I am using or-tools with a SCIP to solve some Mixed Integer Linear Program. In other solvers, I know there are options to stop the solver once a certain objective value has been reached, for example the BestObjStop option in GUROBI. Is there a similar option in SCIP as well? If so, is this option accessible via or-tools in C++?
Currently, there is no function implemented that directly does this in SCIP. There is a workaround that should work though.
You can set the objective limit (function SCIPsetObjlimit) to only accept solutions that are better than the objective stop you want. Then you set SCIP to stop as soon as you found a solution (parameter limits/bestsol set to 1).
I am not an or-tools user, so I am not sure how this should best be achieved in or-tools. This recent thread has an answer that tells you how to set specific SCIP parameters from or-tools. Looking at the code on github, it at least seems to me that you can set the objective limit when you call the Solve method with the right GScipParameters. Maybe an or-tools expert can improve this answer.
Related
I am trying to understand how Gurobi works and have the following question.
Suppose I start with an ILP model 'm' and obtain a solution 'S' using m.optimize(). Now, I add another constraint to the model and re-optimize. Does Gurobi solve the whole problem from scratch or does it use from the found solution 'S' as the starting point and then proceed?
Thank you.
Gurobi, as well as every good solver out there, will try to use an available solution as the starting point to the modified problem, if appropriate. What you are asking is referred to as a warm start.
Specifically, this paragraph from Gurobi's documentation here is relevant to your question:
For linear models, the previously computed solution can be used as an
efficient warm start for the modified model. The Gurobi solver retains
the previous solution, so the next optimize call automatically starts
from the previous solution.
So, yes, it will use thre previous solution S, and will proceed to re-optimize from there, including the new constraint you added.
I have a set of data z(0), z(1), z(2)...,z(n) that I am currently fitting with a 2 variables polynomial of the kind p(x,y) = a(1)*x^2+a(2)*y^2+a(3)*x*y+a(4). I have i=1,...,n (x(i),y(i)) coordinates that I impose to be p(x(i),y(i))=z(i). In this way I have a Overdetermined System that I can solve using Eigen SVD . I am looking for a more sophisticated method that can take care of outliers, like a Least Median of Squares robust regression (as described here) but I haven't found a C++ implementation for 2 variables. I looked in GSL but it seems there is nothing for 2 variable functions. The only other solution I can think of is using a TGraph2D in ROOT. Do you know any other solution? Numerical recipes maybe? Since I am writing C++ code I would prefer C or C++ implementations.
Since non answer has been given yet, but I am still working on this problem, I will share my progresses here.
The class TLinearFitter has a fit method that allows you to select Robust fitting - Least Trimmed Squares regression (LTS):
https://root.cern.ch/root/html532/TLinearFitter.html
Another possible solution, more time consuming maybe, but maybe more efficient on the long run is to write my own function to be minimized, and the use:
https://projects.coin-or.org/Ipopt to minimize it. Although in this approach there is a bigger "step". I don't know how to use the library and I haven't (yet?) found a nice tutorial to understand it.
here: https://wis.kuleuven.be/stat/robust/software there is a Fortran implementation of the LMedS algorithm called PROGRESS. So another possible solution could be to port this software to C/C++ and make a library out of it.
I have a huge problem. I need to solve a non linear sistem of 3 equations in 3 variables with a C++ function or class. I thought about using Newton-Raphson method to perform the solution. Unlukily I didn't find a source code that can do that for me. There would be someone that knows a program like that? I'm near deciding to build it myself. Thanks
A 3x3 system is not huge; it's actually a very small problem. People routinely solve nonlinear systems of equations with thousands (and more) of variables and constraints.
Given that your system is 3x3 and possibly nasty, a more appropriate choice of method would be a line search method. You get global convergence to a local minimum of the residual this way; it's very easy to make straight Newton's method diverge.
Steepest descent with backtracking line search is the simplest line search method possible. You might try implementing it first.
First, see related questions What good libraries are there for solving a system of non-linear equations in C++? and https://stackoverflow.com/questions/4914967/could-you-explain-how-newton-raphson-for-a-set-of-equations-works-code-inside. Also, try to use boost.
Consider this cozy C++ library
My professor gave me a binary linear programming problem, but this problem is slightly different from optimization problems I used to solve(i.e. this is probably not maximizing or minimizing the object function.)
The problem is as follows,
Given a matrix M, for entries m_ij != 0, there are corresponding x_ijk variables.
Entries m_ij = 0 can be ignored.
x_ijk is either 0 or 1, and I want to try 5 x_ijk variables for each m_ij (that is, x_ij1, x_ij2, x_ij3, x_ij4, and x_ij5. One of them is 1 and the others are 0) are enough to satisfy some conditions(a set of inequalities).
More simply, this is to check if the set of constraints involving 5 x_ijk variables for each m_ij is a valid(or feasible) constraints.
I have solved some optimization problems, but I have never solved a problem without an objective function.
What should I set as my objective function here?
0? nothing?
I might be using lp_solve or CPLEX.
Thank you in advance for your advice!
That is correct, you can set an arbitrary constant value as an objective function.
Most of the solvers I have tried allow an empty objective function. Simply leave it out from your model.
Depending on the solver and the API you are using, it can happen that you have to set the coefficients of all variables in the objective to zero.
Don't worry, it has to work.
In response to your comment: Yes, constraint programming tools can provide better performance on feasibility problems than LP solvers (such as CPLEX). I have played with the IBM ILOG CPLEX CP Optimizer a few months ago, it is free for Academic users. Both the LP solver and the CP solver failed on my problems. Don't expect a miracle from constraint programming.
Keep in mind the that time needed to solve a constraint program grows exponentially with the size of the problem in the worse case. Sooner or later, your problems will most likely become unsolvable with either tool.
Just for your information: in the end, the constraint programming solver will call the LP solver (for example CPLEX).
My advice is: try the tool you already have / use the problem formulation that is more natural to you. Check whether the tool can solve your problem. Switch tool only if the tool fails and you cannot improve your model.
I am doing (trying to do) numerical optimization in Fortran 90, on a Windows 7 machine with the gfortran compiler. I have a function, pre-written by someone else, which returns the loglikelihood of a function, given a large set of parameters (about 60 parameters in total) passed in. I am trying to replicate someone's results, so I know the final parameter values, but I was to try and re-estimate them and, eventually, extend their model and use different data. I've been trying the uobyqa.f90 routine available here, which has not been particularly successful thus far.
My questions are: First, for an optimization problem with a large number of parameters (over 60), can anyone suggest the best freely available routine? Derivatives are not available, and would be costly to estimate numerically, hence trying the uobyqa routine first. Also, would implementing parallelization aid significantly in solving this problem? And, if so, could anyone suggest an optimization routine that already implements parallelization using openmp?
Thanks!
I don't have a good suggestion for a specific optimization strategy, but the NLopt package has a few derivative-free optimizers that can handle larger numbers of variables. Worth checking out. I've found the Fortran interface to be very easy to use.
Do a regular (published academic) literature search on this question first.
Maybe try including "LAPACK" with your other search terms (e.g. "optimization", "uobyqa", etc) to see relavant work by other parties.