Hello. I am doing the optimization of transmission planning. I am confused about the definition and declaration of the dynamic set over an equation. I simplify the question as follows:

```
sets
nd node (bus) /n1*n6/
cl(nd,nd) candidate lines /n1.n2,n2.n3/
y /y1/;
alias (nd,nf,ni)
variable
xl(y,nf,ni)
TotalInvCost ;
equations
Objective
InvContLine(y,nd,nd);
Objective .. TotalInvCost =e= sum((y,cl), xl(y,cl));
InvContLine(y,cl(nd,nd)).. xl(y,cl) =g= 1;
model a /all/;
solve a using lp min TotalInvCost;
```

I tried different syntax for the domain set over the equation “InvContLine” to test. There are three results shown ：

- optimal

syntax 1:

```
InvContLine(y,cl(nf,ni)).. xl(y,cl) =g= 1;
```

syntax 2:

```
InvContLine(y,cl(nf,ni)).. xl(y,nf,ni) =g= 1;
```

syntax 3:

```
InvContLine(y,cl).. xl(y,cl) =g= 1;
```

- wrong

syntax 4:

```
InvContLine(y,cl).. xl(y,nf,ni) =g= 1;
```

- unbounded

syntax 5:

```
InvContLine(y,cl(nd,nd)).. xl(y,cl) =g= 1;
```

Now, my question is:

- Compare syntax 2 and syntax 4, what’s the difference? Why is the syntax 4 wrong?
- Comparing syntax 5 and syntax 1, I notice that in the equation list, Constraint “InvContLine” shows none, which is the reason of unbounded result. However, what’s the difference of cl(nd,nd) and cl(nf,ni) in the definition over equations. Is there any restriction on the use of Alias?