Communication and Computation in DCSP Algorithms · 2003. 1. 25. · Communication and Computation...
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Communication and Computation in DCSP Algorithms Universitat de Lleida C` esar Fern` andez Ram´ on B´ ejar Intelligent Information Systems Institute C ORNELL . . Bhaskar Krishnamachari Carla Gomes September, 10th 2002
Transcript of Communication and Computation in DCSP Algorithms · 2003. 1. 25. · Communication and Computation...
Communication and Computationin DCSP Algorithms
Universitat de Lleida
Cesar FernandezRamon Bejar
Intelligent InformationSystems Institute
CORNELL.
.
Bhaskar KrishnamachariCarla Gomes
September, 10th 2002
Testing DisCSP algorithms in real environments Contents
Testing DisCSP algorithms in real environments
The need for realistic DisCSP benchmarks
• We need problem instances that capture the structure of real DisCSP
• But we need an easy way to generate instances with different constrainedness
Our proposal: a distributed resource allocation problem
The effect of the communication network
• In real scenarios, agents will experience the delays of the communication network
• We should investigate how delays affect the performance of the algorithms
Our proposal: a discrete event-simulator able to simulate different delay distributions
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Testing DisCSP algorithms in real environments Contents
Contents
• DisCSP
• SensorDCSP benchmark
• DisCSP algorithms
• Complexity profiles of DisCSP algorithms onSensorDCSP
• The effect of the communication network load
– Delays actively added by the Agents– Delays because of the network load
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Distributed Constraint Satisfaction Problem (DisCSP) Contents
Distributed Constraint Satisfaction Problem (DisCSP)
Agents need to solve different CSPs
• Local constraints (within Agents)
• Global constraints (between Agents)
How do Agents solve it ?
• Local constraints: computation
• Global constraints: computation + communication
What is the impact of the communication network in the performance ?
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SensorDCSP benchmark Contents
SensorDCSP benchmark
Input:
• Multiple sensors (si) and mobiles (tj) randomly scattered
• Constraints:
– sensor visibility bipartite graph (Pv): sensors that can track a given mobile
– every sensor can track at most one mobile
– sensor compatibility graph (Pc): compatibility relation between sensors
Objective: Assign to each mobile 3 pair-wise compatible sensors that can track it
s1
s2
s3
s4
s5
s6
t1
t2
.
.
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SensorDCSP benchmark Contents
SensorDCSP benchmark
Input:
• Multiple sensors (si) and mobiles (tj) randomly scattered
• Constraints:
– sensor visibility bipartite graph (Pv): sensors that can track a given mobile
– every sensor can track at most one mobile
– sensor compatibility graph (Pc): compatibility relation between sensors
Objective: Assign to each mobile 3 pair-wise compatible sensors that can track it
s1
s2
s3
s4
s5
s6
t1
t2
.
.
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SensorDCSP benchmark Contents
SensorDCSP benchmark
Input:
• Multiple sensors (si) and mobiles (tj) randomly scattered
• Constraints:
– sensor visibility bipartite graph (Pv): sensors that can track a given mobile
– every sensor can track at most one mobile
– sensor compatibility graph (Pc): compatibility relation between sensors
Objective: Assign to each mobile 3 pair-wise compatible sensors that can track it
s1
s2
s3
s4
s5
s6
t1
t2
.
.
6
SensorDCSP benchmark Contents
SensorDCSP benchmark
Input:
• Multiple sensors (si) and mobiles (tj) randomly scattered
• Constraints:
– sensor visibility bipartite graph (Pv): sensors that can track a given mobile
– every sensor can track at most one mobile
– sensor compatibility graph (Pc): compatibility relation between sensors
Objective: Assign to each mobile 3 pair-wise compatible sensors that can track it
s1
s2
s3
s4
s5
s6
t1
t2
.
.
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DisCSP algorithms Contents
DisCSP algorithms
Messages exchanged:
• Ok: inform about assignments to its neighbors
• nogood: ask a neighbor to change its assignment
Algorithms:
• Asynchronous Backtracking (ABT)
– static ordering between agents– random selection among values consistent with higher (priority) agents
• Asynchronous Weak-Commitment Search (AWC)
– dynamic priority ordering– random selection among values consistent with higher agents
and that minimize constraint violations with lower agents
Implemented using a distributed discrete-event network simulator
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Complexity profiles of DisCSP algorithms on SensorDCSP Contents
Complexity profiles of DisCSP algorithms on SensorDCSP
• Experimental scenario
– Inter-agent communication delays: exponentially distributed, mean 1 time unit– 3 mobiles and 15 sensors. Pc and Pv ranging from 0.1 to 0.9– 19 instances per point. 9 independent runs for instance
Ratio of satisfiable instances
0.2
0.4
0.6
0.8
Pv0.40.6
0.8
Pc
0
0.2
0.4
0.6
0.8
1
Psat
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Complexity profiles of DisCSP algorithms on SensorDCSP Contents
Mean solution time
AWC
0.2
0.4
0.6
0.8
Pv0.2
0.4
0.6
0.8
Pc
0
2000
4000
6000
Time units
Psat = 0.8
Psat = 0.2
NP-complete for Pc < 1
harder for lower Pc
ABT
0.2
0.4
0.6
0.8
Pv0.2
0.4
0.6
0.8
Pc
0
100
200
300
400
Time units
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Restarting strategy for ABT Contents
Restarting strategy for ABT
• Higher priority agent initiates the restarting of the search
• Performance depends on cutoff time
• Not suitable for AWC due to its inherent dynamic priority behavior
Mean solution time on a hard instance
50
60
70
80
90
100
110
120
10 100
Time units
Cutoff time units
ABT with restarting
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Active delaying of messages Contents
Active delaying of messages
• Adding delay introduces a controlled source of randomization.
• Controlling the level of randomization:
– p, probability that an agent adds extra delay– 0 ≤ r ≤ 1, amount of added delay (fraction of the delay of the link)
Median values for a hard instance (AWC in a fixed delay scenario)
0.1 0.3 0.5 0.7 0.9
p0.3
0.50.7
0.9
r
30405060708090
Time units
0.1 0.3 0.5 0.7 0.9
p0.3
0.50.7
0.9
r
300400500600700800900
Number of messages
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The effect of the communication network load Contents
The effect of the communication network load
• Different traffic conditions modeled by different delay distributions
• Random delays impact algorithms performance in different ways:
– ABT: Fixed delays better than random delays.The greater the variance of the delays,the worse the performance of ABT
– ABT with restarting:Fairly robust to the variance of the delays
– AWC: Random delays better than fixed delays.Extremely robust to the variance of the delays
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The effect of the communication network load Contents
Cumulative density functions of time to solve a hard instance (ABT)
0.001
0.01
0.1
1
10 100 1000
1-C
DF
Time units
ABT
Fixed
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The effect of the communication network load Contents
Cumulative density functions of time to solve a hard instance (ABT)
0.001
0.01
0.1
1
10 100 1000
1-C
DF
Time units
ABT
Fixed
Negative Exponential (σ2 = 1)
Log-normal (σ2 = 10)
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The effect of the communication network load Contents
Cumulative density functions of time to solve a hard instance (ABT)
0.001
0.01
0.1
1
10 100 1000
1-C
DF
Time units
ABT
Fixed
Negative Exponential (σ2 = 1)
Log-normal (σ2 = 10)
Neg. Exp. with restart (σ2 = 1)
Log-normal with restart (σ2 = 10)
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The effect of the communication network load Contents
Cumulative density functions of time to solve a hard instance (AWC)
0.001
0.01
0.1
1
5 10 20 50 100 200
1-C
DF
Time units
AWC
Fixed
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The effect of the communication network load Contents
Cumulative density functions of time to solve a hard instance (AWC)
0.001
0.01
0.1
1
5 10 20 50 100 200
1-C
DF
Time units
AWC
Fixed
Negative Exponential (σ2 = 1)
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The effect of the communication network load Contents
Cumulative density functions of time to solve a hard instance (AWC)
0.001
0.01
0.1
1
5 10 20 50 100 200
1-C
DF
Time units
AWC
Fixed
Negative Exponential (σ2 = 1)
Log-normal (σ2 = 5)
Log-normal (σ2 = 10)
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Conclusions Contents
Conclusions
• Introduction of the SensorDCSP benchmark. Phase transition behavior insatisfiability. Constrainedness adjusted by the visibility and compatibility graphs
• Discrete-event simulator used to determine the impact of different network trafficconditions on the algorithms performance:
– ABT performance worse for random delays
– ABT improved using restarting
– AWC performance better for random delays.Robustness in front of large random delay variations
– AWC improved in fixed delay scenarios by the active addition of random delays
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Conclusions Contents
Conclusions
• Introduction of the SensorDCSP benchmark. Phase transition behavior insatisfiability. Constrainedness adjusted by the visibility and compatibility graphs
• Discrete-event simulator used to determine the impact of different network trafficconditions on the algorithms performance:
– ABT performance worse for random delays
– ABT improved using restarting
– AWC performance better for random delays.Robustness in front of large random delay variations
– AWC improved in fixed delay scenarios by the active addition of random delays
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Conclusions Contents
Conclusions
• Introduction of the SensorDCSP benchmark. Phase transition behavior insatisfiability. Constrainedness adjusted by the visibility and compatibility graphs
• Discrete-event simulator used to determine the impact of different network trafficconditions on the algorithms performance:
– ABT performance worse for random delays
– ABT improved using restarting
– AWC performance better for random delays.Robustness in front of large random delay variations
– AWC improved in fixed delay scenarios by the active addition of random delays
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