Kadir
January 13, 2021, 8:00pm
1
Hi everyone,
I can run my model with different weight sets for 2 objectives as follows;

set u /1*11/;

loop(u,
w1=1-(ord(u)-1)*0.1;
w2=1-w1;

However, when it comes to 3 objective, I was stuck. Could you help me about this issue? (For intervals of 0.1 similarly above statement)

Renger
January 16, 2021, 9:50am
2
Hi Kaidr
Why don’t you use the random number generator and generate a set of random weights? Something like this:

```
set u /1*11/;
Option Seed=12
parameter w1(u), w2(u), w3(u), delta(u);
w1(u) = uniformInt(0,10);
w2(u) = uniformInt(0,10);
w3(u) = uniformInt(0,10);
delta(u) = w1(u) + w2(u) + w3(u);
w1(u) = round(w1(u)/delta(u),1);
w2(u) = round(w2(u)/delta(u),1);
w3(u) = 1 - w1(u) - w2(u);
parameter check(u);
check(u) = w1(u) + w2(u) + w3(u);
display w1,w2, w3, check;
```

Cheers
Renger

Kadir
January 16, 2021, 10:45am
3
Dear Renger,
Thank you for your answer. It absolutely works but, it may not generate all possible weight pairs, am I right? Or some weight pairs can repeat? This may cause missing some Pareto optimal solutions. Is there a way of producing all possible weights as increasing way such as:

w1 w2 w3
0.1 0 0.9
0.1 0.1 0.8
0.1 0.2 0.7
…
0.1 0.9 0
…
0.9 0.1 0.

Actually, such an approach will cause so many subproblems and will increase the solution effort and times. I think that I can use the epsilon constraint method but I am not sure how will I apply the epsilon constraint method to three objectives. Could you also help me with this issue?

Renger
January 16, 2021, 4:30pm
4
Hi
According to me, you will have 55 combinations of weights. I used this code (there might be a more subtle way to do this):

```
set ln1 /1*10/;
set cnt /1*110/ Counter;
parameter w, w1, w2, w3, delta;
parameter counter;
* Set the first value (as not calculated in the loop)
w("1","1") = 1;
w("1","2") = 0;
w("1","3") = 0;
counter = 0;
loop(ln1,
w1 = 1 - (ord(ln1) -1)*0.1 + EPS;
delta = 1 - w1;
w2 = 0;
w3 = 0;
counter = counter + 1;
while(delta > 0.01,
counter = counter + 1;
w2 = w2 + 0.1;
w(cnt,"1")$(ord(cnt) = counter) = w1;
w(cnt,"2")$(ord(cnt) = counter) = w2;
w(cnt,"3")$(ord(cnt) = counter) = 1 - w1 - w2 + EPS;
delta = 1 - w1 - w2;
);
);
display w;
```

Cheers
Renger

Kadir
January 16, 2021, 7:02pm
5
Dear Renger,
Thank you very much. It is working perfectly.