Improving DPOP with Branch Consistency for Solving Distributed - PowerPoint PPT Presentation

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Improving DPOP with Branch Consistency for Solving Distributed Constraint Optimization Problems Ferdinando Fioretto 1 , 2 Tiep Le 1 William Yeoh 1 Enrico Pontelli 1 Tran Cao Son 1 1 Dept. Computer Science, New Mexico State University 2 Dept. Mathematics and Computer Science, University of Udine Sept. 9, 2014

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Talk Outline Motivation and Background 1 Branch Consistency for Pseudo-Trees 2 Experiments and Results 3 Conclusions 4

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Distributed Optimization: Motivations Some problems cannot be realistically addressed in a centralized fashion. Agents cooperate to achieve a common objective. Simultaneously they can purse private goals. Agents are constrained by limited communication capabilities. Source: http://kenanaonline.com/users/antennamaker

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Distributed Optimization: Motivations Some problems cannot be realistically addressed in a centralized fashion. Agents cooperate to achieve a common objective. Simultaneously they can purse private goals. Agents are constrained by limited communication capabilities. Solving time is important!

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Distributed Constrained Optimization (DCOP) A DCOP is defined by a tuple �A , X , D , F α � , where: A is a set of agents ; X is a set of variables . D is a set of finite domains . F is a set of utility functions , f i : × x j ∈ scope ( f i ) D j �→ N ∪ { 0 , −∞} . α : X → A maps each variable to one agent. a 1 x 1 > < x 1 x 5 Utilities x 1 < > 0 0 20 x 2 x 3 a 2 a 3 0 1 8 x 2 x 3 = = 0 2 10 soft soft 0 3 3 x 4 a 4 x 4 = . . . = 3 3 2 a 5 x 5 x 5 Constraint Graph Pseudo-tree Soft Constraint Table

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Distributed Constrained Optimization (DCOP) A DCOP is defined by a tuple �A , X , D , F α � , where: A is a set of agents ; X is a set of variables . D is a set of finite domains . F is a set of utility functions , f i : × x j ∈ scope ( f i ) D j �→ N ∪ { 0 , −∞} . α : X → A maps each variable to one agent. a 1 x 1 > < x 1 x 3 Utilities x 1 < > 0 0 −∞ x 2 x 3 a 2 a 3 0 1 0 x 2 x 3 = = 0 2 0 soft soft 0 3 0 x 4 a 4 x 4 = . . . = −∞ 3 3 a 5 x 5 x 5 Constraint Graph Pseudo-tree Hard Constraint Table

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Solving DCOP Find an utility maximal assignment for all the variables of the problem. Agents communicate exchanging messages. This is often the bottleneck!

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Solving DCOP (cont.) Distributed Pseudo-Tree Optimization Procedure (DPOP) x 1 > < Pseudo-Tree Construction Phase. 1 x 2 x 3 UTIL propagation phase. 2 = VALUE propagation phase. 3 x 4 soft = x 5 UTIL Phase Computations of a 5 ( x 5 ) : UTIL Table x 1 x 5 Utilities x 1 x 4 Utilities 0 0 20 max(20+0, 8- ∞ , 10- ∞ , 3- ∞ ) 0 0 = 20 0 1 8 0 1 max(20- ∞ , 8+0, 10- ∞ , 3- ∞ ) = 8 0 2 10 max(20- ∞ , 8- ∞ , 10+0, 3- ∞ ) 0 2 = 10 0 3 3 0 3 max(20- ∞ , 8- ∞ , 10- ∞ , 3+0) = 3 . . . . . . . . .

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Solving DCOP (cont.) Distributed Pseudo-Tree Optimization Procedure (DPOP) x 1 > < Pseudo-Tree Construction Phase. 1 x 2 x 3 UTIL propagation phase. 2 = VALUE propagation phase. 3 x 4 soft = x 5 UTIL Phase Computations of a 5 ( x 5 ) : UTIL Table x 1 x 5 Utilities x 1 x 4 Utilities 0 0 20 max(20+0, 8- ∞ , 10- ∞ , 3- ∞ ) 0 0 = 20 0 1 8 0 1 max(20- ∞ , 8+0, 10- ∞ , 3- ∞ ) = 8 0 2 10 max(20- ∞ , 8- ∞ , 10+0, 3- ∞ ) 0 2 = 10 0 3 3 0 3 max(20- ∞ , 8- ∞ , 10- ∞ , 3+0) = 3 . . . . . . . . .

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Solving DCOP (cont.) Distributed Pseudo-Tree Optimization Procedure (DPOP) x 1 > < Pseudo-Tree Construction Phase. 1 x 2 x 3 UTIL propagation phase. 2 = VALUE propagation phase. 3 x 4 soft = x 5 UTIL Phase Computations of a 5 ( x 5 ) : UTIL Table x 1 x 5 Utilities x 1 x 4 Utilities 0 0 20 max(20+0, 8- ∞ , 10- ∞ , 3- ∞ ) 0 0 = 20 0 1 8 0 1 max(20- ∞ , 8+0, 10- ∞ , 3- ∞ ) = 8 0 2 10 max(20- ∞ , 8- ∞ , 10+0, 3- ∞ ) 0 2 = 10 0 3 3 0 3 max(20- ∞ , 8- ∞ , 10- ∞ , 3+0) = 3 . . . . . . . . .

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Solving DCOP (cont.) Distributed Pseudo-Tree Optimization Procedure (DPOP) x 1 > < Pseudo-Tree Construction Phase. 1 x 2 x 3 UTIL propagation phase. 2 = VALUE propagation phase. 3 x 4 soft = x 5 UTIL Phase Computations of a 5 ( x 5 ) : UTIL Table x 1 x 5 Utilities x 1 x 4 Utilities 0 0 20 max(20+0, 8- ∞ , 10- ∞ , 3- ∞ ) 0 0 = 20 0 1 8 0 1 max(20- ∞ , 8+0, 10- ∞ , 3- ∞ ) = 8 0 2 10 max(20- ∞ , 8- ∞ , 10+0, 3- ∞ ) 0 2 = 10 0 3 3 0 3 max(20- ∞ , 8- ∞ , 10- ∞ , 3+0) = 3 . . . . . . . . .

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Solving DCOP (cont.) Distributed Pseudo-Tree Optimization Procedure (DPOP) x 1 > < Pseudo-Tree Construction Phase. 1 x 2 x 3 UTIL propagation phase. 2 = VALUE propagation phase. 3 x 4 soft = x 5 UTIL Phase Computations of a 5 ( x 5 ) : UTIL Table x 1 x 5 Utilities x 1 x 4 Utilities 0 0 20 max(20+0, 8- ∞ , 10- ∞ , 3- ∞ ) 0 0 = 20 0 1 8 0 1 max(20- ∞ , 8+0, 10- ∞ , 3- ∞ ) = 8 0 2 10 max(20- ∞ , 8- ∞ , 10+0, 3- ∞ ) 0 2 = 10 0 3 3 0 3 max(20- ∞ , 8- ∞ , 10- ∞ , 3+0) = 3 . . . . . . . . .

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Solving DCOP (cont.) Distributed Pseudo-Tree Optimization Procedure (DPOP) x 1 > < Pseudo-Tree Construction Phase. 1 x 2 x 3 UTIL propagation phase. 2 = VALUE propagation phase. 3 x 4 soft = x 5 UTIL Phase Computations of a 5 ( x 5 ) : UTIL Table x 1 x 5 Utilities x 1 x 4 Utilities 0 0 20 max(20+0, 8- ∞ , 10- ∞ , 3- ∞ ) 0 0 = 20 0 1 8 0 1 max(20- ∞ , 8+0, 10- ∞ , 3- ∞ ) = 8 0 2 10 max(20- ∞ , 8- ∞ , 10+0, 3- ∞ ) 0 2 = 10 0 3 3 0 3 max(20- ∞ , 8- ∞ , 10- ∞ , 3+0) = 3 . . . . . . . . .

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Solving DCOP (cont.) Distributed Pseudo-Tree Optimization Procedure (DPOP) x 1 > < Pseudo-Tree Construction Phase. 1 x 2 x 3 UTIL propagation phase. 2 = VALUE propagation phase. 3 x 4 soft = x 5 UTIL Phase Computations of a 5 ( x 5 ) : UTIL Table x 1 x 5 Utilities x 1 x 4 Utilities 0 0 20 max(20+0, 8- ∞ , 10- ∞ , 3- ∞ ) 0 0 = 20 0 1 8 0 1 max(20- ∞ , 8+0, 10- ∞ , 3- ∞ ) = 8 0 2 10 max(20- ∞ , 8- ∞ , 10+0, 3- ∞ ) 0 2 = 10 0 3 3 0 3 max(20- ∞ , 8- ∞ , 10- ∞ , 3+0) = 3 . . . . . . . . .

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Solving DCOP (cont.) Distributed Pseudo-Tree Optimization Procedure (DPOP) x 1 > < Pseudo-Tree Construction Phase. 1 x 2 x 3 UTIL propagation phase. 2 = VALUE propagation phase. 3 x 4 soft = x 5 UTIL Phase Computations of a 5 ( x 5 ) : UTIL Table x 1 x 5 Utilities x 1 x 4 Utilities 0 0 20 max(20+0, 8- ∞ , 10- ∞ , 3- ∞ ) 0 0 = 20 0 1 8 0 1 max(20- ∞ , 8+0, 10- ∞ , 3- ∞ ) = 8 0 2 10 max(20- ∞ , 8- ∞ , 10+0, 3- ∞ ) 0 2 = 10 0 3 3 0 3 max(20- ∞ , 8- ∞ , 10- ∞ , 3+0) = 3 . . . . . . . . .

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Solving DCOP (cont.) Distributed Pseudo-Tree Optimization Procedure (DPOP) x 1 > < Pseudo-Tree Construction Phase. 1 x 2 x 3 UTIL propagation phase. 2 = VALUE propagation phase. 3 x 4 soft = x 5 UTIL Phase Computations of a 5 ( x 5 ) : UTIL Table x 1 x 5 Utilities x 1 x 4 Utilities 0 0 20 max(20+0, 8- ∞ , 10- ∞ , 3- ∞ ) 0 0 = 20 0 1 8 0 1 max(20- ∞ , 8+0, 10- ∞ , 3- ∞ ) = 8 0 2 10 max(20- ∞ , 8- ∞ , 10+0, 3- ∞ ) 0 2 = 10 0 3 3 0 3 max(20- ∞ , 8- ∞ , 10- ∞ , 3+0) = 3 . . . . . . . . .

Motivation and Background Branch Consistency for Pseudo-Trees Experiments and Results Conclusions Solving DCOP (cont.) Distributed Pseudo-Tree Optimization Procedure (DPOP) x 1 > < Pseudo-Tree Construction Phase. 1 x 2 x 3 UTIL propagation phase. 2 = VALUE propagation phase. 3 x 4 soft = x 5 UTIL Phase Computations of a 5 ( x 5 ) : UTIL Table x 1 x 5 Utilities x 1 x 4 Utilities 0 0 20 max(20+0, 8- ∞ , 10- ∞ , 3- ∞ ) 0 0 = 20 0 1 8 0 1 max(20- ∞ , 8+0, 10- ∞ , 3- ∞ ) = 8 0 2 10 max(20- ∞ , 8- ∞ , 10+0, 3- ∞ ) 0 2 = 10 0 3 3 0 3 max(20- ∞ , 8- ∞ , 10- ∞ , 3+0) = 3 . . . . . . . . .