Hybridization of
  complete and
   incomplete
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      CSP
                                   Hybridization...
Hybridization of
                                Constraint programming process
  complete and
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Hybridization of
                         Problems are modeled as CSPs (X , D, C)
  complete and
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Hybridization of
                               Example : Sudoku problem
  complete and
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Hybridization of
                                   Example : 8 Queens
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Hybridization of
                                                CSP solving
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Hybridization of
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Hybridization of
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                            Solving CSP
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Hybridization of
                            complete/incomplete methods
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Hybridization of
                                         Solving CSP
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Hybridization of
                                       Complete methods
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Hybridization of
                                          First approach
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Hybridization of
                        Backtracking for 4 - Queens
  complete and
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Hybridization of
                        Constraint propagation : reducing domains
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Hybridization of
                        Forward Checking
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      CSP
   Tony...
Hybridization of
                                 Constraint propagation
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Hybridization of
                              Constraint propagation framework
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Hybridization of
                                 Abstract model K.R. Apt [CP99]
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Hybridization of
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Hybridization of
                               Example of reduction functions (1)
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                              Example of reduction functions (2)
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Hybridization of
                            A Generic Algorithm to reach fixpoint
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Hybridization of
                                        Solving CSP
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Hybridization of
                                        Second Approach
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Hybridization of
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Hybridization of
                                                    Local search (1)
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Hybridization of
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Hybridization of
                                                            Local search (3)
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Hybridization of
                                                            Local search (4)
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Hybridization of
                                       Genetic algorithms (1)
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Hybridization of
                                       Genetic algorithms (2)
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Hybridization of
                                 Genetic algorithms (3)
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Hybridization of
  complete and
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                                  Solving CSP
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Hybridization of
                              Hybridization : getting the best of the both
  complete and
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Hybridization of
                                             Hybridization : Overview
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Hybridization of
                                                                       CP for LS
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Hybridization of
                              CP for GA (1)
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      CSP
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Hybridization of
                              CP for GA (2)
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      CSP
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Hybridization of
                              Hybridization : getting the best of the both
  complete and
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Hybridization of
  complete and
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                             Solving CSP
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Hybridization of
                                            Our purpose :
  complete and
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Hybridization of
                                       Search Tree
  complete and
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      C...
Hybridization of
                               Idea 1 : Integrate split in GI
  complete and
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Hybridization of
                            Theoretical model for CSP solving (2)
  complete and
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Hybridization of
                              Theoretical model for CSP solving (3)
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Hybridization of
                              Theoretical model for CSP solving (1)
  complete and
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Hybridization of
  complete and
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                               Solving CSP
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Hybridization of
                                              Our purpose :
  complete and
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Hybridization of
                                    Idea 2 : Integrate LS and CP
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Hybridization of
                                  LS as moves on partial ordering
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Hybridization of
                                   Integrate samples for LS
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Hybridization of
                                Theoretical model for hybridization (3)
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                                          General process CP+LS
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Hybridization of
                           Strategies through reduction functions
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Hybridization of
                                   Strategies : ratio LS-CP
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                                        Implementation
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Hybridization of
                                                                  Langford number 4 2
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Hybridization of
                                                              SEND + MORE = MONEY
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Hybridization of
                                                  Ranges
  complete and
   incomplete
 methods to solve
 ...
Hybridization of
  complete and
   incomplete
 methods to solve
                                Solving CSP
              ...
Hybridization of
                                               Our purpose :
  complete and
   incomplete
 methods to sol...
Hybridization of
                            Idea 3 : GA = moves in a partial ordering
  complete and
   incomplete
 metho...
Hybridization of
                                                 GA ordering
  complete and
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Hybridization of
                            Integrate generations for GA in CSPs
  complete and
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Hybridization of
                            Theoretical model for hybridization CP+GA
  complete and
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Hybridization of
                                                  Algorithm
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Hybridization of
                            Application BACP (to optimize loads of
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                                            Experimentations
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Hybridization of
                                                  BACP8
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Hybridization of
                                                BACP10
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Hybridization of
                                                     BACP12
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Hybridization of
  complete and
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 methods to solve
                            Solving CSP
                  ...
Hybridization of
                                            Motivation
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Hybridization of
                                      Search Tree
  complete and
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      CS...
Hybridization of
                                     Example : Local Search
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Hybridization of
                               Example : Genetic algorithms
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Hybridization of
                                 Idea 4 : break up methods
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Hybridization of
                                                 Basic fonctions
  complete and
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Hybridization of
                                         Reduction functions (1)
  complete and
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Hybridization of
                        Reduction functions (2) Genetic Algorithms
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   incomplete
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Hybridization of
                                          Properties
  complete and
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 methods to solve
     ...
Hybridization of
  complete and
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                            Solving CSP
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                                        Conclusion
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      C...
Hybridization of
                                               Future
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    ...
Hybridization of
  complete and
   incomplete
 methods to solve
      CSP
                                   Hybridization...
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Slides Ph D Defense Tony Lambert

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Hybridization of complete and
incomplete methods to solve CSP

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Slides Ph D Defense Tony Lambert

  1. 1. Hybridization of complete and incomplete methods to solve CSP Hybridization of complete and Tony Lambert incomplete methods to solve CSP Solving CSP Hybrid solving : need a framework Integrate split in GI Tony Lambert Theoretical model for hybridization CP + LS LERIA, Angers, France Theoretical model for hybridization LINA, Nantes, France CP + GA To an uniform October 27th, 2006 framework CP + GA + LS Conclusion and future works Rapporteurs : François FAGES Directeur de Recherche, INRIA Rocquencourt Bertrand NEVEU, Ingénieur en Chef des Ponts et Chaussées, HDR Examinateurs : Steven PRESTWICH, Associate Professor, University College Cork Jin-Kao HAO, Professeur à l’Université d’Angers Directeurs de thèse : Éric MONFROY, Professeur à l’Université de Nantes Frédéric SAUBION, Professeur à l’Université d’Angers 1 / 86
  2. 2. Hybridization of Constraint programming process complete and incomplete methods to solve CSP Formulate the problem with constraints as a CSP Tony Lambert constraint : a relation on variables and their domains Solving CSP Constraint Satisfaction Problem (CSP) : a set of Hybrid solving : need a framework constraints together with a set of variable domains Integrate split in GI Theoretical model CSP model for hybridization CP + LS Theoretical model C2 Y for hybridization X = {x1 , . . . , xn } set of n C1 CP + GA U To an uniform variables, X C4 C5 framework CP + GA + LS D = {Dx1 , . . . , Dxn } set Conclusion and Z T of n domains, C3 future works C = {c1 , . . . , cm } set of m constraints. Variables Constraints 2 / 86
  3. 3. Hybridization of Problems are modeled as CSPs (X , D, C) complete and incomplete methods to solve CSP Tony Lambert Some variables to represent objects Solving CSP (X = {X1 , . . . , Xn }) Hybrid solving : need a framework Integrate split in GI Domains over which variables can range Theoretical model for hybridization (D = D1 × . . . × Dn ) CP + LS Theoretical model for hybridization Some constraints to set relation between objects CP + GA To an uniform framework CP + C1 : X ≤ Y ∗ 3 GA + LS C2 : Z = X − Y Conclusion and future works ... 3 / 86
  4. 4. Hybridization of Example : Sudoku problem complete and incomplete methods to solve 6 9 2 1 4 CSP 3 6 9 8 Tony Lambert 8 2 Solving CSP 1 9 7 2 Hybrid solving : need a framework 9 5 Integrate split in GI 8 4 6 7 Theoretical model 9 5 for hybridization CP + LS 2 3 5 1 Theoretical model 1 5 6 3 7 for hybridization CP + GA 1 2 3 4 5 6 7 8 9 To an uniform framework CP + GA + LS X = { all the cells in the grid}, Conclusion and future works D = { to each cell a value in [1..9]}, C = { set of alldiff constraints : all digits appears only once in each row ; once in each column and once in each 3 × 3 square the grid has been subdivided} 4 / 86
  5. 5. Hybridization of Example : 8 Queens complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : need a framework Integrate split in GI Theoretical model for hybridization CP + LS Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS X = {x1 , ...x8 } Columns, Conclusion and future works D = {Dx1 , ..., Dx8 } for each columns, the row the queen is placed Dxi = [1..8], C = { not 2 queens in the same row or same diagonal} 5 / 86
  6. 6. Hybridization of CSP solving complete and incomplete methods to solve A solution CSP Tony Lambert Given a search space S = Dx1 × ... × Dxn an assignment s is a solution if : Solving CSP Hybrid solving : s ∈ S and need a framework ∀c ∈ C, s ∈ c Integrate split in GI Theoretical model for hybridization Solving a CSP can be : CP + LS compute whether the CSP has a solution Theoretical model for hybridization (satisfiability) CP + GA To an uniform framework CP + find A solution GA + LS Conclusion and find ALL solutions future works find optimal solutions (global optimum) find A good solution (local optimum) 6 / 86
  7. 7. Hybridization of Outline complete and incomplete methods to solve CSP Tony Lambert Solving CSP 1 Solving CSP Hybrid solving : need a framework 2 Hybrid solving : need a framework Integrate split in GI Integrate split in GI 3 Theoretical model for hybridization CP + LS Theoretical model for hybridization CP + LS 4 Theoretical model for hybridization CP + GA Theoretical model for hybridization CP + GA 5 To an uniform framework CP + GA + LS To an uniform framework CP + GA + LS 6 Conclusion and future works Conclusion and future works 7 7 / 86
  8. 8. Hybridization of complete and incomplete methods to solve Solving CSP 1 CSP Tony Lambert Hybrid solving : need a framework 2 Solving CSP Propagation + Split Local Search Genetic Algorithms Integrate split in GI 3 Hybrid solving : need a framework Integrate split in GI Theoretical model for hybridization CP + LS 4 Theoretical model for hybridization CP + LS Theoretical model for hybridization CP + GA 5 Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS 6 To an uniform framework CP + GA + LS Conclusion and Conclusion and future works 7 future works 8 / 86
  9. 9. Hybridization of complete/incomplete methods complete and incomplete methods to solve CSP Tony Lambert complete methods (such as propagation + split) complete exploration of the search space Solving CSP Propagation + Split Local Search detect if no solution Genetic Algorithms Hybrid solving : global optimum need a framework Integrate split in GI generally slow for hard combinatorial problems Theoretical model for hybridization CP + LS incomplete methods (such as local search) Theoretical model for hybridization focus on some “promising” parts of the search space CP + GA To an uniform do not detect if no solution framework CP + GA + LS no global optimum Conclusion and future works “fast” to find a “good” solution 9 / 86
  10. 10. Hybridization of Solving CSP complete and incomplete methods to solve CSP Tony Lambert Solving CSP Propagation + Split Local Search Genetic Algorithms Hybrid solving : Methods need a framework Integrate split in GI Complete methods Theoretical model Incomplete methods for hybridization CP + LS Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 10 / 86
  11. 11. Hybridization of Complete methods complete and incomplete methods to solve CSP Tony Lambert Solving CSP Propagation + Split Local Search General methods that can be adapted to several Genetic Algorithms Hybrid solving : types of constraints and several types of variables need a framework search methods : to explore the search space Integrate split in GI Theoretical model constraint propagation algorithms : to repeatedly for hybridization CP + LS remove inconsistent values from domains of Theoretical model variables for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 11 / 86
  12. 12. Hybridization of First approach complete and incomplete methods to solve CSP Tony Lambert Solving CSP Complete Methods Propagation + Split Local Search Genetic Algorithms Search space : Dx1 × · · · × Dxn Hybrid solving : Enumerate all assignments need a framework Integrate split in GI Theoretical model Backtracking for hybridization CP + LS search (backtrack) Theoretical model for hybridization Select variables CP + GA Split / enumeration To an uniform framework CP + GA + LS Conclusion and future works 12 / 86
  13. 13. Hybridization of Backtracking for 4 - Queens complete and incomplete methods to solve CSP Tony Lambert Solving CSP Propagation + Split Local Search Genetic Algorithms Hybrid solving : need a framework Integrate split in GI Theoretical model for hybridization CP + LS Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 13 / 86
  14. 14. Hybridization of Constraint propagation : reducing domains complete and incomplete methods to solve CSP Tony Lambert Generally : Solving CSP Propagation + Split reduce domains using constraint and domains Local Search Genetic Algorithms → reduce the search space Hybrid solving : need a framework Integrate split in GI Generic domain reduction : Theoretical model for hybridization given a constraint C over x1 , . . . , xn with domains CP + LS D1 , . . . , Dn Theoretical model for hybridization select a variable xi reduce its domain CP + GA To an uniform delete from Di all values for xi that do not participate framework CP + GA + LS in a solution of C Conclusion and future works 14 / 86
  15. 15. Hybridization of Forward Checking complete and incomplete methods to solve CSP Tony Lambert Solving CSP Propagation + Split Local Search Genetic Algorithms Hybrid solving : need a framework Integrate split in GI Theoretical model for hybridization CP + LS Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 15 / 86
  16. 16. Hybridization of Constraint propagation complete and incomplete methods to solve CSP Tony Lambert Solving CSP Propagation + Split Local Search Genetic Algorithms constraint propagation mechanism : repeatedly Hybrid solving : need a framework reduce domains Integrate split in GI replace a CSP by a CSP which is : Theoretical model for hybridization equivalent (same set of solutions) CP + LS “smaller” (domains are reduced) Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 16 / 86
  17. 17. Hybridization of Constraint propagation framework complete and incomplete methods to solve CSP Tony Lambert Can be seen as a fixed point of application of Solving CSP reduction functions Propagation + Split Local Search reduction function to reduce domains or constraints Genetic Algorithms Hybrid solving : can be seen as an abstraction of the constraints by need a framework Integrate split in GI reduction functions Theoretical model for hybridization Chaotic iteration CP + LS Theoretical model Compute a limit of a set of functions [Cousot and for hybridization CP + GA Cousot 77] To an uniform monotonic and inflationary functions in a generic framework CP + GA + LS algorithm to achieve consistency [Apt 97] Conclusion and future works 17 / 86
  18. 18. Hybridization of Abstract model K.R. Apt [CP99] complete and incomplete For propagation (based on chaotic iterations) methods to solve CSP Tony Lambert Abstraction Solving CSP Reduction functions Constraint Propagation + Split Local Search Genetic Algorithms Hybrid solving : need a framework Integrate split in GI Theoretical model for hybridization CP + LS Theoretical model Application for hybridization CP + GA of functions CSP To an uniform Fixed point framework CP + GA + LS Partial Ordering Conclusion and future works 18 / 86
  19. 19. Hybridization of Partial ordering and functions complete and incomplete methods to solve Partial Ordering CSP Tony Lambert Given a CSP (X , D, C) P(D) : all possible subset from D Solving CSP Propagation + Split Local Search : subset relation ⊇ Genetic Algorithms Hybrid solving : need a framework =⇒ (P(D), ) is a partial ordering Integrate split in GI Theoretical model Functions for hybridization CP + LS Given a set F of functions on D, every f ∈ F is : Theoretical model for hybridization inflationary : x f (x) CP + GA To an uniform monotonic : x y implies f (x) f (y ) framework CP + GA + LS idempotent : f (f (x)) = f (x) Conclusion and future works =⇒ Every sequence of elements d0 d1 ... with dj = fij (dj−1 ) stabilizes to a fix point. 19 / 86
  20. 20. Hybridization of Example of reduction functions (1) complete and incomplete methods to solve Constraint x < y CSP 5 Tony Lambert 3 6 4 Solving CSP 7 Propagation + Split 5 Local Search 8 Genetic Algorithms 6 9 Hybrid solving : 7 need a framework 10 Integrate split in GI D D x y Theoretical model for hybridization CP + LS Arc_consistence on Dx and Arc_consistence on Dy Theoretical model 5 5 for hybridization CP + GA 3 3 6 6 To an uniform 4 4 7 7 framework CP + GA + LS 5 5 8 8 Conclusion and 6 6 9 9 future works 7 7 10 10 D D D D x y x y 20 / 86
  21. 21. Hybridization of Example of reduction functions (2) complete and incomplete methods to solve CSP Arc consistency Tony Lambert Consider a constraint x < y with Dx = [5..10] and Solving CSP Dy = [3..7] then 2 functions D → D : Propagation + Split Local Search Arc_consistence 1 : Genetic Algorithms Hybrid solving : need a framework (Dx , Dy ) → (Dx , Dy ) Integrate split in GI Theoretical model s.t. for hybridization CP + LS Dx = {a ∈ Dx | ∃b ∈ Dy , a < b} Theoretical model for hybridization Arc_consistence 2 : CP + GA To an uniform framework CP + (Dx , Dy ) → (Dx , Dy ) GA + LS Conclusion and future works s.t. Dy = {b ∈ Dy | ∃a ∈ Dx , a < b} 21 / 86
  22. 22. Hybridization of A Generic Algorithm to reach fixpoint complete and incomplete methods to solve CSP Tony Lambert for constraint propagation : ordering on size of domains Solving CSP Propagation + Split work on a CSP Local Search F = { set of propagation functions} Genetic Algorithms Hybrid solving : X = initial CSP need a framework G=F Integrate split in GI While G = ∅ Theoretical model for hybridization choose g ∈ G CP + LS G = G − {g} Theoretical model for hybridization G = G ∪ update(G, g, X ) CP + GA To an uniform X = g(X ) framework CP + EndWhile GA + LS Conclusion and future works 22 / 86
  23. 23. Hybridization of Solving CSP complete and incomplete methods to solve CSP Tony Lambert Solving CSP Propagation + Split Local Search Genetic Algorithms Hybrid solving : Methods need a framework Integrate split in GI Complete methods Theoretical model Incomplete methods for hybridization CP + LS Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 23 / 86
  24. 24. Hybridization of Second Approach complete and incomplete methods to solve CSP Tony Lambert Incomplete methods Solving CSP heuristics algorithms Propagation + Split Local Search Metaheuristics Genetic Algorithms Hybrid solving : need a framework two families Integrate split in GI Local search Theoretical model for hybridization Simulated annealing [Kirkpatrick et al, 1983] CP + LS Tabu Search [Glover, 1986] Theoretical model for hybridization ... CP + GA Evolutionary Algorithms To an uniform framework CP + Genetic Algorithms [Holland, 1975] GA + LS Genetic programming [Koza, 1992] Conclusion and future works ... 24 / 86
  25. 25. Hybridization of Incomplete methods complete and incomplete methods to solve CSP Tony Lambert Definitions Explore a D1 × D2 × · · · × Dn search space Solving CSP Propagation + Split Local Search Move from neighbor to neighbor (resp. generation to Genetic Algorithms generation) thanks to an evaluation function Hybrid solving : need a framework Intensification Integrate split in GI Diversification Theoretical model for hybridization CP + LS Properties : Theoretical model for hybridization focus on some “promising” parts of the search space CP + GA does not answer to unsat. problems To an uniform framework CP + GA + LS no guaranteed Conclusion and “fast” to find a “good” solution future works 25 / 86
  26. 26. Hybridization of Local search (1) complete and incomplete methods to solve Search space : set of possible configurations CSP Tony Lambert Tools : neighborhood and evaluation function Solving CSP Propagation + Split Local Search Genetic Algorithms Hybrid solving : need a framework Set of Integrate split in GI possible configurations Theoretical model for hybridization CP + LS Theoretical model s 3 s for hybridization 4 CP + GA s 6 s s 1 2 s 5 To an uniform framework CP + GA + LS Conclusion and future works 26 / 86
  27. 27. Hybridization of Local search (2) complete and incomplete methods to solve Search space : set of possible configurations CSP Tony Lambert Tools : neighborhood and evaluation function Solving CSP Propagation + Split Local Search Genetic Algorithms Hybrid solving : Neighborhood need a framework of s Set of Integrate split in GI possible configurations Theoretical model for hybridization CP + LS Theoretical model s 3 s for hybridization 4 CP + GA s 6 s s 1 2 s 5 To an uniform framework CP + GA + LS Conclusion and future works 27 / 86
  28. 28. Hybridization of Local search (3) complete and incomplete methods to solve Search space : set of possible configurations CSP Tony Lambert Tools : neighborhood and evaluation function Solving CSP Propagation + Split Local Search Genetic Algorithms Hybrid solving : Neighborhood need a framework of s Set of Integrate split in GI possible configurations Theoretical model for hybridization CP + LS Theoretical model s 3 s for hybridization 4 CP + GA s 6 s s 1 2 s 5 To an uniform framework CP + GA + LS Conclusion and future works 28 / 86
  29. 29. Hybridization of Local search (4) complete and incomplete methods to solve CSP Search space : set of possible configurations Tony Lambert Tools : neighborhood and evaluation function Solving CSP Propagation + Split Local Search Genetic Algorithms Hybrid solving : need a framework Neighborhood Set of of s Integrate split in GI possible configurations Theoretical model for hybridization LS(p) = p’ CP + LS p=( s ,s , ..., s ) 1 2 n Theoretical model s p’ = ( s ,s , ..., s ,s ) 3 1 2 s n n+1 for hybridization 4 CP + GA s 6 s s 1 2 s 5 To an uniform framework CP + GA + LS Conclusion and future works 29 / 86
  30. 30. Hybridization of Genetic algorithms (1) complete and incomplete methods to solve CSP Search space : set of possible configurations Tony Lambert Tools : population, crossing, mutations, and Solving CSP evaluation function Propagation + Split Local Search Genetic Algorithms Hybrid solving : need a framework Population k Integrate split in GI Theoretical model for hybridization x 1 4 9 4 2 5 CP + LS y Theoretical model for hybridization 1 4 2 4 2 9 Population k+1 CP + GA To an uniform 8 6 2 41 9 framework CP + GA + LS Conclusion and future works 30 / 86
  31. 31. Hybridization of Genetic algorithms (2) complete and incomplete methods to solve CSP Search space : set of possible configurations Tony Lambert Tools : population, crossing, mutations, and Solving CSP evaluation function Propagation + Split Local Search Genetic Algorithms Hybrid solving : need a framework Population k Integrate split in GI Theoretical model for hybridization x 1 4 9 4 2 5 CP + LS y Theoretical model for hybridization 1 4 9 4 8 5 Population k+1 CP + GA To an uniform framework CP + GA + LS Conclusion and future works 31 / 86
  32. 32. Hybridization of Genetic algorithms (3) complete and incomplete methods to solve CSP Search space : set of possible configurations Tony Lambert Tools : population, crossing, mutations, and Solving CSP evaluation function Propagation + Split Local Search Genetic Algorithms Hybrid solving : need a framework Population k Integrate split in GI Croisement Theoretical model for hybridization CP + LS Mutation Theoretical model for hybridization Population k+1 CP + GA To an uniform framework CP + Nouvelle Population GA + LS Conclusion and future works 32 / 86
  33. 33. Hybridization of complete and incomplete methods to solve Solving CSP 1 CSP Tony Lambert Hybrid solving : need a framework 2 Solving CSP Hybrid solving : need a framework Integrate split in GI 3 Why hybridization complete/incomplete Hybridization : getting the best of the both Theoretical model for hybridization CP + LS Integrate split in GI 4 Theoretical model for hybridization CP + LS Theoretical model for hybridization CP + GA 5 Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS 6 To an uniform framework CP + GA + LS Conclusion and future works 7 Conclusion and future works 33 / 86
  34. 34. Hybridization of Hybridization : getting the best of the both complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : need a framework Efficiency : faster complete solver Why hybridization complete/incomplete Quality : better solutions (better optimum) Hybridization : getting the best of the both Generally : Integrate split in GI Theoretical model Ad-hoc systems (designed from scratch) for hybridization CP + LS Dedicated to a class of problems Theoretical model Master-slave approaches (LS for CP, CP for LS) for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 34 / 86
  35. 35. Hybridization of Hybridization : Overview complete and incomplete methods to solve CSP Tony Lambert complete and incomplete methods combinations Solving CSP Hybrid solving : need a framework Why hybridization complete/incomplete collaborative combinations Hybridization : getting the best of the both Integrate split in GI Theoretical model for hybridization integrative combinaisons CP + LS Theoretical model for hybridization CP + GA Incorporate a complete method in metaheuristics To an uniform framework CP + GA + LS Conclusion and Incorporate a metaheuristic in complete methods future works 35 / 86
  36. 36. Hybridization of CP for LS complete and incomplete methods to solve CSP Tony Lambert Solving CSP Neighborhood Hybrid solving : of s Set of need a framework possible Why hybridization configurations complete/incomplete Hybridization : getting the best of the both Integrate split in GI s Theoretical model 3 s 4 for hybridization s CP + LS 6 s s 1 2 s 5 Reduced Theoretical model for hybridization search space CP + GA To an uniform framework CP + Valid neighborhood GA + LS of s Conclusion and future works 36 / 86
  37. 37. Hybridization of CP for GA (1) complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : Set of need a framework possible configurations Why hybridization complete/incomplete Hybridization : getting the best of the both Integrate split in GI Theoretical model for hybridization CP + LS Theoretical model Population for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 37 / 86
  38. 38. Hybridization of CP for GA (2) complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : Set of need a framework possible configurations Why hybridization complete/incomplete Hybridization : getting the best of the both Integrate split in GI Theoretical model for hybridization CP + LS Theoretical model for hybridization Feasible population CP + GA To an uniform framework CP + GA + LS Conclusion and future works 38 / 86
  39. 39. Hybridization of Hybridization : getting the best of the both complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : need a framework Idea : Why hybridization complete/incomplete Hybridization : getting the fine grain hybridization best of the both finer strategies Integrate split in GI every technique at the same level Theoretical model for hybridization one algorithm squeleton CP + LS easier to modify, extend, compare, ... Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 39 / 86
  40. 40. Hybridization of complete and incomplete methods to solve Solving CSP 1 CSP Tony Lambert Hybrid solving : need a framework 2 Solving CSP Hybrid solving : need a framework Integrate split in GI 3 Integrate split in GI Constraint propagation Domain splitting Theoretical model for hybridization CP + LS 4 Theoretical model for hybridization CP + LS Theoretical model Theoretical model for hybridization CP + GA 5 for hybridization CP + GA To an uniform To an uniform framework CP + GA + LS 6 framework CP + GA + LS Conclusion and future works Conclusion and future works 7 40 / 86
  41. 41. Hybridization of Our purpose : complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : Use of an existing theoretical model for CSP solving need a framework Definition of the solving process Integrate split in GI Constraint propagation Domain splitting Theoretical model Integrate : for hybridization CP + LS Split Theoretical model for hybridization LS CP + GA GA To an uniform framework CP + GA + LS Conclusion and future works 41 / 86
  42. 42. Hybridization of Search Tree complete and incomplete methods to solve CSP Tony Lambert CSP1 propagation Solving CSP CSP1’ Hybrid solving : split need a framework Integrate split in GI CSP2 CSP3 propagation Constraint propagation Domain splitting CSP2’ CSP3 Theoretical model split for hybridization CP + LS CSP5 CSP4 CSP3 propagation Theoretical model for hybridization CP + GA CSP5 CSP4 CSP3’ split To an uniform framework CP + CSP6 CSP4 CSP5 CSP7 CSP8 GA + LS propagation Conclusion and future works CSP6’ CSP5 CSP7 CSP8 42 / 86
  43. 43. Hybridization of Idea 1 : Integrate split in GI complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : need a framework Integrate split in GI use the CP framework algorithm Constraint propagation Domain splitting split and reduction at the same level Theoretical model for hybridization work on union of CSP CP + LS Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 43 / 86
  44. 44. Hybridization of Theoretical model for CSP solving (2) complete and incomplete methods to solve CSP Reduction : by constraint propagation : Tony Lambert Solving CSP Ω Ω’ Hybrid solving : need a framework Integrate split in GI Constraint propagation Domain splitting Theoretical model Ω for hybridization CSP1 CSP2 CSP3 CP + LS Theoretical model for hybridization CP + GA Constraint Propagation To an uniform framework CP + GA + LS Ω’ Conclusion and CSP1 CSP2’ CSP3 future works 44 / 86
  45. 45. Hybridization of Theoretical model for CSP solving (3) complete and incomplete methods to solve CSP Tony Lambert Reduction by domain splitting : Solving CSP Hybrid solving : Ω Ω’ need a framework Integrate split in GI Constraint propagation Domain splitting Theoretical model Ω for hybridization CSP1 CSP2 CSP3 CP + LS Theoretical model Split for hybridization CP + GA To an uniform framework CP + Ω’ GA + LS CSP1 CSP2’ CSP2’’ CSP2’’’ CSP3 Conclusion and future works 45 / 86
  46. 46. Hybridization of Theoretical model for CSP solving (1) complete and incomplete methods to solve Partial ordering : CSP Tony Lambert Ω1 Solving CSP Hybrid solving : Application of a reduction : need a framework domain reduction function or Ω2 Integrate split in GI splitting function Constraint propagation Domain splitting Theoretical model for hybridization Ω3 CP + LS Set of CSP Theoretical model for hybridization CP + GA Ω4 To an uniform framework CP + GA + LS Conclusion and Ω5 future works Terminates with a fixed point : set of solutions or inconsistent CSP 46 / 86
  47. 47. Hybridization of complete and incomplete methods to solve Solving CSP 1 CSP Tony Lambert Hybrid solving : need a framework 2 Solving CSP Hybrid solving : need a framework Integrate split in GI 3 Integrate split in GI Theoretical model for hybridization Theoretical model for hybridization CP + LS 4 CP + LS LS as moves on a partial ordering Integrate samples for LS Ordering σCSP Theoretical model for hybridization CP + GA 5 A Generic Algorithm Experimentation Theoretical model To an uniform framework CP + GA + LS 6 for hybridization CP + GA To an uniform framework CP + Conclusion and future works 7 GA + LS Conclusion and future works 47 / 86
  48. 48. Hybridization of Our purpose : complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : Use of an existing theoretical model for CSP solving need a framework Definition of the solving process Integrate split in GI Theoretical model for hybridization CP + LS Integrate : LS as moves on a partial ordering Split Integrate samples for LS Ordering σCSP A Generic Algorithm LS Experimentation GA Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 48 / 86
  49. 49. Hybridization of Idea 2 : Integrate LS and CP complete and incomplete methods to solve CSP Local Search Tony Lambert In theory : infinite Solving CSP In practice : number of iteration Hybrid solving : need a framework Integrate split in GI Characteristics of a LS path Theoretical model for hybridization notion of solution CP + LS LS as moves on a partial Operational (computational) point of view : path = ordering Integrate samples for LS samples Ordering σCSP A Generic Algorithm Experimentation maximum length Theoretical model for hybridization CP + GA Goal : To an uniform framework CP + LS ordering GA + LS integrate LS in CSP Conclusion and future works 49 / 86
  50. 50. Hybridization of LS as moves on partial ordering complete and incomplete methods to solve CSP Tony Lambert p Solving CSP Function to pass from one LS 1 state to another Hybrid solving : need a framework p Integrate split in GI 2 Theoretical model for hybridization State of LS CP + LS p LS as moves on a partial ordering 3 Integrate samples for LS Ordering σCSP A Generic Algorithm p Experimentation 4 Theoretical model for hybridization CP + GA p To an uniform 5 framework CP + GA + LS Terminates with a fixed point : local minimum, maximum number of iteration Conclusion and future works 50 / 86
  51. 51. Hybridization of Integrate samples for LS complete and incomplete methods to solve CSP Tony Lambert A sample : Solving CSP Depends on a CSP Hybrid solving : need a framework Corresponds to a LS state Integrate split in GI Theoretical model for hybridization an SCSP contains (LS+domain reduction) : CP + LS LS as moves on a partial A set of domains ; ordering Integrate samples for LS Ordering σCSP A (list of) sample for local search (a LS path). A Generic Algorithm Experimentation Theoretical model for hybridization an σCSP contains (LS+domain reduction+split) : CP + GA A set of SCSP To an uniform framework CP + GA + LS Conclusion and future works 51 / 86
  52. 52. Hybridization of Theoretical model for hybridization (3) complete and incomplete methods to solve Ordering over σCSP CSP Tony Lambert Ω1 Solving CSP Hybrid solving : Application of a reduction : need a framework Ω2 function : Integrate split in GI − domain reduction, Theoretical model − splitting, for hybridization − or LS step. CP + LS Ω3 LS as moves on a partial ordering Integrate samples for LS Set of SCSP Ordering σCSP A Generic Algorithm Ω4 Experimentation Theoretical model for hybridization CP + GA Ω5 To an uniform framework CP + GA + LS A solution before the end of the process, given by LS Conclusion and Terminates with a fixed point : set of solutions or inconsistent SCSP future works 52 / 86
  53. 53. Hybridization of Algorithm complete and incomplete methods to solve CSP Tony Lambert Always the GI algorithm Solving CSP In the chaotic iteration framework Hybrid solving : need a framework Finite domains (sets of SCSP) Integrate split in GI Theoretical model Monotonic functions (LS move, domain reduction, for hybridization CP + LS splitting) LS as moves on a partial ordering Integrate samples for LS Decreasing functions Ordering σCSP A Generic Algorithm Experimentation → termination and computation of fixed point Theoretical model for hybridization (solution of CP) CP + GA To an uniform Practically : can stop before with a LS solution framework CP + GA + LS Conclusion and future works 53 / 86
  54. 54. Hybridization of General process CP+LS complete and incomplete methods to solve CSP Tony Lambert Solving CSP Sets of Constraint Hybrid solving : Application SCSP need a framework of functions Integrate split in GI Theoretical model for hybridization CP + LS LS as moves on a partial ordering Integrate samples for LS Ordering σCSP A Generic Algorithm Experimentation LS solution Theoretical model Global for hybridization CP + GA Fixed point To an uniform framework CP + GA + LS Conclusion and future works 54 / 86
  55. 55. Hybridization of Strategies through reduction functions complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : need a framework Reduction / Split / LS functions Integrate split in GI Theoretical model Choose a / several SCPS to apply functions for hybridization CP + LS LS as moves on a partial Choose a / several domains (Prop. - Split) ordering Integrate samples for LS Ordering σCSP A Generic Algorithm Tests : Random - Depth first - FC Experimentation Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 55 / 86
  56. 56. Hybridization of Strategies : ratio LS-CP complete and incomplete methods to solve CSP Tony Lambert Solving CSP Ratio of LS and CP functions applied : (red%,split%,ls%) Hybrid solving : need a framework 10% of split compared to reduction Integrate split in GI Theoretical model CP alone : (90,10,0) for hybridization CP + LS LS alone : (0,0,100) LS as moves on a partial ordering Integrate samples for LS Ordering σCSP LS strategy : tabu A Generic Algorithm Experimentation Theoretical model Choose : LS, reduction, or split but keep the given for hybridization CP + GA ratios To an uniform framework CP + GA + LS Conclusion and future works 56 / 86
  57. 57. Hybridization of Implementation complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : need a framework Integrate split in GI Theoretical model C++ for hybridization CP + LS Generic Algorithm LS as moves on a partial ordering Integrate samples for LS choose function with percentages Ordering σCSP A Generic Algorithm Experimentation Theoretical model for hybridization CP + GA To an uniform framework CP + GA + LS Conclusion and future works 57 / 86
  58. 58. Hybridization of Langford number 4 2 complete and incomplete cooperation area methods to solve CSP Tony Lambert 800 Solving CSP Hybrid solving : 700 need a framework Integrate split in GI 600 Theoretical model for hybridization CP + LS Number of operations 500 LS as moves on a partial ordering Integrate samples for LS 400 Ordering σCSP A Generic Algorithm Experimentation 300 Theoretical model for hybridization CP + GA 200 Average To an uniform framework CP + 100 GA + LS Conclusion and future works 0 10 20 30 40 50 60 70 80 90 100 Propagation percentage 58 / 86
  59. 59. Hybridization of SEND + MORE = MONEY complete and incomplete cooperation area methods to solve CSP Tony Lambert 1600 Solving CSP Hybrid solving : need a framework 1400 Integrate split in GI Theoretical model 1200 for hybridization CP + LS Number of operations LS as moves on a partial 1000 ordering Integrate samples for LS Ordering σCSP A Generic Algorithm 800 Experimentation Theoretical model for hybridization 600 CP + GA Average To an uniform framework CP + 400 GA + LS Conclusion and future works 200 10 20 30 40 50 60 70 80 90 100 Propagation percentage 59 / 86
  60. 60. Hybridization of Ranges complete and incomplete methods to solve CSP Tony Lambert Problem S+M LN42 Zebra M. square Golomb Solving CSP Rate FC 70 - 80 15 - 25 60 - 70 30 - 45 30 - 40 Hybrid solving : need a framework Best range of propagation rate (α) to compute a solution Integrate split in GI Strategy Method S+M LN42 M. square Golomb Theoretical model Random LS 1638 383 3328 3442 for hybridization CP+LS 1408 113 892 909 CP + LS LS as moves on a partial CP 3006 1680 1031 2170 ordering Integrate samples for LS D-First LS 1535 401 3145 3265 Ordering σCSP A Generic Algorithm CP+LS 396 95 814 815 Experimentation CP 1515 746 936 1920 Theoretical model for hybridization FC LS 1635 393 3240 3585 CP + GA CP+LS 22 192 570 622 To an uniform CP 530 425 736 1126 framework CP + GA + LS Avg. nb. of operations to compute a first solution Conclusion and future works 60 / 86
  61. 61. Hybridization of complete and incomplete methods to solve Solving CSP 1 CSP Tony Lambert Hybrid solving : need a framework 2 Solving CSP Hybrid solving : need a framework Integrate split in GI 3 Integrate split in GI Theoretical model for hybridization Theoretical model for hybridization CP + LS 4 CP + LS Theoretical model for hybridization CP + GA Theoretical model for hybridization CP + GA 5 GA : moves in a partial ordering GA ordering Integrate generations for To an uniform framework CP + GA + LS 6 GA in CSPs Algorithm Application BACP (to optimize loads of periods Conclusion and future works 7 To an uniform framework CP + GA + LS Conclusion and future works 61 / 86
  62. 62. Hybridization of Our purpose : complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : Use of an existing theoretical model for CSP solving need a framework Definition of the solving process Integrate split in GI Theoretical model for hybridization CP + LS Integrate : Theoretical model Split for hybridization CP + GA LS GA : moves in a partial ordering GA ordering GA Integrate generations for GA in CSPs Algorithm Application BACP (to optimize loads of periods To an uniform framework CP + GA + LS Conclusion and future works 62 / 86
  63. 63. Hybridization of Idea 3 : GA = moves in a partial ordering complete and incomplete methods to solve CSP Population Tony Lambert Génération k Solving CSP Hybrid solving : Sélection need a framework Probabilité Pc Probabilité Pm Integrate split in GI Theoretical model for hybridization p p1 p2 CP + LS Theoretical model Mutation for hybridization Croisement CP + GA GA : moves in a partial ordering p’ GA ordering c1 c2 Integrate generations for GA in CSPs Algorithm Evaluation Application BACP (to optimize loads of periods To an uniform Population framework CP + Génération k+1 GA + LS Conclusion and future works 63 / 86
  64. 64. Hybridization of GA ordering complete and incomplete methods to solve CSP Tony Lambert Solving CSP Characteristics of a GA path Hybrid solving : need a framework notion of solution Integrate split in GI maximum length Theoretical model for hybridization Operational (computational) point of view : path = CP + LS generations Theoretical model for hybridization CP + GA GA : moves in a partial Here a macroscopic point of view : ordering GA ordering Integrate generations for GA in CSPs 1 iteration = 1 generation Algorithm Application BACP (to optimize loads of periods To an uniform framework CP + GA + LS Conclusion and future works 64 / 86
  65. 65. Hybridization of Integrate generations for GA in CSPs complete and incomplete methods to solve CSP Tony Lambert a generation : Solving CSP depends on a CSP Hybrid solving : need a framework corresponds to a GA search state Integrate split in GI Theoretical model for hybridization an ogCSP contains (GA+domain reduction) : CP + LS a set of domains ; Theoretical model for hybridization CP + GA a (list of) population(s) for GA (a GA path). GA : moves in a partial ordering GA ordering Integrate generations for an OGCSP contains (GA+domain reduction+split) : GA in CSPs Algorithm Application BACP (to a set of ogCSPs optimize loads of periods To an uniform framework CP + GA + LS Conclusion and future works 65 / 86
  66. 66. Hybridization of Theoretical model for hybridization CP+GA complete and incomplete Ordering over OGCSPs methods to solve CSP Tony Lambert Ω1 Solving CSP Hybrid solving : Application of a reduction: need a framework Ω2 function: Integrate split in GI − domain reduction Theoretical model − split for hybridization CP + LS Ω3 − or GA. Theoretical model for hybridization set of ogCSP CP + GA GA : moves in a partial Ω4 ordering GA ordering Integrate generations for GA in CSPs Algorithm Ω5 Application BACP (to optimize loads of periods To an uniform framework CP + an optimal solution given by GA before the end of the process GA + LS fixed point: set of solutions or inconsistency Conclusion and future works 66 / 86
  67. 67. Hybridization of Algorithm complete and incomplete methods to solve CSP Tony Lambert Always the GI algorithm Solving CSP In the chaotic iteration framework Hybrid solving : need a framework Finite domains (set of OGCSP) Integrate split in GI Theoretical model Monotonic functions (GA move, domain reduction, for hybridization CP + LS splitting) Theoretical model for hybridization Decreasing functions CP + GA GA : moves in a partial ordering → termination and computation of fixed point GA ordering Integrate generations for GA in CSPs (solution of CP) Algorithm Application BACP (to optimize loads of periods Practically : can stop before with an optimum for GA To an uniform framework CP + GA + LS Conclusion and future works 67 / 86
  68. 68. Hybridization of Application BACP (to optimize loads of complete and incomplete periods) methods to solve CSP Tony Lambert Lectures Constraints Solving CSP a before b g a e d cquot; quot;j Hybrid solving : need a framework b c hquot; quot;b i h Integrate split in GI f j k iquot; quot;f Theoretical model fquot; quot;j for hybridization CP + LS kquot; quot;c Theoretical model dquot; quot;e for hybridization Max CP + GA GA : moves in a partial Min k ordering i e j GA ordering h Integrate generations for c f GA in CSPs Algorithm b d Application BACP (to g a optimize loads of periods To an uniform Periods framework CP + GA + LS Conclusion and future works 68 / 86
  69. 69. Hybridization of Experimentations complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : need a framework Integrate split in GI On optimization problems Theoretical model for hybridization Here, ratios are (45,5,50) CP + LS Theoretical model Mesure the real impact on the resolution for hybridization CP + GA GA : moves in a partial ordering GA ordering Integrate generations for GA in CSPs Algorithm Application BACP (to optimize loads of periods To an uniform framework CP + GA + LS Conclusion and future works 69 / 86
  70. 70. Hybridization of BACP8 complete and incomplete methods to solve CSP Tony Lambert 100 propagation Solving CSP genetic algorithm Hybrid solving : split need a framework 80 Integrate split in GI Theoretical model 60 for hybridization range CP + LS Theoretical model for hybridization 40 CP + GA GA : moves in a partial ordering GA ordering 20 Integrate generations for GA in CSPs Algorithm Application BACP (to optimize loads of periods 0 To an uniform 25 24 23 22 21 20 19 18 17 16 framework CP + GA + LS evaluation Conclusion and future works 70 / 86
  71. 71. Hybridization of BACP10 complete and incomplete methods to solve CSP Tony Lambert 100 propagation Solving CSP genetic algorithm Hybrid solving : split need a framework 80 Integrate split in GI Theoretical model 60 for hybridization range CP + LS Theoretical model for hybridization 40 CP + GA GA : moves in a partial ordering GA ordering 20 Integrate generations for GA in CSPs Algorithm Application BACP (to optimize loads of periods 0 To an uniform 24 22 20 18 16 14 12 framework CP + GA + LS evaluation Conclusion and future works 71 / 86
  72. 72. Hybridization of BACP12 complete and incomplete methods to solve CSP Tony Lambert 100 propagation Solving CSP genetic algorithm Hybrid solving : split need a framework 80 Integrate split in GI Theoretical model 60 for hybridization range CP + LS Theoretical model for hybridization 40 CP + GA GA : moves in a partial ordering GA ordering 20 Integrate generations for GA in CSPs Algorithm Application BACP (to optimize loads of periods 0 To an uniform 25 24 23 22 21 20 19 18 17 framework CP + GA + LS evaluation Conclusion and future works 72 / 86
  73. 73. Hybridization of complete and incomplete methods to solve Solving CSP 1 CSP Tony Lambert Hybrid solving : need a framework 2 Solving CSP Hybrid solving : need a framework Integrate split in GI 3 Integrate split in GI Theoretical model for hybridization Theoretical model for hybridization CP + LS 4 CP + LS Theoretical model for hybridization CP + GA Theoretical model for hybridization CP + GA 5 To an uniform framework CP + GA + LS To an uniform framework CP + GA + LS 6 Search Trees Reduction fonctions Conclusion and future works Conclusion and future works 7 73 / 86
  74. 74. Hybridization of Motivation complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : need a framework LS + CP : a search path Integrate split in GI GA + CP : a sequence of generations Theoretical model for hybridization But : GA + CP + LS ? CP + LS Theoretical model =⇒ Notion of sample = generation for hybridization CP + GA =⇒ Need to consider sample and individual at the same To an uniform level : CSP level framework CP + GA + LS Search Trees Reduction fonctions Conclusion and future works 74 / 86
  75. 75. Hybridization of Search Tree complete and incomplete methods to solve CSP Tony Lambert CSP1 propagation Solving CSP CSP1’ Hybrid solving : split need a framework Integrate split in GI CSP2 CSP3 propagation Theoretical model for hybridization CSP2’ CSP3 CP + LS split Theoretical model CSP5 CSP4 CSP3 for hybridization propagation CP + GA To an uniform CSP5 CSP4 CSP3’ framework CP + split GA + LS Search Trees CSP6 CSP4 CSP5 CSP7 CSP8 Reduction fonctions propagation Conclusion and future works CSP6’ CSP5 CSP7 CSP8 75 / 86
  76. 76. Hybridization of Example : Local Search complete and incomplete methods to solve CSP Tony Lambert CSP1 CSP2 Solving CSP Hybrid solving : Generate new samples need a framework CSP3 CSP5 CSP6 CSP7 CSP1 CSP2 CSP4 CSP8 Integrate split in GI Theoretical model for hybridization CSP3 CSP5 CSP6 CSP7 CSP1 CSP2 CSP4 CSP8 Chose a sample CP + LS CSP3 CSP5 CSP6 CSP7 CSP1 CSP2 CSP4 CSP8 Theoretical model for hybridization CP + GA To an uniform Generate new samples framework CP + CSP7 CSP12 CSP10 CSP9 CSP11 CSP1 CSP6 CSP8 GA + LS Search Trees Reduction fonctions CSP7 CSP12 CSP10 CSP9 CSP11 CSP1 CSP6 CSP8 Chose a sample Conclusion and future works CSP7 CSP12 CSP10 CSP9 CSP11 CSP1 CSP6 CSP8 76 / 86
  77. 77. Hybridization of Example : Genetic algorithms complete and incomplete methods to solve CSP Tony Lambert CSP3 CSP5 CSP1 CSP2 CSP4 Solving CSP Hybrid solving : Crossover need a framework CSP3 CSP5 CSP6 CSP1 CSP2 CSP4 Integrate split in GI Theoretical model for hybridization CP + LS Theoretical model Mutation CSP3 CSP5 CSP6 CSP7 CSP1 CSP2 CSP4 for hybridization CP + GA To an uniform framework CP + GA + LS Search Trees Selection Reduction fonctions CSP3 CSP5 CSP6 CSP7 CSP1 CSP4 Conclusion and future works 77 / 86
  78. 78. Hybridization of Idea 4 : break up methods complete and incomplete methods to solve CSP Tony Lambert Basic components Solving CSP Hybrid solving : reducing is a search component need a framework Integrate split in GI splitting is a search component Theoretical model generating a neighborhood is a search component for hybridization CP + LS moving to sample is a search component Theoretical model for hybridization CP + GA Basic behaviours To an uniform framework CP + splitting and generating a neighborhood GA + LS Search Trees reducing, selecting and moving to sample Reduction fonctions Conclusion and future works 78 / 86
  79. 79. Hybridization of Basic fonctions complete and incomplete Sampling S : methods to solve CSP P( X , C, P(D1 ) × · · · × P(Dn ) ) Tony Lambert Solving CSP → P( X , C, P(D1 ) × · · · × P(Dn ) ) Hybrid solving : need a framework {φ1 , . . . , φn } → {φ1 , . . . , φn , φn+1 } Integrate split in GI Theoretical model for hybridization s.t. ∃φi with φi φn+1 CP + LS Theoretical model Reducing R : for hybridization CP + GA P( X , C, P(D1 ) × · · · × P(Dn ) ) To an uniform framework CP + GA + LS → P( X , C, P(D1 ) × · · · × P(Dn ) ) Search Trees Reduction fonctions Conclusion and {φ1 , . . . , φi , . . . , φn } → {φ1 , . . . , φi , . . . , φn } future works Where φi = ∅ or φ = X , C, Di and φ = X , C, Di s.t. Di ⊆ Di . 79 / 86
  80. 80. Hybridization of Reduction functions (1) complete and incomplete methods to solve CSP Domain reduction (DR) Tony Lambert {φ1 , . . . , φi , . . . , φn } →DR {φ1 , . . . , φi , . . . , φn } Solving CSP Hybrid solving : Where DR = Rm with m > 0 need a framework Integrate split in GI Split (SP) Theoretical model for hybridization CP + LS Theoretical model {φ1 , . . . , φi , . . . , φn } →SP {φ1 , . . . , φ1 , . . . , φm , . . . , φn } for hybridization i i CP + GA To an uniform Where SP = S m R framework CP + GA + LS Search Trees Local Search (LS) Reduction fonctions Conclusion and future works {φ1 , . . . , φi , . . . , φn } →LS {φ1 , . . . , φi , . . . , φn } Where LS = S m Rm−1 80 / 86
  81. 81. Hybridization of Reduction functions (2) Genetic Algorithms complete and incomplete methods to solve CSP Crossover Tony Lambert Solving CSP {φ1 , . . . , φn } →CR {φ1 , . . . , φn , φn+1 } Hybrid solving : need a framework Where CR = S Integrate split in GI Theoretical model Mutation for hybridization CP + LS {φ1 , . . . , φi , . . . , φn } →MU {φ1 , . . . , φi , . . . , φn } Theoretical model for hybridization CP + GA Where MU = SR To an uniform framework CP + GA + LS Selection Search Trees Reduction fonctions {φ1 , . . . , φn } →SE {φ1 , . . . , φn } Conclusion and future works Where SE = Rm . 81 / 86
  82. 82. Hybridization of Properties complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : need a framework Integrate split in GI a strategy is a sequence of words Theoretical model ∈ {DR, SP, LS, SE, CR, MU} for hybridization CP + LS is it finite sequences ? Theoretical model for hybridization need conditions to avoid loops CP + GA To an uniform framework CP + GA + LS Search Trees Reduction fonctions Conclusion and future works 82 / 86
  83. 83. Hybridization of complete and incomplete methods to solve Solving CSP 1 CSP Tony Lambert Hybrid solving : need a framework 2 Solving CSP Hybrid solving : need a framework Integrate split in GI 3 Integrate split in GI Theoretical model for hybridization Theoretical model for hybridization CP + LS 4 CP + LS Theoretical model for hybridization CP + GA Theoretical model for hybridization CP + GA 5 To an uniform framework CP + GA + LS To an uniform framework CP + GA + LS 6 Conclusion and future works Assessment Conclusion and future works Future 7 83 / 86
  84. 84. Hybridization of Conclusion complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : need a framework A generic model for hybridizing complete (CP) and Integrate split in GI incomplete (LS and GA) methods Theoretical model for hybridization Implementation of modules working on the same CP + LS structure Theoretical model for hybridization CP + GA Complementarity of methods : hybridization To an uniform framework CP + GA + LS Conclusion and future works Assessment Future 84 / 86
  85. 85. Hybridization of Future complete and incomplete methods to solve CSP Tony Lambert Solving CSP Hybrid solving : synergies between : need a framework complete + incomplete methods, Integrate split in GI CP + AI + OR + . . . Theoretical model for hybridization learning strategies, rules based system with a CP + LS language Theoretical model for hybridization CP + GA providing more tools in a generic environment To an uniform Design of strategies framework CP + GA + LS Conclusion and future works Assessment Future 85 / 86
  86. 86. Hybridization of complete and incomplete methods to solve CSP Hybridization of complete and Tony Lambert incomplete methods to solve CSP Solving CSP Hybrid solving : need a framework Integrate split in GI Tony Lambert Theoretical model for hybridization CP + LS LERIA, Angers, France Theoretical model for hybridization LINA, Nantes, France CP + GA To an uniform October 27th, 2006 framework CP + GA + LS Conclusion and future works Rapporteurs : François FAGES Directeur de Recherche, INRIA Rocquencourt Assessment Bertrand NEVEU, Ingénieur en Chef des Ponts et Chaussées, HDR Future Examinateurs : Steven PRESTWICH, Associate Professor, University College Cork Jin-Kao HAO, Professeur à l’Université d’Angers Directeurs de thèse : Éric MONFROY, Professeur à l’Université de Nantes Frédéric SAUBION, Professeur à l’Université d’Angers 86 / 86

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