How can I reduce computational time in a OPL script using CPLEX? - performance

I'm an engineering student, new user of CPLEX and OPL. I modelled an electric vehicle scheduling problem, using OPL in CPLEX.
It takes around 20min to give me an optimal solution for an instance of 4 service trips, 2 depots and 2 charging stations.
I'm currently trying to run a real example of 100 service trips, 1 depot and 1 charging station, but is taking me forever to get an answer (it is running for the last 17h).
Any suggestions on how to speed up the process?

You could set a time limit and then instead of an optimal solution you'll get a solution after the time limit. You could also try to see with the profiler where time is spent.
A few links to help you:
Performance Tuning Using CPLEX Optimization Studio IDE
MIP Tuning
CPO Introduction

Related

I have got an requirement for load testing . i was given both avg. and peak TPH. also avg and peak user load

I have to do performance testing of an ecommerce application where i got the details needed like Avg TPH and peak TPH . also Avg User and Peak User.
for e.g., an average of 1000 orders/hour, the peak of 3000 orders/hour during the holiday season, expected to grow to 6000 orders/hour next holiday season.
I was afraid which value to be considered for current users and TPH for performing load test for an hour.
also what load will be preferable foe stress testing and scalability testing.
It would be a great helpful not only for the test point of view but also will help me in understanding the conceptually which would help me in a great deal down the lane.
This is a high business risk endeavor. Get it wrong and your ledger doesn't go from red to black on the day after thanksgiving, plus you have a high probability of winding up with a bad public relations event on Twitter. Add to that greater than 40% of people who hit a website failure will not return.
That being said, do your skills match the risk to the business. If not, the best thing to do is to advise your management to acquire a higher skilled team. Then you should shadow them in all of their actions.
I think it helps to have some numbers here. There are roughly 35 days in this year's holiday shopping season. This translates to 840 hours.
#$25 avg sale, you are looking at revenue of $21 million
#$50 avg sale, ...42 Million
#100 avg sale, ...84 Million
Numbers based upon the average of 1000 sales per hour over 840 hours.
Every hour of downtime at peak costs you
#$25 avg sale, ...$75K
#$50 avg sale, ...$150K
#$100 avg sale, ...$300K
Numbers based upon 3000 orders per hour at peak. If you have downtime then greater than 40% of people will not return based upon latest studies. And you have the Twitter affect where people complain loudly and draw off potential site visitors.
I would advise you to bring in a team. Act fast, the really good engineers are quickly being snapped up for Holiday work. These are not numbers to take lightly nor is it work to press someone into that hasn't done it before.
If you are seriously in need and your marketing department knows exactly how much increased conversion they get from a faster website, then I can find someone for you. They will do the work upfront at no charge, but they will charge a 12 month residual based upon the decrease in response time and the increased conversion that results
Normally Performance Testing technique is not limited to only one scenario, you need to run different performance test types to assess various aspects of your application.
Load Testing - which goal is to check how does your application behave under anticipated load, in your case it would be simulating 1000 orders per hour.
Stress Testing - putting the application under test under maximum anticipated load (in your case 3000 TPH). Another approach is gradually increasing the load until response time starts exceeding acceptable thresholds or errors start occurring (whatever comes the first) or up to 6000 TPH if you don't plan to scale up. This way you will be able to identify the bottleneck and determine what will be the component which fails which could be in
lack of hardware power
problems with database
inefficient algorithms used in your application
You can also consider executing a Soak Test - putting your application under prolonged load, this way you will be able to catch the majority of memory leaks

how to get the lowest cost when arrange moveable jobs

it's a very hard dynamic programming question, and I want to share with you and we can discuss a little bit toward its solution:
You will put your new application to cloud server; you have to schedule your job in order to get lowest cost. you don't need to care about the number of jobs running at the same time on the same server. every job k is given by a release time sk, a deadline fk, and a duration dk with dk ≤ fk - sk. This job needs to be scheduled for an interval of dk consecutive minutes between time sk and fk. server company would charges per minute per server. You only need one virtual server and you can save money moving jobs from sk to fk around to maximize the amount of time without running any jobs or, in other word, to minimize the amount of time running one or more jobs. using dynamic programming to solve problem. Your algorithm should be polynomial in n, the number of jobs.
This is the problem of minimizing busy time.
See Theorem 17 of this paper:
Rohit Khandekar, Baruch Schieber, Hadas Shachnai, and Tami Tamir. Minimizing busy time in multiple machine real-time
scheduling. In Proceedings of the 30th Annual Conference on Foundations of Software Technology and Theoretical Computer
Science (FSTTCS), pages 169 – 180, 2010
For a description of a polynomial time algorithm.
The key is:
To realize there are only certain interesting times that need to be considered (if you have a schedule, consider delaying each busy interval until you hit a deadline for one of the jobs being processed)
To consider when the longest duration job is done. This splits the problem into two pieces; before and after, which can be solved independently in the normal dynamic programming fashion.

Would communication and inter-connection have any impact on a computation bound application on multinode?

I have a computation bound application. I have executed it on multi-nodes ( 4nodes, 8nodes) I'm wondering if communication between the nodes could have any effect on the run time? If so, how would it be possible? because as far as I found, computation bound application just depends on the computing capability of system.
Also, can I consider CPU amount of my system as computing capability?
Any help would be appreciated.
Updated:
In order to see if the application is memory-bound or compute-bound, I've run the application over 1 nodes using different number of cores. For that application (NPB-LU), the run time decreased linearly by increasing the number of cores. So I found this application could be compute-bound (I didn't have another option to figure it out).
Then, I have predicted the run time of the application with a model which considers the latency(in my case it's message-time) in different connection levels like inter-socket, inter-node. There are some difference in the predicted time which achieved by different latency connection levels although the application seemed to be computation-bound.
n:grid size, p:number of cores, m(total Mops/s), f(Mop/s/core)
Imagine you have horse that is drinking water, let's say 1 liter per minute.
In order to give the water to the horse you have a water well where you can take the water from. Imagine you can pump up to 1.5 liters per minute.
Having this situation your water consumption is horse-bounded.
Then it turns out that you have two horses drinking the same amount of water: 1 liter each per minute. Then your water consumption is no longer horse-bounded but well-bounded.
Your application behavior can change depending of the environment. In order to determine what is happening to your application I recommend you to profile your app. You have a lot of alternatives such as gprof, perf, PAPI and many others to better observe what is your application behaviour.
Then you can determine experimentally very intersting metrics like Instructions per Clock cycle, which can give you a better understanding of the behaviour of your app.

Variation of the job scheduling prob

I'm doing some administration work for an aviation transport company. They build aircraft containers and such here. One of the things they want me to code is a order optimization script that the guys on the floor can use to get the most out of the given material. To give a simple overview: say we order a certain amount beams that are 10 meters per unit. We need beam chunks of 5x 6m, 10x 3.5m, 4x 3m, which are acquired by cutting the 10m in smaller parts. What would be the minimum amount of 10m beams we need to order?
There are some parallels with the multiprocessor job scheduling problem (one beam is a processor, each chunk a job), although that focusses on minimizing the time required to perform all jobs instead of minimizing the amount of processors needed to perform all jobs within a pre-set time. The multiprocessor job scheduling problem is in NP-complete, but I wonder if my variation of the problem is too. Does anybody know similar problems and methods for solving them?
This problem is exactly: http://en.wikipedia.org/wiki/Cutting_stock_problem (more generally http://en.wikipedia.org/wiki/Bin_packing_problem). You can use any old ILP solver. I like http://lpsolve.sourceforge.net/5.5/, its quite friendly to use.

How to create a system with 1500 servers that deliver results instantaneously?

I want to create a system that delivers user interface response within 100ms, but which requires minutes of computation. Fortunately, I can divide it up into very small pieces, so that I could distribute this to a lot of servers, let's say 1500 servers. The query would be delivered to one of them, which then redistributes to 10-100 other servers, which then redistribute etc., and after doing the math, results propagate back again and are returned by a single server. In other words, something similar to Google Search.
The problem is, what technology should I use? Cloud computing sounds obvious, but the 1500 servers need to be prepared for their task by having task-specific data available. Can this be done using any of the existing cloud computing platforms? Or should I create 1500 different cloud computing applications and upload them all?
Edit: Dedicated physical servers does not make sense, because the average load will be very, very small. Therefore, it also does not make sense, that we run the servers ourselves - it needs to be some kind of shared servers at an external provider.
Edit2: I basically want to buy 30 CPU minutes in total, and I'm willing to spend up to $3000 on it, equivalent to $144,000 per CPU-day. The only criteria is, that those 30 CPU minutes are spread across 1500 responsive servers.
Edit3: I expect the solution to be something like "Use Google Apps, create 1500 apps and deploy them" or "Contact XYZ and write an asp.net script which their service can deploy, and you pay them based on the amount of CPU time you use" or something like that.
Edit4: A low-end webservice provider, offering asp.net at $1/month would actually solve the problem (!) - I could create 1500 accounts, and the latency is ok (I checked), and everything would be ok - except that I need the 1500 accounts to be on different servers, and I don't know any provider that has enough servers that is able to distribute my accounts on different servers. I am fully aware that the latency will differ from server to server, and that some may be unreliable - but that can be solved in software by retrying on different servers.
Edit5: I just tried it and benchmarked a low-end webservice provider at $1/month. They can do the node calculations and deliver results to my laptop in 15ms, if preloaded. Preloading can be done by making a request shortly before the actual performance is needed. If a node does not respond within 15ms, that node's part of the task can be distributed to a number of other servers, of which one will most likely respond within 15ms. Unfortunately, they don't have 1500 servers, and that's why I'm asking here.
[in advance, apologies to the group for using part of the response space for meta-like matters]
From the OP, Lars D:
I do not consider [this] answer to be an answer to the question, because it does not bring me closer to a solution. I know what cloud computing is, and I know that the algorithm can be perfectly split into more than 300,000 servers if needed, although the extra costs wouldn't give much extra performance because of network latency.
Lars,
I sincerely apologize for reading and responding to your question at a naive and generic level. I hope you can see how both the lack of specifity in the question itself, particularly in its original form, and also the somewhat unusual nature of the problem (1) would prompt me respond to the question in like fashion. This, and the fact that such questions on SO typically emanate from hypotheticals by folks who have put but little thought and research into the process, are my excuses for believing that I, a non-practionner [of massively distributed systems], could help your quest. The many similar responses (some of which had the benefits of the extra insight you provided) and also the many remarks and additional questions addressed to you show that I was not alone with this mindset.
(1) Unsual problem: An [apparently] mostly computational process (no mention of distributed/replicated storage structures), very highly paralellizable (1,500 servers), into fifty-millisecondish-sized tasks which collectively provide a sub-second response (? for human consumption?). And yet, a process that would only be required a few times [daily..?].
Enough looking back!
In practical terms, you may consider some of the following to help improve this SO question (or move it to other/alternate questions), and hence foster the help from experts in the domain.
re-posting as a distinct (more specific) question. In fact, probably several questions: eg. on the [likely] poor latency and/or overhead of mapreduce processes, on the current prices (for specific TOS and volume details), on the rack-awareness of distributed processes at various vendors etc.
Change the title
Add details about the process you have at hand (see many questions in the notes of both the question and of many of the responses)
in some of the questions, add tags specific to a give vendor or technique (EC2, Azure...) as this my bring in the possibly not quite unbuyist but helpful all the same, commentary from agents at these companies
Show that you understand that your quest is somewhat of a tall order
Explicitly state that you wish responses from effective practionners of the underlying technologies (maybe also include folks that are "getting their feet wet" with these technologies as well, since with the exception of the physics/high-energy folks and such, who BTW traditionnaly worked with clusters rather than clouds, many of the technologies and practices are relatively new)
Also, I'll be pleased to take the hint from you (with the implicit non-veto from other folks on this page), to delete my response, if you find that doing so will help foster better responses.
-- original response--
Warning: Not all processes or mathematical calculations can readily be split in individual pieces that can then be run in parallel...
Maybe you can check Wikipedia's entry from Cloud Computing, understanding that cloud computing is however not the only architecture which allows parallel computing.
If your process/calculation can efficitively be chunked in parallelizable pieces, maybe you can look into Hadoop, or other implementations of MapReduce, for an general understanding about these parallel processes. Also, (and I believe utilizing the same or similar algorithms), there also exist commercially available frameworks such as EC2 from amazon.
Beware however that the above systems are not particularly well suited for very quick response time. They fare better with hour long (and then some) data/number crunching and similar jobs, rather than minute long calculations such as the one you wish to parallelize so it provides results in 1/10 second.
The above frameworks are generic, in a sense that they could run processes of most any nature (again, the ones that can at least in part be chunked), but there also exist various offerings for specific applications such as searching or DNA matching etc. The search applications in particular can have very short response times (cf Google for example) and BTW this is in part tied to fact that such jobs can very easily and quickly be chunked for parallel processing.
Sorry, but you are expecting too much.
The problem is that you are expecting to pay for processing power only. Yet your primary constraint is latency, and you expect that to come for free. That doesn't work out. You need to figure out what your latency budgets are.
The mere aggregating of data from multiple compute servers will take several milliseconds per level. There will be a gaussian distribution here, so with 1500 servers the slowest server will respond after 3σ. Since there's going to be a need for a hierarchy, the second level with 40 servers , where again you'll be waiting for the slowest server.
Internet roundtrips also add up quickly; that too should take 20 to 30 ms of your latency budget.
Another consideration is that these hypothethical servers will spend much of their time idle. That means they're powered on, drawing electricity yet not generating revenue. Any party with that many idle servers would turn them off, or at the very least in sleep mode just to conserve electricity.
MapReduce is not the solution! Map Reduce is used in Google, Yahoo and Microsoft for creating the indexes out of the huge data (the whole Web!) they have on their disk. This task is enormous and Map Reduce was built to make it happens in hours instead of years, but starting a Master controller of Map Reduce is already 2 seconds, so for your 100ms this is not an option.
Now, from Hadoop you may get advantages out of the distributed file system. It may allow you to distribute the tasks close to where the data is physically, but that's it. BTW: Setting up and managing an Hadoop Distributed File System means controlling your 1500 servers!
Frankly in your budget I don't see any "cloud" service that will allow you to rent 1500 servers. The only viable solution, is renting time on a Grid Computing solution like Sun and IBM are offering, but they want you to commit to hours of CPU from what I know.
BTW: On Amazon EC2 you have a new server up in a couple of minutes that you need to keep for an hour minimum!
Hope you'll find a solution!
I don't get why you would want to do that, only because "Our user interfaces generally aim to do all actions in less than 100ms, and that criteria should also apply to this".
First, 'aim to' != 'have to', its a guideline, why would u introduce these massive process just because of that. Consider 1500 ms x 100 = 150 secs = 2.5 mins. Reducing the 2.5 mins to a few seconds its a much more healthy goal. There is a place for 'we are processing your request' along with an animation.
So my answer to this is - post a modified version of the question with reasonable goals: a few secs, 30-50 servers. I don't have the answer for that one, but the question as posted here feels wrong. Could even be 6-8 multi-processor servers.
Google does it by having a gigantic farm of small Linux servers, networked together. They use a flavor of Linux that they have custom modified for their search algorithms. Costs are software development and cheap PC's.
It would seem that you are indeed expecting at least 1000-fold speedup from distributing your job to a number of computers. That may be ok. Your latency requirement seems tricky, though.
Have you considered the latencies inherent in distributing the job? Essentially the computers would have to be fairly close together in order to not run into speed of light issues. Also, the data center in which the machines would be would again have to be fairly close to your client so that you can get your request to them and back in less than 100 ms. On the same continent, at least.
Also note that any extra latency requires you to have many more nodes in the system. Losing 50% of available computing time to latency or anything else that doesn't parallelize requires you to double the computing capacity of the parallel portions just to keep up.
I doubt a cloud computing system would be the best fit for a problem like this. My impression at least is that the proponents of cloud computing would prefer to not even tell you where your machines are. Certainly I haven't seen any latency terms in the SLAs that are available.
You have conflicting requirements. You're requirement for 100ms latency is directly at odds with your desire to only run your program sporadically.
One of the characteristics of the Google-search type approach you mentioned in your question is that the latency of the cluster is dependent on the slowest node. So you could have 1499 machines respond in under 100ms, but if one machine took longer, say 1s - whether due to a retry, or because it needed to page you application in, or bad connectivity - your whole cluster would take 1s to produce an answer. It's inescapable with this approach.
The only way to achieve the kinds of latencies you're seeking would be to have all of the machines in your cluster keep your program loaded in RAM - along with all the data it needs - all of the time. Having to load your program from disk, or even having to page it in from disk, is going to take well over 100ms. As soon as one of your servers has to hit the disk, it is game over for your 100ms latency requirement.
In a shared server environment, which is what we're talking about here given your cost constraints, it is a near certainty that at least one of your 1500 servers is going to need to hit the disk in order to activate your app.
So you are either going to have to pay enough to convince someone to keep you program active and in memory at all times, or you're going to have to loosen your latency requirements.
Two trains of thought:
a) if those restraints are really, absolutely, truly founded in common sense, and doable in the way you propose in the nth edit, it seems the presupplied data is not huge. So how about trading storage for precomputation to time. How big would the table(s) be? Terabytes are cheap!
b) This sounds a lot like a employer / customer request that is not well founded in common sense. (from my experience)
Let´s assume the 15 minutes of computation time on one core. I guess thats what you say.
For a reasonable amount of money, you can buy a system with 16 proper, 32 hyperthreading cores and 48 GB RAM.
This should bring us in the 30 second range.
Add a dozen Terabytes of storage, and some precomputation.
Maybe a 10x increase is reachable there.
3 secs.
Are 3 secs too slow? If yes, why?
Sounds like you need to utilise an algorithm like MapReduce: Simplified Data Processing on Large Clusters
Wiki.
Check out Parallel computing and related articles in this WikiPedia-article - "Concurrent programming languages, libraries, APIs, and parallel programming models have been created for programming parallel computers." ... http://en.wikipedia.org/wiki/Parallel_computing
Although Cloud Computing is the cool new kid in town, your scenario sounds more like you need a cluster, i.e. how can I use parallelism to solve a problem in a shorter time.
My solution would be:
Understand that if you got a problem that can be solved in n time steps on one cpu, does not guarantee that it can be solved in n/m on m cpus. Actually n/m is the theoretical lower limit. Parallelism is usually forcing you to communicate more and therefore you'll hardly ever achieve this limit.
Parallelize your sequential algorithm, make sure it is still correct and you don't get any race conditions
Find a provider, see what he can offer you in terms of programming languages / APIs (no experience with that)
What you're asking for doesn't exist, for the simple reason that doing this would require having 1500 instances of your application (likely with substantial in-memory data) idle on 1500 machines - consuming resources on all of them. None of the existing cloud computing offerings bill on such a basis. Platforms like App Engine and Azure don't give you direct control over how your application is distributed, while platforms like Amazon's EC2 charge by the instance-hour, at a rate that would cost you over $2000 a day.

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