Originally posted by: Xifeng

Hi, everyone! I want to solve a multi-objective optimization problem, one of whose objectives is described as a normal cumulative distribution function. Can it be solved using CPLEX? 

Hi,

The function staticLex defines a multi-criteria policy, ordering the different criteria and performing lexicographic optimization. The first criterion is considered to be the most important one; any improvement of this criterion is worth any loss on the other criteria. The second criterion is the second most important one, and so on. The last criterion is the least important one.

regards

Originally posted by: Xifeng

Hi Alex,

Thank you very much for your kindly help and support! Further, if one of the component objectives is an expression of cumulative distribution function, how to do it? In the Help files, I cannot find any statistical function. I'm a beginner in CPLEX and need your guidance.

Best regards

Hi,

let s consider the cdf as an array of value.

Let me give you a small example I derived from the floatexpr example with the cdf of uniform distribution:

using CP;

dvar int i in 1..100;
dvar int j in 1..100;
dvar int k in 1..99;

float cdf[k in 0..100]=k/100;

dexpr float kf = k/100;
dexpr float ar[i in 1..10] = k/i;

minimize staticLex(kf + sum(i in 1..10)ar[i],cdf[k]);

subject to {
   i*(1+kf) == j;
}

 

regards

Originally posted by: Xifeng

Hi Alex,

You are a good teacher, thank you so much for your help! There are other two questions: the first one is how to get the minimum non-negative number in a matrix; and the second one is why the time of solving a multi-objective problem is unacceptable using CP optimizer, while each component objective can be solved efficiently by CPLEX optimizer?

I appreciate your time and look forward to you guidance!

Best regards

Hi

about

why the time of solving a multi-objective problem is unacceptable using CP optimizer

have you set a time limit ?

regards

Originally posted by: Xifeng

Hi Alex,

I think you might have misunderstood me because my description was unclear. My question is whether or not the time spent solving a multi-objective problem with CP optimizer is subject to not only the problem size but also the number of its objectives.

Kind regards

Originally posted by: Petr Vilím

Hello,

it is very hard to estimate the time needed to solve a CP problem. It cannot be easily said that it depends on number of variables, number of constraints or, to your question, number of objectives. The only reliable way is to solve the problem multiple times using multiple random seeds and compare the results (see executable cpoptimizer and its command "tools runseeds". Or even better, compare on multiple instances of the same problem.

As Alex noted, often you have to use time limit since you cannot wait for proof of optimality.

Best regards, Petr

Originally posted by: Xifeng

Hello Petr,

Thank you so much for your answer and guidance!

Best regards,

Xifeng