First time asking question, apologies if incorrect.
What would be the best way to approach this problem (Similar to travelling salesman, but I'm not sure if it runs into the same issues).
You have a list of "tasks" at certain locations (Cities) and a group of "people" that can complete those tasks (Salesmen). This is structured over a day, where some tasks may need to be completed before a specific time and may require specific "tools" (Set number available). The difference is that the length between each location is the same in all circumstances, but they all have to return to the start. Therefore, rather than trying to minimise the distance travelled, instead you want to maximise the time each salesmen spends moving and stays at the initial staring node. This also gives you pre-defined requirements.
The program doesn't need to find an optimal solution, just an acceptable one (Greater than a certain value.) Would you just bash out each case? If so, what would be the best language to use for bashing out the solutions?
Thanks
EDIT - Just to confirm, the pre-requisite where all the cities are the same distance from each other is just for simplification of the problem, not reflective of real life.
Related
I am researching a problem that is pretty unique.
Imagine a roadside assistance company that wants to dynamically route its vehicles. Hence for each packet of new incidents wants to create routes that will satisfy them, according to some constraints (time constraints, road accessibility, vehicle - incident matching).
The company has an heterogeneous fleet of vehicle (motorbikes for easy cases, up to tow trucks for the hard cases) and each incident states it's uniqueness (we know if it wants just fuel, or needs towing).
There is no depot, only the vehicles roaming on the streets.
The objective is to dynamically create routes on the way, having in mind the minimization of time and the total traveled distance.
Have you ever met such a problem? Do you have any idea in which VRP variant it belongs?
I have seen two previous questions but unfortunately they don't fit with my problem.
The respected optaplanner - VRP but with no depot and Does optaplanner out of box support VRP with multiple trips and no depot, which are both open VRPs.
Unfortunately I don't have code right now, as I am still modelling the way I will approach this problem.
I am really sorry for creating a suggestion question and not a real one.
Thank you so much in advance.
It's a rich dynamic/realtime vehicle routing problem. You won't find an exact name for your problem, as when VRPs get too complex they don't fit inside any of the standard categories.
It's clearly a dynamic/realtime problem (the terms are used interchangeably) as you would typically only find out about roadside breakdowns at short notice.
Sometimes you're servicing a broken down car, which would be a single stop (so a vehicle routing problem). Sometimes you're towing a car, which would be a pick-up delivery problem. So you have a mix of both together.
You would want to get to the broken down vehicles ASAP and some would need fixing sooner than others (think a car broken down in a dangerous position on a motorway). You would therefore need soft time windows so you can penalise lateness instead of the standard hard time windows supported in most VRP formulations.
Also for you to be able to scale to larger problems, you need an incremental optimiser that can restart from the previous (possibly now infeasible) solution when new jobs are added, vehicle positions are changed etc. This isn't supported out of the box in the open source solvers I know of.
We developed a commercial engine which does the above. We started off using the jsprit library, which supports mixing single stop and pickup delivery problems together. We later had to replace jsprit due to the amount of code we had to override to get it running happily for realtime problems, however jsprit may still prove a useful starting point for you. We discuss some of the early technical obstacles we had to overcome in getting jsprit to handle realtime problems in this white paper.
I've written a GA to model a handful of stocks (4) over a period of time (5 years). It's impressive how quickly the GA can find an optimal solution to the training data, but I am also aware that this is mainly due to it's tendency to over-fit in the training phase.
However, I still thought I could take a few precautions and and get some kind of prediction on a set of unseen test stocks from the same period.
One precaution I took was:
When multiple stocks can be bought on the same day the GA only buys one from the list and it chooses this one randomly. I thought this randomness might help to avoid over-fitting?
Even if over-fitting is still occurring,shouldn't it be absent in the initial generations of the GA since it hasn't had a chance to over-fit yet?
As a note, I am aware of the no-free-lunch theorem which demonstrates ( I believe) that there is no perfect set of parameters which will produce an optimal output for two different datasets. If we take this further, does this no-free-lunch theorem also prohibit generalization?
The graph below illustrates this.
->The blue line is the GA output.
->The red line is the training data (slightly different because of the aforementioned randomness)
-> The yellow line is the stubborn test data which shows no generalization. In fact this is the most flattering graph I could produce..
The y-axis is profit, the x axis is the trading strategies sorted from worst to best ( left to right) according to there respective profits (on the y axis)
Some of the best advice I've received so far (thanks seaotternerd) is to focus on the earlier generations and increase the number of training examples. The graph below has 12 training stocks rather than just 4, and shows only the first 200 generations (instead of 1,000). Again, it's the most flattering chart I could produce, this time with medium selection pressure. It certainly looks a little bit better, but not fantastic either. The red line is the test data.
The problem with over-fitting is that, within a single data-set it's pretty challenging to tell over-fitting apart from actually getting better in the general case. In many ways, this is more of an art than a science, but here are some general guidelines:
A GA will learn to do exactly what you attach fitness to. If you tell it to get really good at predicting one series of stocks, it will do that. If you keep swapping in different stocks to predict, though, you might be more successful at getting it to generalize. There are a few ways to do this. The one that has had perhaps the most promising results for reducing over-fitting is imposing spatial structure on the population and evaluating on different test cases in different cells, as in the SCALP algorithm. You could also switch out the test cases on a time basis, but I've had more mixed results with that sort of an approach.
You are correct that over-fitting should be less of a problem early on. Generally, the longer you run a GA, the more over-fitting will be possible. Typically, people tend to assume that the general rules will be learned first, before the rote memorization of over-fitting takes place. However, I don't think I've actually ever seen this studied rigorously - I could imagine a scenario where over-fitting was so much easier than finding general rules that it happens first. I have no idea how common that is, though. Stopping early will also reduce the ability of the GA to find better general solutions.
Using a larger data-set (four stocks isn't that many) will make your GA less susceptible to over-fitting.
Randomness is an interesting idea. It will definitely hurt the GA's ability to find general rules, but it should also reduce over-fitting. Without knowing more about the specifics of your algorithm, it's hard to say which would win out.
That's a really interesting thought about the no free lunch theorem. I'm not 100% sure, but I think it does apply here to some extent - better fitting some data will make your results fit other data worse, by necessity. However, as wide as the range of possible stock behaviors is, it is much narrower than the range of all possible time series in general. This is why it is possible to have optimization algorithms at all - a given problem that we are working with tends produce data that cluster relatively closely together, relative to the entire space of possible data. So, within that set of inputs that we actually care about, it is possible to get better. There is generally an upper limit of some sort on how well you can do, and it is possible that you have hit that upper limit for your data-set. But generalization is possible to some extent, so I wouldn't give up just yet.
Bottom line: I think that varying the test cases shows the most promise (although I'm biased, because that's one of my primary areas of research), but it is also the most challenging solution, implementation-wise. So as a simpler fix you can try stopping evolution sooner or increasing your data-set.
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Basically, I have a reasonably large list (a year's worth of data) of times that a single discrete event occurred (for my current project, a list of times that someone printed something). Based on this list, I would like to construct a statistical model of some sort that will predict the most likely time for the next event (the next print job) given all of the previous event times.
I've already read this, but the responses don't exactly help out with what I have in mind for my project. I did some additional research and found that a Hidden Markov Model would likely allow me to do so accurately, but I can't find a link on how to generate a Hidden Markov Model using just a list of times. I also found that using a Kalman filter on the list may be useful but basically, I'd like to get some more information about it from someone who's actually used them and knows their limitations and requirements before just trying something and hoping it works.
Thanks a bunch!
EDIT: So by Amit's suggestion in the comments, I also posted this to the Statistics StackExchange, CrossValidated. If you do know what I should do, please post either here or there
I'll admit it, I'm not a statistics kind of guy. But I've run into these kind of problems before. Really what we're talking about here is that you have some observed, discrete events and you want to figure out how likely it is you'll see them occur at any given point in time. The issue you've got is that you want to take discrete data and make continuous data out of it.
The term that comes to mind is density estimation. Specifically kernel density estimation. You can get some of the effects of kernel density estimation by simple binning (e.g. count the number events in a time interval such as every quarter hour or hour.) Kernel density estimation just has some nicer statistical properties than simple binning. (The produced data is often 'smoother'.)
That only takes care of one of your problems, though. The next problem is still the far more interesting one -- how do you take a time line of data (in this case, only printer data) and produced a prediction from it? First thing's first -- the way you've set up the problem may not be what you're looking for. While the miracle idea of having a limited source of data and predicting the next step of that source sounds attractive, it's far more practical to integrate more data sources to create an actual prediction. (e.g. maybe the printers get hit hard just after there's a lot of phone activity -- something that can be very hard to predict in some companies) The Netflix Challenge is a rather potent example of this point.
Of course, the problem with more data sources is that there's extra legwork to set up the systems that collect the data then.
Honestly, I'd consider this a domain-specific problem and take two approaches: Find time-independent patterns, and find time-dependent patterns.
An example time-dependent pattern would be that every week day at 4:30 Suzy prints out her end of the day report. This happens at specific times every day of the week. This kind of thing is easy to detect with fixed intervals. (Every day, every week day, every weekend day, every Tuesday, every 1st of the month, etc...) This is extremely simple to detect with predetermined intervals -- just create a curve of the estimated probability density function that's one week long and go back in time and average the curves (possibly a weighted average via a windowing function for better predictions).
If you want to get more sophisticated, find a way to automate the detection of such intervals. (Likely the data wouldn't be so overwhelming that you could just brute force this.)
An example time-independent pattern is that every time Mike in accounting prints out an invoice list sheet, he goes over to Johnathan who prints out a rather large batch of complete invoice reports a few hours later. This kind of thing is harder to detect because it's more free form. I recommend looking at various intervals of time (e.g. 30 seconds, 40 seconds, 50 seconds, 1 minute, 1.2 minutes, 1.5 minutes, 1.7 minutes, 2 minutes, 3 minutes, .... 1 hour, 2 hours, 3 hours, ....) and subsampling them via in a nice way (e.g. Lanczos resampling) to create a vector. Then use a vector-quantization style algorithm to categorize the "interesting" patterns. You'll need to think carefully about how you'll deal with certainty of the categories, though -- if your a resulting category has very little data in it, it probably isn't reliable. (Some vector quantization algorithms are better at this than others.)
Then, to create a prediction as to the likelihood of printing something in the future, look up the most recent activity intervals (30 seconds, 40 seconds, 50 seconds, 1 minute, and all the other intervals) via vector quantization and weight the outcomes based on their certainty to create a weighted average of predictions.
You'll want to find a good way to measure certainty of the time-dependent and time-independent outputs to create a final estimate.
This sort of thing is typical of predictive data compression schemes. I recommend you take a look at PAQ since it's got a lot of the concepts I've gone over here and can provide some very interesting insight. The source code is even available along with excellent documentation on the algorithms used.
You may want to take an entirely different approach from vector quantization and discretize the data and use something more like a PPM scheme. It can be very much simpler to implement and still effective.
I don't know what the time frame or scope of this project is, but this sort of thing can always be taken to the N-th degree. If it's got a deadline, I'd like to emphasize that you worry about getting something working first, and then make it work well. Something not optimal is better than nothing.
This kind of project is cool. This kind of project can get you a job if you wrap it up right. I'd recommend you do take your time, do it right, and post it up as function, open source, useful software. I highly recommend open source since you'll want to make a community that can contribute data source providers in more environments that you have access to, will to support, or time to support.
Best of luck!
I really don't see how a Markov model would be useful here. Markov models are typically employed when the event you're predicting is dependent on previous events. The canonical example, of course, is text, where a good Markov model can do a surprisingly good job of guessing what the next character or word will be.
But is there a pattern to when a user might print the next thing? That is, do you see a regular pattern of time between jobs? If so, then a Markov model will work. If not, then the Markov model will be a random guess.
In how to model it, think of the different time periods between jobs as letters in an alphabet. In fact, you could assign each time period a letter, something like:
A - 1 to 2 minutes
B - 2 to 5 minutes
C - 5 to 10 minutes
etc.
Then, go through the data and assign a letter to each time period between print jobs. When you're done, you have a text representation of your data, and that you can run through any of the Markov examples that do text prediction.
If you have an actual model that you think might be relevant for the problem domain, you should apply it. For example, it is likely that there are patterns related to day of week, time of day, and possibly date (holidays would presumably show lower usage).
Most raw statistical modelling techniques based on examining (say) time between adjacent events would have difficulty capturing these underlying influences.
I would build a statistical model for each of those known events (day of week, etc), and use that to predict future occurrences.
I think the predictive neural network would be a good approach for this task.
http://en.wikipedia.org/wiki/Predictive_analytics#Neural_networks
This method is also used for predicting f.x. weather forecasting, stock marked, sun spots.
There's a tutorial here if you want to know more about how it works.
http://www.obitko.com/tutorials/neural-network-prediction/
Think of a markov chain like a graph with vertex connect to each other with a weight or distance. Moving around this graph would eat up the sum of the weights or distance you travel. Here is an example with text generation: http://phpir.com/text-generation.
A Kalman filter is used to track a state vector, generally with continuous (or at least discretized continuous) dynamics. This is sort of the polar opposite of sporadic, discrete events, so unless you have an underlying model that includes this kind of state vector (and is either linear or almost linear), you probably don't want a Kalman filter.
It sounds like you don't have an underlying model, and are fishing around for one: you've got a nail, and are going through the toolbox trying out files, screwdrivers, and tape measures 8^)
My best advice: first, use what you know about the problem to build the model; then figure out how to solve the problem, based on the model.
I'd like to collect some kind of geographical information from website users - for given set of data they will mark checkbox indicating whether place has or has not given property. Are there any tools/frameworks for detecting fraud or spam submissions based on whole colected data set (and possibly other info)? I'd like to get filtered, more reliable data.
Not sure if that's exactly what you're asking for, but here are some tips from my experience using Amazon Turk:
There are several academic papers dealing with such problems. here is a good one.
In addition, based on the following general recommendations, I've created a custom procedure which worked on my data:
a. Include an open question, and filter out cases where it wasn't answered. It's harder to answer such a question automatically, and it might also be more time-consuming, thus less attractive, for a fraudster.
b. If possible, don't use a binary scale (i.e. a checkbox), but some grade (e.g. 1-4 or 1-6). This would give you more data to work with.
c. If available, filter out cases where the time spent in filling your form was too short. (especially useful if you include that open question)
d. If you have multiplicity of inputs per user, check for repetitive answers, and for users which consistently give far-from-average answers.
If each user submits only a single "form", consider putting more than a single element/question in it, so you'll get multiple submissions per-user.
e. If you have only a single submission per user or user-id, your options are more limited. I can suggest filtering out outliars, (e.g. data points farther than 3 standard deviations from the average), in case you have enough data.
f. After all the filtering, check the agreement or disagreement in your data (e.g. by checking what proportion of your data points fall within x standard deviations from the average). In case of agreement, use the average; in case of disagreement, collect some more data.
Hope it helps,
For an ecommerce website how do you measure if a change to your site actually improved usability? What kind of measurements should you gather and how would you set up a framework for making this testing part of development?
Multivariate testing and reporting is a great way to actually measure these kind of things.
It allows you to test what combination of page elements has the greatest conversion rate, providing continual improvement on your site design and usability.
Google Web Optimiser has support for this.
Similar methods that you used to identify the usability problems to begin with-- usability testing. Typically you identify your use-cases and then have a lab study evaluating how users go about accomplishing certain goals. Lab testing is typically good with 8-10 people.
The more information methodology we have adopted to understand our users is to have anonymous data collection (you may need user permission, make your privacy policys clear, etc.) This is simply evaluating what buttons/navigation menus users click on, how users delete something (i.e. changing quantity - are more users entering 0 and updating quantity or hitting X)? This is a bit more complex to setup; you have to develop an infrastructure to hold this data (which is actually just counters, i.e. "Times clicked x: 138838383, Times entered 0: 390393") and allow data points to be created as needed to plug into the design.
To push the measurement of an improvement of a UI change up the stream from end-user (where the data gathering could take a while) to design or implementation, some simple heuristics can be used:
Is the number of actions it takes to perform a scenario less? (If yes, then it has improved). Measurement: # of steps reduced / added.
Does the change reduce the number of kinds of input devices to use (even if # of steps is the same)? By this, I mean if you take something that relied on both the mouse and keyboard and changed it to rely only on the mouse or only on the keyboard, then you have improved useability. Measurement: Change in # of devices used.
Does the change make different parts of the website consistent? E.g. If one part of the e-Commerce site loses changes made while you are not logged on and another part does not, this is inconsistent. Changing it so that they have the same behavior improves usability (preferably to the more fault tolerant please!). Measurement: Make a graph (flow chart really) mapping the ways a particular action could be done. Improvement is a reduction in the # of edges on the graph.
And so on... find some general UI tips, figure out some metrics like the above, and you can approximate usability improvement.
Once you have these design approximations of user improvement, and then gather longer term data, you can see if there is any predictive ability for the design-level usability improvements to the end-user reaction (like: Over the last 10 projects, we've seen an average of 1% quicker scenarios for each action removed, with a range of 0.25% and standard dev of 0.32%).
The first way can be fully subjective or partly quantified: user complaints and positive feedbacks. The problem with this is that you may have some strong biases when it comes to filter those feedbacks, so you better make as quantitative as possible. Having some ticketing system to file every report from the users and gathering statistics about each version of the interface might be useful. Just get your statistics right.
The second way is to measure the difference in a questionnaire taken about the interface by end-users. Answers to each question should be a set of discrete values and then again you can gather statistics for each version of the interface.
The latter way may be much harder to setup (designing a questionnaire and possibly the controlled environment for it as well as the guidelines to interpret the results is a craft by itself) but the former makes it unpleasantly easy to mess up with the measurements. For example, you have to consider the fact that the number of tickets you get for each version is dependent on the time it is used, and that all time ranges are not equal (e.g. a whole class of critical issues may never be discovered before the third or fourth week of usage, or users might tend not to file tickets the first days of use, even if they find issues, etc.).
Torial stole my answer. Although if there is a measure of how long it takes to do a certain task. If the time is reduced and the task is still completed, then that's a good thing.
Also, if there is a way to record the number of cancels, then that would work too.