Consider two matrices \( Z \) and \( U \) with sizes \( 10 \times 4 \times 10 \) and \( 10 \times 50 \). Suppose we want to perform a maximization operation such that there are three kind of constraints.

  1. Constraints on \( Z \).
  2. Constraints on \( U \).
  3. Constraints that uses both \( Z \) and \( U \).

I was wondering if it is a good practice to first find a matrix \( Z \) satisfying constraints 1, and then find a matrix \( U \) such that it satisfies both constraints 2 and 3. Do you think defining all the constraints 1, 2 and 3 together and calling the optimization function in MATLAB once is a better option. My intuition comes from the fact that the size of Z and U are very large and if we can break it in two pieces, it may speed up the process.

My second question is that if I need to find all solution in the feasible set defined by constraints 1,2 and 3, the objective function goes out of the picture. When I put the objective function as a constant value, all I can get from MATLAB routine is one solution, whereas I require to iterate through all the feasible set. If the set of feasible solutions is large, which of the following option is a better one.

  1. Choosing a random objective function for example a random vector f with the objective function f'x in MATLAB's bintprog routine. My observation is that it results in many duplicate feasible solutions.
  2. Coming up with a solution and then use it as a constraint for the next iteration. However, since I want to iterate through 1000's of solutions, I guess this option is not feasible for me. The constraint matrix size will become very large with iterations.

Is there any other way to iterate through all the feasible solutions?

P.S. Even though a previous poster told me that LATEX is enabled on this forum and directed me to a link, I am unable to write LATEX code in my posts after following the directions on the link. I would be grateful if someone can edit this question and make \(Z\) and \(U\) matrices in LATEX.

asked 26 Aug '15, 05:16

UbaAbd's gravatar image

UbaAbd
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edited 26 Aug '15, 07:16

@UbaAbd: I fixed your latex syntax problem. Compare the edited version and the previous one. The difference is doing the trick.

(26 Aug '15, 06:11) Ehsan ♦

1) AFAIK, MIP optimization is not a strong suit of MATLAB and its built-in libraries. So an important question to consider is that how big is your problem. It would be a good idea to tell us more about your problem dimensions (i.e., number of variable and constraints).

2) What is your maximization criterion that you cannot explicitly state it in MATLAB?

Please note that the main essence of optimization and operations research is that, generally, you don't have enumerate all the feasible solutions to find the best one. Therefore, you should not need to iterate over all the feasible solutions.

(26 Aug '15, 07:08) Ehsan ♦

@Ehsan I have updated the question with matrix sizes. Actually, I want to iterate through all the feasible solutions in my case. I know it is not exactly optimization problem, but solving it using combinatorics and then checking if they satisfy all these constraints was even more hectic. Therefore, I want to come up with all the feasible solutions.

(26 Aug '15, 07:18) UbaAbd

Z and U are variables (not model parameters)? Are their domains restricted (integer, bounded integer, binary, ...)?

(26 Aug '15, 15:12) Paul Rubin ♦♦

@PAUL yes both Z and U are binary.

(26 Aug '15, 16:13) UbaAbd

I would recommend revising the title of the question as it is way to general for what you are asking.

(01 Sep '15, 12:27) Joris Kinable
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Asked: 26 Aug '15, 05:16

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Last updated: 01 Sep '15, 12:27

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