I have a simple optimization problem and am looking for java software for that.
The Apache math optimization software looks just like what I want but I cant find documentation to suit my needs (where those needs are to useful to a beginner / non maths professional!)
Does anyone know of a worked, simple, example?
In case it helps, the problem is that I want to find the max r where
r1 = s1 * m1
r2 = s2 * m2
and there are some constraints and formula for defining the relationship between the variables. The Excel Solver works fine for this problem. I got LPSolve working great, but this problem requires a multiplication of s and m, so I understand LPSolve cant help as this makes the problem non linear.
I recently ported the derivative-free non-linear constrained optimization code COBYLA2 to Java. Since it does not explicitly rely on derivatives, the algorithm may require quite a few iterations for larger problems. Nonetheless, you are able to formulate your problem with both a non-linear objective function and (potentially) non-linear constraints.
You can read more about it and download the source code from here.
I am not aware of a simple Java-based NLP solver. (I did find an example of Quadratic programming (QP) in Apache Math Works, but it doesn't qualify since you asked for a non-math professional example.)
I have two suggestions for you to solve your non-linear program:
1.. Excel's Solver does have the ability to tackle non-linear problems. (Don't use LPSOLVE.) In fact, NLP is the default mode in Solver.
Here are two links to using Excel to solve NLPs: Example 1 - Step by step Solver walk-through that covers NLP and
Example 2 - A General Neural network example in Excel
Also for Excel, I like Paul Jensen's (utexas) ORMM Add-in's.
He has a module called Teach NLP. Chapter 10 of his book deals with NLP and is available from his site.
2.. If you are going to be doing even some amount of data analysis, then I recommend investing a few hours to download and learn the basics of R.
R has numerous packages and libraries for optimization. optim() and nlme are relavant for solving non-linear programs.
Just for completeness, I mention SAS, MATLAB and CPLEX as other options. If you have access to any of these, they all do a very good job with solving non-linear programs.
Hope these pointers help.
Related
Which of the following optimisation methods can't be done in an optimisation software such as CPLEX? Why not?
Dynamic programming
Integer programming
Combinatorial optimisation
Nonlinear programming
Graph theory
Precedence diagram method
Simulation
Queueing theory
Can anyone point me in the right direction? I didn't find too much information regarding the limitations of CPLEX on the IBM website.
Thank you!
That's kind-of a big shopping list, and most of the things on it are not optimisation methods.
For sure CPLEX does integer programming, non-linear programming (just quadratic, SOCP, and similar but not general non-linear) and combinatoric optimisation out of the box.
It is usually possible to re-cast things like DP as MILP models, but will obviously require a bit of work. Lots of MILP models are also based on graphs, so yes it is certainly possible to solve a lot of graph problems using a MILP solver such as CPLEX.
Looking wider at topics like simulation, then that is quite a different approach. Simulation really is NOT an optimisation method, but it can be used alongside optimisation to get extra insights which may be useful in a business context. Might be used for example to discover some empirical relationships that could be used in an optimisation model by CPLEX.
The same can probably also be said for things like queuing theory, precedence, etc. Basically, use CPLEX as an optimisation tool to solve part or all of your problem once you have structured and analysed it via one of these other approaches.
Hope that helps.
Recently, I have been trying to learn a bit about CPLEX and was hoping someone could help me understand the complexity when solving for integer vs. binary constraints.
For example, say we are trying to allocate a pie around 10 people for maximum utility, where each person has a utility that is linear with the amount of pie they receive. However, we want to introduce the constraint that at least 3 people have to get a bit of pie.
What's the difference between thinking of this as a single integer constraint (number_of_people_with_pie >= 3) vs. 10 binary variables (person_1_has_pie + person_2_has_pie + ... person_10_has_pie >= 3)? I would imagine the former is simplest but wonder if there is any benefits to forming the problem in terms of binary variables?
In addition to this, any recommended reading for better understanding MIP and CPLEX would be greatly appreciated, especially in better understanding where the problem becomes NP or in what situations simplex struggles to find the global minima.
Thanks!
I agree with Alex and Erwin's comment that this really depends on what you want to model. For this particular model I disagree with Alex: to me it makes more sense to use one decision variable per person, otherwise it may become hard to figure out which person gets how much of the pie.
A problem becomes NP hard as soon as you add integrality or SOS constraints. A good reading for MIP in general is Alex Schrijver's "Theory of Integer and Linear Programming". That should cover all the topics you need for an in-depth understanding of things.
It really depends on the case but in yours I would use 1 decision variable rather than 10.
Sometimes, that's not obvious and trying and measuring can prove oneself right or wrong. And that's one of the reason why using high modeling languages can help. (Abstract modeling languages such as OPL)
I recommend a MOOC on cognitive class : https://cognitiveclass.ai/courses/mathematical-optimization-for-business-problems/
and the OPL language manual : https://www.ibm.com/support/knowledgecenter/SSSA5P_12.7.0/ilog.odms.studio.help/pdf/opl_languser.pdf
I am using Tensorflow Probability to build a VAE which includes image pixels as well as some other variables. The output of the VAE:
tfp.distributions.Independent(tfp.distributions.Bernoulli(logits), 2, name="decoder-dist")
I am trying to understand how to form other conditional distributions based on this which I can use with the inference methods (MCMC or VI). Say the output above was P(A,B,C | Z), how would I take that distribution to form a posterior P(A|B, C, Z) that I could perform inference on? I have been trying to read through the docs but I am having some trouble grasping them.
The answer to your question depends very much on the nature of the joint model within which you'd like to do the conditioning. Much has been written about the topic, and in short it's a very hard problem in general :). Without knowing a bit more about the particulars of your problem, it's near impossible to recommend a useful generic inference procedure. However, we do have a bunch of examples (scripts and jupyter/colab notebooks) in the TFP repo here: https://github.com/tensorflow/probability/tree/master/tensorflow_probability/examples
In particular, there's
The Hierarchical Linear Model example, which is a sort of Rosetta stone showing how to do posterior inference using Hamiltonian Monte Carlo (an MCMC technique) in TFP, R, and Stan,
The Linear Mixed Effects Model example, showing how you might use VI to solve a standard LME problem,
among many others. You can click the "Run in Google Colab" link at the top of any of these notebooks to open and run on them on https://colab.research.google.com.
Please feel free, also, to reach out on to us via email at tfprobability#tensorflow.org. This is a public Google Group where users can engage with the team that builds TFP directly. If you provide us some more info there on what you'd like to do, we're happy to provide guidance on modeling and inference with TFP.
Hope this is gives at least a start in the right direction!
I am trying to solve some problems that can be mapped in convex optimisation problem.
In particular is for analysis of quantum state tomography data.
In Matlab there are some tools to help you do this, like SeDuMi or CVX
http://sedumi.ie.lehigh.edu
http://cvxr.com/cvx/
But I could not find anything similar in Mathematica, on the web or in the forums.
Does anybody know if there is an easy way of implementing this kind of algorithm in Mathematica?
I would like to avoid to be forced to switch to Matlab to solve this problem. Nothing against it, but I have most of the programming for this state tomography developed in Mathematica.
Thank you very much.
I had also some troubles with Mathematica in
optimization, exactly on convex problems.
I suggest you export to CVX, which will require
some work because it wants the problem in matrix notation.
Otherwise, to remain with the algebraic formulation,
you could try with Maple, which has, as far
as I can tell, better optimizers than Mathematica.
(check the doc to have an idea)
I've been out of the modeling biz, so to speak, for a while now. When I was in college, most of the models I worked with were written in FORTRAN, which I never liked. I'm looking to get back into science, so I'm wondering if there are modern languages with feature sets suited for this kind of application. What would you consider to be an optimal language for simulating complex physics systems?
While certainly Fortran was the absolute ruler for this, Python is being used more and more exactly for this purpose. While it is very hard to say which is the BEST program for this, I've found python pretty useful for physics simulations and physics education.
It depends on the task
C++ is good at complicated data structures, but it is bad at slicing and multiply matrices. (This task equires you to spend a lot of time writing for loops.)
FORTRAN has a nice notation for slicing and multiplying matrices, but it is clumsy for creating complicated data structure such as graphs and linked lists.
Python/scipy has a nice notation for everything, but python is an interepreted language, so it is slow at certain tasks.
Some people are interested in languages like CUDA that allow you to use your GPU to speed up your simulations.
In the molecular dynamics community c++ seems to be popular, because you need somewhat complicated data structures to represent the shapes of the molecules.
I think it's arguable that FORTRAN is still dominant when it comes to solving large-scale problems in physics, as long as we're talking about serial calculations.
I know that parallelization is changing the game. I'm less certain about whether or not parallelized versions of LINPACK and other linear algebra packages are still written in FORTRAN.
A lot of engineers are using MATLAB and Mathematica these days, because they combine numerical and graphics capabilities.
I'd also point out that there's a difference between calculation and display engines. The former might still be written in FORTRAN, but the latter may be using more modern languages and OpenGL.
I'm also unsure about how much modeling has crept into biology. Physical chemistry might be a very different animal altogether.
If you write a terrific parallel linear algebra package in Scala or F# or Haskell that performs well, the world will beat a path to your door.
Python + Matplotlib + NumPy + α
The nuclear/particle/high energy physics community has moved heavily toward c++ (in part due to ROOT and Geant4), with some interest in Python (because it has ROOT bindings).
But you'll note that this is sub-discipline dependent..."physics" and "modeling" are big, broad topics, so there is no one answer.
Modelica is a specialized language for modeling (and simulating) physical systems. OpenModelica is an open source implementation of Modelica.
Python is very popular among science-oriented people, as is Matlab. The issue with these is that they are both VERY slow (to run). If you want to do large simulations that may take minutes/hours/days, you're going to have to pick another language.
As long as you are picking a language for speed, suck it up and use C/C++, maybe with CUDA depending on your needs.
Final thought though: if it takes you two days longer to write and debug your model in C than in python, and the resulting code takes 10 minutes to run instead of an hour, have your really saved any time?
There's also a lot of capability with MATLAB. Especially when interfacing your simulations with hardware, or if you need your results visualised.
I'll chime in with Python but you should also look to R for any statistical work you may need to do. You should really be asking more about what packages for which languages to use rather than the language itself.