Need Help In Solving A Constraint Problem (2nd)
I have solved the following constraint processing task. Can you please verify if it is correct?
One of the prisoners of a high-level security prison sees a way to escape. Almost
free, he reaches a corridor of 20 meters long, guarded by 5 cameras, behind
which is the exit. In Figure 3, we provide a schematic overview of the corridor.
The prisoner has only 10 seconds to reach the end of the corridor and may
not be noticed by the cameras in doing so. After 10 seconds, or when seen by a
camera, the prison is put under total lock-down, which will prevent his escape.
We will consider the following constraints:
• A camera can only see 3 meters and cannot see its own position. E.g., the
camera at position 9 is able to see the positions 6, 7 and 8, or 10, 11 and
12, depending on the orientation of the camera.
• At time point 0, all cameras are oriented towards the end of the corridor.
Thus, the camera at position 9 sees positions 10, 11 and 12.
• Every two seconds the cameras change their orientation. Thus, at time
point 2 the camera at position 9 will see the positions 6, 7 and 8.
• Every second, the prisoner can move 0, 1, 2 or 3 meters forward. He
cannot move backward. Thus, if the prisoner is standing at position 2 at
time point 2, then, at time point 3, he can be on position 2, 3, 4 or 5.
Formulate the problem above as a constraint problem. Come up with a useful
representation of the problem in terms of the constraint processing tool. Provide
an explanation of indices, variables and domains. Furthermore, provide for every
introduced constraint, the meaning of the constraint in natural language.
This is my solution and want you guys to check for me where am doing wrong:
***MY VARIABLES***
Name: T, domain: 0..10 // T = the time from 0 to 10 seconds
Name: P, domain: 0..3 // P = Prisoner can move 0, 1, 2, 3 meters
Name: C1, domain: 2 // C1 = camera 1
Name: C2, domain: 4 // C2 = camera 2
Name: C3, domain: 9 // C3 = camera 3
Name: C4, domain: 12 // C4 = camera 14
Name: C5, domain: 17 // C5 = camera 5
Name: View1, domain: -1..5 // camera1 view
Name: View2, domain: 1..7 // camera2 view
Name: View3, domain: 6..12 // camera3 view
Name: View4, domain: 9..15 // camera4 view
Name: View5, domain: 14..20 // camera5 view
MY CONSTRAINTS
I declared the constraints in such a way that at each time the view of the cameras are changed alternatively when the time is even number but when the time is oneven, only the prisoner can move. Constraint: (T=0/\View1=(C1+3)/\View2=(C2+3)/\View3=(C3+3)/\View4=(C4+3)/\View5=(C5+3)/\P(i)), range: i>-1
Constraint: (T=1/\P(i)), range: i>0
Constraint: (T=2/\View1=(C1-3)/\View2=(C2-3)/\View3=(C3-3)/\View4=(C4-3)/\View5=(C5-3)/\P(i)), range: i>-1
Constraint: (T=3/\P(i)), range: i>0
Constraint: (T=4/\View1=(C1+3)/\View2=(C2+3)/\View3=(C3+3)/\View4=(C4+3)/\View5=(C5+3)/\P(i)), range: i>-1
Constraint: (T=5/\P(i)), range: i>0
Constraint: (T=6/\View1=(C1-3)/\View2=(C2-3)/\View3=(C3-3)/\View4=(C4-3)/\View5=(C5-3)/\P(i)), range: i>-1
Constraint: (T=7/\P(i)), range: i>0
Constraint: (T=8/\View1=(C1+3)/\View2=(C2+3)/\View3=(C3+3)/\View4=(C4+3)/\View5=(C5+3)/\P(i)), range: i>-1
Constraint: (T=9/\P(i)), range: i>0
Constraint: (T=10/\View1=(C1-3)/\View2=(C2-3)/\View3=(C3-3)/\View4=(C4-3)/\View5=(C5-3)/\P(i)), range: i>-1
Guys, i know am doing something wrong so help me to rectify it.
Thanks for your help. I posted a similar question yesterday, so if you want to know the syntax for the variables and constraints, then t开发者_开发百科his is the link: Variable and Constraint syntax in this post
Thanks for your help
You've forgotten that a camera cannot see itself : "A camera can only see 3 meters and cannot see its own position".Thus, View1, View2... View5 should be modified.
Als, you need one variable for the position of the prisoner (you have one only for the movement of the prisoner)
I'm looking for other mistakes.
精彩评论