ProjectSCooP-Sakura · ProjectSCooP-Sakura Presentation, Progress, Perspectives...
Transcript of ProjectSCooP-Sakura · ProjectSCooP-Sakura Presentation, Progress, Perspectives...
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Project SCooP-SakuraPresentation, Progress, Perspectives
NII, Japan, and LINA, France
Martine Ceberio
LINA, Nantes France / University of Texas at El Paso
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 1/29
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Outline of the presentation
• Context and general presentation of the project
• What is this about?, and what are our objectives?
• Besides constraints, other issues we will have to tackle
• Conclusion and future plans
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 2/29
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Getting acquainted with:
SCooP-Sakura
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 3/29
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What is SCooP-Sakura?
SCooP
• . Soft and Continuous Constraint Programming
• Cooperative project between NII (Tokyo) and LINA (Nantes)
• Part of the MOU between these institutes
• Objectives of SCooP: integrate all projects related to soft
and / or continuous constraints between NII and LINA
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 4/29
![Page 5: ProjectSCooP-Sakura · ProjectSCooP-Sakura Presentation, Progress, Perspectives NII,Japan,andLINA,France Martine Ceberio LINA, Nantes France / University of Texas at El Paso FJCP,](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8fe69d415425097a66c1f7/html5/thumbnails/5.jpg)
What is SCooP-Sakura?
SCooP
• . Soft and Continuous Constraint Programming
• Cooperative project between NII (Tokyo) and LINA (Nantes)
• Part of the MOU between these institutes
• Objectives of SCooP: integrate all projects related to soft
and / or continuous constraints between NII and LINA
Projects integrated to SCooP
• Speculative Constraint Processing in Multi-Agent Systems
Members: Ken Satoh, Hiroshi Hosobe, Makoto Yokoo, Katsutoshi
Hirayama, Martine Ceberio
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 4/29
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What is SCooP-Sakura?
SCooP
• . Soft and Continuous Constraint Programming
• Cooperative project between NII (Tokyo) and LINA (Nantes)
• Part of the MOU between these institutes
• Objectives of SCooP: integrate all projects related to soft
and / or continuous constraints between NII and LINA
Projects integrated to SCooP
• Speculative Constraint Processing in Multi-Agent Systems
• Dynamic CSP
Members: Ken Satoh, Hiroshi Hosobe, Narendra Jussien
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 4/29
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What is SCooP-Sakura?
SCooP
• . Soft and Continuous Constraint Programming
• Cooperative project between NII (Tokyo) and LINA (Nantes)
• Part of the MOU between these institutes
• Objectives of SCooP: integrate all projects related to soft
and / or continuous constraints between NII and LINA
Projects integrated to SCooP
• Speculative Constraint Processing in Multi-Agent Systems
• Dynamic CSP
• project Sakura
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 4/29
![Page 8: ProjectSCooP-Sakura · ProjectSCooP-Sakura Presentation, Progress, Perspectives NII,Japan,andLINA,France Martine Ceberio LINA, Nantes France / University of Texas at El Paso FJCP,](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8fe69d415425097a66c1f7/html5/thumbnails/8.jpg)
More about Sakura
Continuous Soft Constraintsand Graphical Applications
Funded by:
• the French Ministry of Foreign Affairs (program: Égide PAI)
• the Japan Society for the Promotion of Science (JSPS)
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 5/29
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More about Sakura
Continuous Soft Constraintsand Graphical Applications
Funded by:
• the French Ministry of Foreign Affairs (program: Égide PAI)
• the Japan Society for the Promotion of Science (JSPS)
Members:
• NII: Ken Satoh, Hiroshi Hosobe
• LINA: Frederic Benhamou, Christophe Jermann,
Martine Ceberio
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 5/29
![Page 10: ProjectSCooP-Sakura · ProjectSCooP-Sakura Presentation, Progress, Perspectives NII,Japan,andLINA,France Martine Ceberio LINA, Nantes France / University of Texas at El Paso FJCP,](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8fe69d415425097a66c1f7/html5/thumbnails/10.jpg)
More about Sakura
Continuous Soft Constraintsand Graphical Applications
Funded by:
• the French Ministry of Foreign Affairs (program: Égide PAI)
• the Japan Society for the Promotion of Science (JSPS)
Members:
• NII: Ken Satoh, Hiroshi Hosobe
• LINA: Frederic Benhamou, Christophe Jermann,
Martine Ceberio
Began since first semester of 2004.
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 5/29
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The nuts and bolts of:
Project Sakura
• Motivation
• Objectives
• Framework
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 6/29
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Constraint satisfaction
Solving a (set of) constraint(s):
determining the instanciations of the variables (within the
specified domains) that meet/satisfy the constraint(s)
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 7/29
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Constraint satisfaction
Solving a (set of) constraint(s):
determining the instanciations of the variables (within the
specified domains) that meet/satisfy the constraint(s)
= Splitting the search space (i.e., the variables’ domains) into:
• the elements satisfying the constraints (consistent elements)
• the elements violating the constraints (inconsistent elements)
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 7/29
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Why be flexible?
1. because constraints may not be compatible:
i.e., no instanciation meets the constraintse.g., the model 6= expected picture of the situation
or too ambitious to be consistent
etc.
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 8/29
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Why be flexible?
1. because constraints may not be compatible:
i.e., no instanciation meets the constraintse.g., the model 6= expected picture of the situation
or too ambitious to be consistent
etc.
2. because it may make no sense to divide accurately the search
space into two precisely bounded parts
e.g., when data not accurate enough, due to machine error
meaningless to define an accurate frontier between elements
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 8/29
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Example
Organizing a meeting with n participants
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 9/29
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Example
Organizing a meeting with n participants
• all participants have a tight schedule
• we know the schedule of each of them: meeting times, timeto go from one meeting to the other (known with uncertainty→ interval), etc.
? is there a time slot, on day d, s.t. all can meet?
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 9/29
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Example
Organizing a meeting with n participants
• all participants have a tight schedule
• we know the schedule of each of them: meeting times, timeto go from one meeting to the other (known with uncertainty→ interval), etc.
? is there a time slot, on day d, s.t. all can meet?
Most probably not...
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 9/29
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Example
Organizing a meeting with n participants
• all participants have a tight schedule
• we know the schedule of each of them: meeting times, timeto go from one meeting to the other (known with uncertainty→ interval), etc.
? is there a time slot, on day d, s.t. all can meet?
Most probably not...
On the other hand:
• this meeting may be held without everybody attending?
• there may be possible other changes in the schedules ofparticipants?
• etc.
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 9/29
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Example
Organizing a meeting with n participants
• all participants have a tight schedule
• we know the schedule of each of them: meeting times, timeto go from one meeting to the other (known with uncertainty→ interval), etc.
? is there a time slot, on day d, s.t. all can meet?
Most probably not...
On the other hand:
• this meeting may be held without everybody attending?
• there may be possible other changes in the schedules ofparticipants?
• etc. Many possible adjustments...
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 9/29
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Objectives of Sakura
• Implement a library for handling such inconsistent problems
◦ objectives of such a tool
NOT to provide the user with expert advise
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 10/29
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Objectives of Sakura
• Implement a library for handling such inconsistent problems
◦ objectives of such a tool
NOT to provide the user with expert advise
BUT to determine solutionsa corresponding to his/her
relaxation
ato be defined later
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 10/29
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Objectives of Sakura
• Implement a library for handling such inconsistent problems
◦ objectives of such a tool
NOT to provide the user with expert advise
BUT to determine solutions corresponding to his/her
relaxation
∗ we may also make suggestions: using qualitative information
about constraints (cf. Christophe Jermann’s work)
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 10/29
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Objectives of Sakura
• Implement a library for handling such inconsistent problems
◦ objectives of such a tool
NOT to provide the user with expert advise
BUT to determine solutions corresponding to his/her
relaxation
∗ we may also make suggestions: using qualitative information
about constraints (cf. Christophe Jermann’s work)
• Design a user-friendly interface
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 10/29
![Page 25: ProjectSCooP-Sakura · ProjectSCooP-Sakura Presentation, Progress, Perspectives NII,Japan,andLINA,France Martine Ceberio LINA, Nantes France / University of Texas at El Paso FJCP,](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8fe69d415425097a66c1f7/html5/thumbnails/25.jpg)
Objectives of Sakura
• Implement a library for handling such inconsistent problems
◦ objectives of such a tool
NOT to provide the user with expert advise
BUT to determine solutions corresponding to his/her
relaxation
∗ we may also make suggestions: using qualitative information
about constraints (cf. Christophe Jermann’s work)
• Design a user-friendly interface
But then: what kind of flexibility?
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 10/29
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Sakura: What kind of flexibility?
Constraint c1 : (x − 7
4)2 + y
2 ≤(
3
2
)2
Constraint c2 : x + 2y2 ≤ −1
4
Solution set = ∅
• stretch the constraints
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 11/29
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Sakura: What kind of flexibility?
Constraint c1 : (x − 7
4)2 + y
2 ≤(
3
2
)2
Constraint c2 : x + 2y2 ≤ −1
4
Solution set = ∅
• stretch the constraints
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 11/29
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Sakura: What kind of flexibility?
Constraint c′1
: (x − 7
4)2 + y
2 ≤(
9
4
)2
Constraint c′2
: x + 2y2 ≤ 1
2
Solution set = ∅ “Extended” solution set
• stretch the constraints
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 11/29
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Sakura: What kind of flexibility?
Constraint c′1
: (x − 7
4)2 + y
2 ≤(
9
4
)2
Constraint c′2
: x + 2y2 ≤ 1
2
Solution set = ∅ “Extended” solution set
• stretch the constraints
• establish orders, with possible interpretations such as:
• preferences over the constraints with possible distances
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 11/29
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Sakura: What kind of flexibility?
Constraint c1 : (x −7
4)2 + y
2 ≤(
3
2
)2
Constraint c2 : x + 2y2 ≤ −1
4
Constraint c3 : (x −3
2)2 + (y −
3
2)2 ≤ 1
Preference order: c1 > c2 > c3
• stretch the constraints
• establish orders, with possible interpretations such as:
• preferences over the constraints with possible distances
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 11/29
![Page 31: ProjectSCooP-Sakura · ProjectSCooP-Sakura Presentation, Progress, Perspectives NII,Japan,andLINA,France Martine Ceberio LINA, Nantes France / University of Texas at El Paso FJCP,](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8fe69d415425097a66c1f7/html5/thumbnails/31.jpg)
Sakura: What kind of flexibility?
Constraint c1 : (x −7
4)2 + y
2 ≤(
3
2
)2
Constraint c2 : x + 2y2 ≤ −1
4
Constraint c3 : (x −3
2)2 + (y −
3
2)2 ≤ 1
Preference order: c1 > c2 > c3
• stretch the constraints
• establish orders, with possible interpretations such as:
• preferences over the constraints with possible distances
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 11/29
![Page 32: ProjectSCooP-Sakura · ProjectSCooP-Sakura Presentation, Progress, Perspectives NII,Japan,andLINA,France Martine Ceberio LINA, Nantes France / University of Texas at El Paso FJCP,](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8fe69d415425097a66c1f7/html5/thumbnails/32.jpg)
Sakura: What kind of flexibility?
Constraint c1 : (x −7
4)2 + y
2 ≤(
3
2
)2
Constraint c2 : x + 2y2 ≤ −1
4
Constraint c3 : (x −3
2)2 + (y −
3
2)2 ≤ 1
Preference order: c1 > c2 > c3
• stretch the constraints
• establish orders, with possible interpretations such as:
• preferences over the constraints with possible distances
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 11/29
![Page 33: ProjectSCooP-Sakura · ProjectSCooP-Sakura Presentation, Progress, Perspectives NII,Japan,andLINA,France Martine Ceberio LINA, Nantes France / University of Texas at El Paso FJCP,](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8fe69d415425097a66c1f7/html5/thumbnails/33.jpg)
Sakura: What kind of flexibility?
Constraint c1 : (x −7
4)2 + y
2 ≤(
3
2
)2
Constraint c2 : x + 2y2 ≤ −1
4
Constraint c3 : (x −3
2)2 + (y −
3
2)2 ≤ 1
Preference order: c1 > c2 > c3
• stretch the constraints
• establish orders, with possible interpretations such as:
• preferences over the constraints with possible distances
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 11/29
![Page 34: ProjectSCooP-Sakura · ProjectSCooP-Sakura Presentation, Progress, Perspectives NII,Japan,andLINA,France Martine Ceberio LINA, Nantes France / University of Texas at El Paso FJCP,](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8fe69d415425097a66c1f7/html5/thumbnails/34.jpg)
Sakura: What kind of flexibility?
Constraint c1 : (x −7
4)2 + y
2 ≤(
3
2
)2
Constraint c2 : x + 2y2 ≤ −1
4
Constraint c3 : (x −3
2)2 + (y −
3
2)2 ≤ 1
Preference order: c1 > c2 > c3
• stretch the constraints
• establish orders, with possible interpretations such as:
• preferences over the constraints with possible distances
• over the constraints as crisp constraints
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 11/29
![Page 35: ProjectSCooP-Sakura · ProjectSCooP-Sakura Presentation, Progress, Perspectives NII,Japan,andLINA,France Martine Ceberio LINA, Nantes France / University of Texas at El Paso FJCP,](https://reader034.fdocuments.net/reader034/viewer/2022042113/5e8fe69d415425097a66c1f7/html5/thumbnails/35.jpg)
Sakura: What kind of flexibility?
Constraint c1 : (x − 7
4)2 + y
2 ≤(
3
2
)2
Constraint c2 : x + 2y2 ≤ −1
4
Solution set = ∅
• stretch the constraints
• establish orders, with possible interpretations such as:
• preferences over the constraints with possible distances
• over the constraints as crisp constraints
• with “if then else” meaning
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 11/29
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Sakura: What kind of flexibility? (cont’d)
• stretch the constraints
• strong preferences: order over the satisfaction of the constraints
• weak preferences: order met only if possible
• priorities
• “if then else” orders: if c1 then c1 ∧ c2, else c3
• hierarchies
• etc.
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 12/29
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Sakura: What kind of flexibility? (cont’d)
• stretch the constraints
• strong preferences: order over the satisfaction of the constraints
• weak preferences: order met only if possible
• priorities
• “if then else” orders: if c1 then c1 ∧ c2, else c3
• hierarchies
• etc.
Objective: be general enoughPractically: we focus on graphical applications
(cf. Hosobe-sensei’s presentation)
Later: we will enrich our application fields
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Sakura: aim of our work
• Based on constraint solving and optimization methods:
◦ optimization: minimization of the violation
◦ constraint solving: to maintain a preference order + for
when non-zero distances to constraints are not allowed
• Be general enough to be able to model many kinds of soft
constraints
◦ yet we will restrict ourselves to some of them
• Use state-of-the-art solvers to benefit from:
◦ their properties
◦ the implementation... already done, tested, optimized
connection between our framework and classical
problems
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Sakura: a glance at the framework we currenlty use
c (c, f)
C (C,A, F, t)
where, at the constraint’s level:
• f stands for any error function: distance, stair function, etc.
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Sakura: a glance at the framework we currenlty use
c (c, f)
C (C,A, F, t)
where, at the constraint’s level:
• f stands for any error function: distance, stair function, etc.
c (c, d)
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Sakura: a glance at the framework we currenlty use
c (c, f)
C (C,A, F, t)
where, at the constraint’s level:
• f stands for any error function: distance, stair function, etc.
cδ
search space E
solution set of c a relaxation of c consistent over E
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Sakura: a glance at the framework we currenlty use
c (c, f)
C (C,A, F, t)
where, at the constraint’s level:
• f stands for any error function: distance, stair function, etc.
c : f (x) ≤ 0
distance to cf (x)
xx2
d2
x1
d1
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Sakura: a glance at the framework we currenlty use
c (c, f)
C (C,A, F, t)
where, at the constraint’s level:
• f stands for any error function: distance, stair function, etc.
Optimization: minimization of error
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Sakura: a glance at the framework we currenlty use
c (c, f)
C (C,A, F, t)
where, at the constraint’s level:
• f stands for any error function: distance, stair function, etc.
and when it comes to sets of constraints C = (c1, . . . , cn):
• F = (f1, . . . , fn)
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Sakura: a glance at the framework we currenlty use
c (c, f)
C (C,A, F, t)
where, at the constraint’s level:
• f stands for any error function: distance, stair function, etc.
and when it comes to sets of constraints C = (c1, . . . , cn):
• F = (f1, . . . , fn)
c1 c2
c3
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Sakura: a glance at the framework we currenlty use
c (c, f)
C (C,A, F, t)
where, at the constraint’s level:
• f stands for any error function: distance, stair function, etc.
and when it comes to sets of constraints C = (c1, . . . , cn):
• F = (f1, . . . , fn)
• A is a vector of aggregation operators
e.g., a = f1 + · · · + fn
Optimization: minimization of the global error a(f1, . . . , fn)
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Sakura: a glance at the framework we currenlty use
c (c, f)
C (C,A, F, t)
where, at the constraint’s level:
• f stands for any error function: distance, stair function, etc.
and when it comes to sets of constraints C = (c1, . . . , cn):
• F = (f1, . . . , fn)
• A is a vector of aggregation operators
• t is a tree representing the order over constraints
Constrained optimization:
minimization of the error while satisfying the order
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Sakura: a glance at the framework... (cont’d)
A few more words on A and t...
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Sakura: a glance at the framework... (cont’d)
A few more words on A and t...
• t a tree of (sets of) constraints, defining the order over constraints
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Sakura: a glance at the framework... (cont’d)
A few more words on A and t...
• t a tree of (sets of) constraints, defining the order over constraints
c1, . . . , cn
◦ No order
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Sakura: a glance at the framework... (cont’d)
A few more words on A and t...
• t a tree of (sets of) constraints, defining the order over constraints
c1
1, . . . , c
1n1
c2
1, . . . , c
2n2
. . .
cp
1, . . . , c
p
np
◦ (Linear) Hierarchies of constraints: level 1 preferred to level 2, and
so on and so forth...
◦ Priorities over (sets of) constraints: if level 1 can be satisfied, then
try to satisfy level 2 too, etc. if level 1 inconsistent, no solution...
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Sakura: a glance at the framework... (cont’d)
A few more words on A and t...
• t a tree of (sets of) constraints, defining the order over constraints
c1
1, . . . , c
1n1
c2
1, . . . , c
2n2
c3
1, . . . , c
3n3
. . .. . .
◦ (More complex) Hierarchies: general treeeach edge stands for the parent being preferred to the children
for k = 2, 3, ∀i ∈ {1, . . . , n1}, jk ∈ {1, . . . , nk}, f1
i (x) 6 fkjk
(x)
and / or:for k = 2, 3, a1(f
1
1 (x), . . . , f1
n1) 6 ak(fk
1 (x), . . . , fknk
)
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Sakura: a glance at the framework... (cont’d)
A few more words on A and t...
• t a tree of (sets of) constraints, defining the order over constraints
c1
1, . . . , c
1n1
c2
1, . . . , c
2n2
c3
1, . . . , c
3n3
. . .. . .
◦ “if . . . then . . . else . . . ” constraint structure: binary tree
if c11∧ · · · ∧ c1n1
then (c11∧ · · · ∧ c1n1
) ∧ (c21∧ · · · ∧ c2n2
)
else c31∧ · · · ∧ c3n3
Problem with this scheme: may lead to inconsistencies too...
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Sakura: a glance at the framework... (cont’d)
A few more words on A and t...
• t a tree of (sets of) constraints, defining the order over constraints
• A a vector of aggregation operators
A = (a0, a1, . . . , ap)
◦ a0 is a global aggregation operator, possibly not defined ( flag “?”)
◦ (a1, . . . , ap) is a vector of additional aggreg. op., possibly empty
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Sakura: a glance at the framework... (cont’d)
A few more words on A and t...
• t a tree of (sets of) constraints, defining the order over constraints
• A a vector of aggregation operators
For instance:
◦ A = (a0) when there is no order, i.e., t=single node tree
◦ A = (?, a1, . . . , ap) when t consists of p nodes
e.g., constraint hierarchies
◦ A = (a0) and t has p nodes: strong hierarchy
◦ A = (?) and t has p nodes: depending on the structure of t,
interpreted as “linear” priority or “if . . . then . . . else . . . ”
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Sakura: examples
Stretching the constraints:
(C, (a0 =∑
), (d1, . . . , dn), t1 =c1, . . . , cn
)
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Sakura: examples
Stretching the constraints: (C, (a0 =P
), (d1, . . . , dn), t1 =c1, . . . , cn
)
Hierarchy of constraints:
(C, (?, a1, . . . , ap), (d1, . . . , dn), t2 =c1
1, . . . , c
1n1
c2
1, . . . , c
2n2
. . .
cp
1, . . . , c
p
np
)
here each level has its aggregated value smaller than lower levels
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Sakura: examples
Stretching the constraints: (C, (a0 =P
), (d1, . . . , dn), t1 =c1, . . . , cn
)
Hierarchy of constraints: 1. (C, (?, a1, . . . , ap), (d1, . . . , dn), t2 =c1
1, . . . , c
1n1
c2
1, . . . , c
2n2
. . .
cp
1, . . . , c
p
np
)
here each level has its aggregated value smaller than lower levels
Hierarchy of constraints:
(C, (a0), (d1, . . . , dn), t2 =c1
1, . . . , c
1n1
c2
1, . . . , c
2n2
. . .
cp
1, . . . , c
p
np
)
here we minimize a0(x) under dji (x) 6 dl
k(x) for all i < j:stronger than former hierarchy scheme
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Sakura: examples
Stretching the constraints: (C, (a0 =P
), (d1, . . . , dn), t1 =c1, . . . , cn
)
Hierarchy of constraints: 1. (C, (?, a1, . . . , ap), (d1, . . . , dn), t2 =c1
1, . . . , c
1n1
c2
1, . . . , c
2n2
. . .
cp
1, . . . , c
p
np
)
here each level has its aggregated value smaller than lower levels
2. (C, (a0), (d1, . . . , dn), t2)
here we minimize a0(x) under dji (x) 6 dl
k(x) for all i < j
Tree structures:
(C, (?, a1, . . . , ap), (d1, . . . , dn), t3 =c1
1, . . . , c
1n1
c2
1, . . . , c
2n2
c3
1, . . . , c
3n3
. . .. . .
)
or (a0)
extension of the former linear hierarchy schemes (1, 2)
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Sakura: examples
Stretching the constraints: (C, (a0 =P
), (d1, . . . , dn), t1 =c1, . . . , cn
)
Hierarchy of constraints: 1. (C, (?, a1, . . . , ap), (d1, . . . , dn), t2 =c1
1, . . . , c
1n1
c2
1, . . . , c
2n2
. . .
cp
1, . . . , c
p
np
)
here each level has its aggregated value smaller than lower levels
2. (C, (a0), (d1, . . . , dn), t2)
here we minimize a0(x) under dji (x) 6 dl
k(x) for all i < j
Tree structures: (C, (?, a1, . . . , ap)or(a0), (d1, . . . , dn), t3 =c1
1, . . . , c
1n1
c2
1, . . . , c
2n2
c3
1, . . . , c
3n3
. . .. . .
)
extension of the former linear hierarchy schemes (1, 2)
“If then else” structures:
(C, (?), (d1, . . . , dn), t3 =c1
1, . . . , c
1n1
c2
1, . . . , c
2n2
c3
1, . . . , c
3n3
. . .. . .
)
constraint satisfaction only: degenerate optimization problem
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We can still...
• set weights on constraints
(C,∑
, (dw1, . . . , dwn
), t = t1)
• value the elements of the search space
all appropriate functions f associated to constraints are allowed
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Remaining issues
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Issues
• Modeling language
• New aggregation operators
• Provide a semantics to the solution set of:
◦ prioritized clusters of constraints,◦ partial orders over prioritized constraints
• What kind of output?
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Modeling language
• choose a standard language (i.e., AMPL or any otherlanguage commonly used as input of classical solvers):◦ we may need to extend such a language, yet keeping
easily useable and standard
• expressive enough to model soft constraints precisely (noambiguity left)◦ possibly adjust the framework (data structure)◦ we have to make clear the correspondence between
modeling and solutions: the user should get what s/heexpects
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Expressiveness of the modeling language
Associating values to constraints is ambiguous
• does it define the aggregation operator?weights weighted sum, valued CSP
a(d1(x), . . . , dn(x)) = w1 × d1(x) + · · · + wn × dn(x)
• or does it define an order : as preference levels for instance
(c1, 5), (c2, 3)?⇔ c1 � c2
but then what kind of preference: crisp? soft?
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Expressiveness of the modeling language
Associating values to constraints is ambiguous
• does it define the aggregation operator?weights weighted sum, valued CSP
a(d1(x), . . . , dn(x)) = w1 × d1(x) + · · · + wn × dn(x)
• or does it define an order : as preference levels for instance
(c1, 5), (c2, 3)?⇔ c1 � c2
but then what kind of preference: crisp? soft?
We need slightly more detail, e.g., a “code” specifying the use ofan order and the kind of this order
is a tree expressive enough?
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 21/29
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New aggregation operators
• Idea: benefit from the Multi-Criteria Decision Making (MCDM)techniques
• no linear aggregation: weighted sum assume linearindependence
• criteria are aggregated using integrals (Choquet, Sugeno),usually discretized
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Improve the semantics of prioritized constraints
Generalize the total-order scheme to more complex ones.
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Improve the semantics of prioritized constraints
Generalize the total-order scheme to more complex ones.
Problems so far:if more than one branch of priority (or a tree for instance), what is a solution?
• a max-length consistent branch?
• all consistent branches?
• should we establish an order over different branches? but then wouldn’twe restrict ourselves too much?
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Improve the semantics of prioritized constraints
Generalize the total-order scheme to more complex ones.
Problems so far:if more than one branch of priority (or a tree for instance), what is a solution?
• a max-length consistent branch?
• all consistent branches?
• should we establish an order over different branches? but then wouldn’twe restrict ourselves too much?
These points constitute perspectives for this project
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What kind of output?
• solutions of the optimization problem
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What kind of output?
• solutions of the optimization problem
• what if no solution? or too many?
◦ should we provide users with suggestions? use of qualitative
information before the solving process? or after?
◦ should we run additional models in case of inconsistency?
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 24/29
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What kind of output?
• solutions of the optimization problem
• what if no solution? or too many?
◦ should we provide users with suggestions? use of qualitative
information before the solving process? or after?
◦ should we run additional models in case of inconsistency?
Need for clear definition of the output:
may be adjusted when experiments are carried out on real problems
FJCP, National Institute of Informatics – Tokyo, 26 October 2004 – p. 24/29
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Conclusionand
Plans for future work
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Conclusion
Already done
• definition of the framework for soft constraints we are goingto use in this project◦ yet, adjustments are still possible
• prototype using this framework:◦ tested on inconsistent camera positioning problems
◦ using classical constraint and optimization solvers: we benefit fromtheir algorithmic power
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Plans for future work in Sakura
• implement a common prototype
◦ probably on top of elisa: constraint solver implemented at LINA
• determine the user needs: experiments on GUI problems
◦ perform experiments on Pr. Hosobe’s set of GUI problems
◦ adjust our solving algorithms w.r.t. these experiments
◦ get preliminary feed-back
• explore possible connections with methods from MCDM
◦ expressiveness may be improved using such techniques
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Plans for future work in Sakura (cont’d)
• apply models different from hierarchies to GUI problems
• extend our target application field (GUI)
• other projects of SCooP
◦ integrate flexibility in speculative constraint processing
◦ benefit from the work performed in the area of dynamic
constraints (e.g., explanations)
• user interface
◦ appropriate modelling language
◦ easy-to-use interface
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The end
Thank you for your attention
Martine CeberioUTEP, Computer Science DepartmentLINA, Nantes Francee-mail. [email protected]
http://www.cs.utep.edu/mceberio
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