1 / 20

Solving BCSP using GA and PBIL

Summer School. Solving BCSP using GA and PBIL. Constraint Satisfaction Problem Group Sana Benhamida Andrea Roli Belgasem Ali

duscha
Download Presentation

Solving BCSP using GA and PBIL

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Summer School Solving BCSP using GA and PBIL Constraint Satisfaction Problem Group Sana Benhamida Andrea Roli Belgasem Ali Problem leader J.V.Hemert Jorge Tavares Group Leader Michele Sebag Samer Saadah

  2. EvolutionaryOptimization 1.Free Optimization < S, F > 2.Constrained Optimization < S, , F> 3.Constraint Satisfaction

  3. What is a constraint satisfaction problem? • A Constraint Satisfaction Problem ( CSP) is a triplet • <Z, D, C>where • • Z is a set of variables, • • D is a function that maps a finite set of objects of arbitrary type to Z. • • and C is a set of constraints that restrict certain simultaneous object assignments.

  4. Objectives • Assign to each an object from such that no is violated • Find all possible instantiations of variables that do not violate a constraint • Prove that there is no solution for a given problem • Find a partial solution (as few violated constraints as possible) for an unsolvable problem .

  5. EXAMPLES • Graph colouring: given a graph, find a k-colouring of the nodes such that nodes connected are colored with different colors. • n-Queens: given a n × n chess board and n queens, place the queens on the board such that no queen attacks another queen. • SAT: given a Boolean formula, find an assignment of variables such that the formula evaluates to true.

  6. Example: graph-k colouring with k =3

  7. Binary Constraint Satisfaction Problems • Binary Constraint Satisfaction Problem (BINCSP) is a CSP where all constraints are associated with at most two variables. • Given <Z, D, C>,

  8. The problems • Generate random Binary CSP problem instances • With various levels of difficulty, controlled from: 1. Number of variables (n) • 2. Domain size of each variable ( | D | = m) • 3. Constraint Density (p1 or d) in [0,1] • 4. Average tightness of a constraint (p2 or t), in[0,1]

  9. Solving csps

  10. Approaches • Simple GA scheme 1- Two-point crossover 2- Global crossover 3- Distribution based crossover • Population-Based Incremental Learning (PBIL, Baluja 1995) scheme.

  11. Representation Problems Solutions Chromosome representation Domain size: between 2 and 15

  12. Global Crossover (Gcx) 1 2 ……..……………………….7 …………… a a d

  13. Distribution Based Crossover (DB-cx) x1 x2 x3 x4 x5 x6 x7 A 0.6 0.3 0.2 0.2 0.15 0.4 0.3 0.2 0.2 0.1 0.2 0.2 0.2 0.3 B C 0.2 0.5 0.7 0.6 0.65 0.4 0.4 A B C B C A C

  14. PBIL SCHEME 1-Initialize probability matrix 2-Generate population 3- Evaluate population 4- Update probability matrix 5- Mutate probability matrix 6- Go to 2.

  15. Updating PBIL distribution • Increase the probability of “good” assignments. • Multiplicative updating rule with Learning Rate.

  16. Parameters • Population size : 10 • Mutation probability : 0.05 • Number of evaluations : 100,000 • Number of runs for each instance :10 • Number of instances : 25 for each value of t. • Mutation probability for PBIL : 0.0025

  17. T/ AlG GA-2cx GA-Gcx GA-Dcx PBIL SAW 0.10 1 1 1 1 1 0.12 1 1 1 1 1 0.14 1 1 1 1 1 0.16 1 0.992 1 1 1 0.18 0.992 0.984 0.998 1 1 0.20 0.972 0.920 0.936 1 1 0.22 0.816 0.684 0.804 1 1 0.24 0.608 0.552 0.644 1 1 0.26 0.456 0.328 0.420 1 1 0.28 0.256 0.176 0.176 1 1 0.30 0.104 0.072 0.056 0.98 1 0.32 0.04 0.028 0.04 0.856 1 Results

  18. Conclusion • Applying PBIL for Constraint Satisfaction • Promising Results for a set of BCSP instances. • GA approach is limited.

  19. Future Research • More experiments with PBIL. • Better mutation operator (on the distribution)

  20. Summer School Solving BCSP using GA and PBIL Constraint Satisfaction Problem Group Sana Benhamida Andrea Roli Belgasem Ali Problem leader J.V.Hemert Jorge Tavares Group Leader Michele Sebag Samer Saadah

More Related