.
What i understood from you question is you want check whether input voltage changed or not using the analog value you got, in my case i'm using 0 to 10v. Just simple store the analog value at max input i mean at 10v and just do the same for 0v and you can simply calculate the value for 1v. All you have do is compare the value with +/- 1v value you got from the calculation. you can do this dynamically with n-number of analog inputs(n= max analog inputs supported by your PLC.)
Have a look at FFL and FFU. They are First-In-First-Out buffers. You specify the length of the buffer you want and use FFL and FFU in pairs on the same buffer. Running averages are not that difficult to compute, and there are a number of ways to best implement depending on the platform (SLC vs CLX). The simplest method that would work on both platforms is to use a counter.ACC as a value to indirectly reference the element number of the FIFO for an addition function, then divide by the number of elements in your FIFO. This can all be done in a single multi-branch rung.
1. Load your value into FIFO buffer at some timer interval using FFL.
2. If you don't need the FIFO values 'Popped out' for use elsewhere, just set .POS to 0 when the FIFO is full and let it continue to update with new values, the values aren't cleared so they are still readable for your Running Average. But you MUST either use FFU to step the .POS back or use a MOV function to change the .POS once it's full or it will stop taking values.
3. Create a counter with a .PRE equal to the .LEN of your FIFO
4. On a parallel Rung, with each increment of the counter.ACC use an ADD function. Here's an example assuming CLX. If you're using SLC you can do the same thing but obviously you can't use tag names:
ADD
Value1: AllValues
Value2: FIFO[IndexCounter.ACC]
Destination: AllValues
5. When your counter.DN bit is set, divide AllValues by FIFO.LEN and store in a RunningAverage Tag, then reset the counter. Have your counter step once for each scan or put it all in a Periodic Function to execute the routine.