I have to solve a multiobjective problem but I don't know if I should use CPLEX or Matlab. Can you explain the advantage and disadvantage of both tools.
Thank you very much!
This is really a question about choosing the most suitable modeling approach in the presence of multiple objectives, rather than deciding between CPLEX or MATLAB.
Multi-criteria Decision making is a whole sub-field in itself. Take a look at: http://en.wikipedia.org/wiki/Multi-objective_optimization.
Once you have decided on the approach and formulated your problem (either by collapsing your multiple objectives into a weighted one, or as series of linear programs) either tool will do the job for you.
Since you are familiar with MATLAB, you can start by using it to solve a series of linear programs (a goal programming approach). This page by Mathworks has a few examples with step-by-step details: http://www.mathworks.com/discovery/multiobjective-optimization.html to get you started.
Probably this question is not a matter of your current concern. However my answer is rather universal, so let me post it here.
If solving a multiobjective problem means deriving a specific Pareto optimal solution, then you need to solve a single-objective problem obtained by scalarizing (aggregating) the objectives. The type of scalarization and values of its parameters (if any) depend on decision maker's preferences, e.g. how he/she/you want(s) to prioritize different objectives when they conflict with each other. Weighted sum, achievement scalarization (a.k.a. weighted Chebyshev), and lexicographic optimization are the most widespread types. They have different advantages and disadvantages, so there is no universal recommendation here.
CPLEX is preferred in the case, where (A) your scalarized problem belongs to the class solved by CPLEX (obviously), e.g. it is a [mixed integer] linear/quadratic problem, and (B) the problem is complex enough for computational time to be essential. CPLEX is specialized in the narrow class of problems, and should be much faster than Matlab in complex cases.
You do not have to limit the choice of multiobjective methods to the ones offered by Matlab/CPLEX or other solvers (which are usually narrow). It is easy to formulate a scalarized problem by yourself, and then run appropriate single-objective optimization (source: it is one of my main research fields, see e.g. implementation for the class of knapsack problems). The issue boils down to finding a suitable single-objective solver.
If you want to obtain some general information about the whole Pareto optimal set, I recommend to start with deriving the nadir and the ideal objective vectors.
If you want to derive a representation of the Pareto optimal set, besides the mentioned population based-heuristics such as GAs, there are exact methods developed for specific classes of problems. Examples: a library implemented in Julia, a recently published method.
All concepts mentioned here are described in the comprehensive book by Miettinen (1999).
Can cplex solve a pareto type multiobjective one? All i know is that it can solve a simple goal programming by defining the lexicographical objs, or it uses the weighted sum to change weights gradually with sensitivity information and "enumerate" the pareto front, which highly depends on the weights and looks very subjective.
You can refer here as how cplex solves the bi-objetive one, which seems not good.
For a true pareto way which includes the ranking, i only know some GA variants can do like NSGA-II.
A different approach would be to use a domain-specific modeling language for mathematical optimization like YALMIP (or JUMP.jl if you like to give Julia a try). There you can write your optimization problem with Matlab with some extra YALMIP functionalities and use CPLEX (or any other supported solver as a backend) without restricting to one solver.
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I try to apply One Class SVM but my dataset contains too many features and I believe feature selection would improve my metrics. Are there any methods for feature selection that do not need the label of the class?
If yes and you are aware of an existing implementation please let me know
You'd probably get better answers asking this on Cross Validated instead of Stack Exchange, although since you ask for implementations I will answer your question.
Unsupervised methods exist that allow you to eliminate features without looking at the target variable. This is called unsupervised data (dimensionality) reduction. They work by looking for features that convey similar information and then either eliminate some of those features or reduce them to fewer features whilst retaining as much information as possible.
Some examples of data reduction techniques include PCA, redundancy analysis, variable clustering, and random projections, amongst others.
You don't mention which program you're working in but I am going to presume it's Python. sklearn has implementations for PCA and SparseRandomProjection. I know there is a module designed for variable clustering in Python but I have not used it and don't know how convenient it is. I don't know if there's an unsupervised implementation of redundancy analysis in Python but you could consider making your own. Depending on what you decide to do it might not be too tricky (especially if you just do correlation based).
In case you're working in R, finding versions of data reduction using PCA will be no problem. For variable clustering and redundancy analysis, great packages like Hmisc and ClustOfVar exist.
You can also read about other unsupervised data reduction techniques; you might find other methods more suitable.
I am using Gurobi 7.0 through Matlab. Based on the documentation, in order to find the n best solutions you need to set the parameters:
PoolSearchMode=2, to find alternative optimal solutions in a systematic way.
PoolSolutions=n, number of of solution in the pool.
When I do this my result contains the same fields as with the default parameters, i.e. only one solution. I have also tried changing the parameter SolutionNumber, but it does not affect the outcome.
I suspect the alternative optimal solutions are being found, since the solver reports on the prompt a solution count equivalent to n with objective values, but I am not able to retrieve them. I hope this is not another limitation of the Gurobi Matlab API.
Also, I know I could find these solutions using integer cuts, but from my understanding that would be much more inefficient since it would require to start the branch and bound tree from the beginning.
It is not possible. The Gurobi Matlab interface is limited because it does not treat the model as a class, even though Matlab offers object oriented programming. This limits many functionalities. CPLEX however allows Matlab users to interact with the model class and retrieve solutions from the solutions pool.
I am currently running a multiple linear regression using MATLAB's LinearModel.fit function, and I am bit confused in regards to how to properly add interaction terms to the model by hand. As I am aware, LinearModel.fit does not standardize variables on its own, so I have been doing so manually.
So far, the way I have done it has been to
Standardize the observations for each variables
Multiply corresponding standardized values from specific variables to create the interaction terms and then add these new variables to the set of regression data
Run the regression
Is this the correct way to go about doing this? Should I standardize the interaction term variables also after calculating the 'raw' terms? Any help would be greatly appreciated!
Whether or not to standardize interaction terms probably depends on what you intend to do with the model. Standardization typically does not affect model performance as much as it allows for more straightforward model interpretation as your learned coefficients will be on similar scales. I suspect whether to do this or not is largely a matter of opinion. Here is a relevant stats.stackexchange post that may help.
My intuition would be the same as how you have described your process so far.
What algorithm is used by the matlab function linopt::minimize ? I have to write the source code for solving a Mixed Integer Linear Programming problem. Please tell me the algorithms I can work upon.
It is not specified in the documentation of Mathlab (c.f. http://www.mathworks.fr/fr/help/symbolic/mupad_ref/linopt-minimize.html). However, they do provide some references at the end of the page (you should have a look there).
My guesses are the following (based on my humble knowledge regarding state-of-the-art methods for solving LP/MILP) :
1-If the problem is not MILP, we usually use the simplex algorithm (http://en.wikipedia.org/wiki/Simplex_algorithm).
2-If the problem is MILP (i.e. there is some integer variables), one usually use a Branch and Bound algorithm in which we might use simplex for improving the search (we call it Branch and Cut)
P.S. This is not an exhaustive response since other methods can be used but the above are the most known ones.
I'm quite surprised not to find one in standard library. Is there some reason it is missing or I just need to use a specific toolbox?
Implementing it myself would be very problematic because of the complexity of algorithm involved.