Transcript Class notes (powerpoint)

Announcements
• Midterm: Oct 30
• Jakob (27th or 31st)
• 4th homework now posted (Due Oct 18th)
• Project descriptions (1pg) due Oct 23rd
– Need to discuss w/ us in advance
Scheduling example: DSN
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Support ground communication to deep-space satellites
Manage scarce resource (26m antennas)
Schedule communication events
Satellites have variety of communication constraints:
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Need 5-10 minute communication windows
Need at least 4 windows per day
Windows should be spaced 4-8 hours apart
Total communication time must exceed 30 minutes per day
– Objective function
• Maximize “value” of schedule
Representation (Smith et.al)
• Map into constraint satisfaction problem (CSP)
– Set of variables X1..Xn
– Set of values for each variable X1,1..X1,m
– Set of constraints between variables
• X1 <> X2
• Map into constraint optimization problem
– CSP + utility function: U(X1...Xn)
– Choose X1..Xn to maximize U
Simple example
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X1 = {1, 2, 3}
X2 = {1, 2, 3}
X1 <> X2
U(X1,X2) = X1+X2
Simple CSP Algorithm
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If a constraint is violated then FAIL
If all variables have a value then SUCCESS
Else assign a value to some unassigned variable
Repeat, backtracking if necessary
(1)
(2)
(3)
(4)
(5)
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X1 => 1
X2 => 1
FAIL… Backtrack
X2 => 2
Success -- Value = 3
For optimization use branch-and-bound search
Slightly less simple algorithm
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If a constraint is violated then FAIL
If all variables have a value then SUCCESS
Else assign a value to some unassigned variable
Propagate assignment through constraints
Repeat, backtracking if necessary
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E.g. Arc-consistency (one-step lookahead)
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Look at each constraint: X1 <> X2
If some information known about X1 use this to simplify domain
of X2:
Fancier propagation strategies
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Classes of constraints allow more powerful propagation
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Linear equality constraints
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Linear inequalities:
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A1*X1 + A2*X2 = Q  can solve algebraically with
B2*X1 + B2*X2 = W
gaussian elimination
A1*X1 + A2*X2 > 12  can solve with simplex
Many scheduling problems can be cast as linear
equalities and inequalities
Scheduling example: DSN
–
–
–
–
Support ground communication to deep-space satellites
Manage scarce resource (26m antennas)
Schedule communication events
Satellites have variety of communication constraints:
•
•
•
•
Need 5-10 minute communication windows
Need at least 4 windows per day
Windows should be spaced 4-8 hours apart
Total communication time must exceed 30 minutes per day
– Objective function
• Maximize “value” of schedule