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SET PARTITIONING Denis Khryashchev INTRODUCTION INTRODUCTION - PowerPoint PPT Presentation

SET PARTITIONING Denis Khryashchev INTRODUCTION INTRODUCTION PROBLEM STATEMENT NUMBER OF PARTITIONS MATHEMATICAL STATEMENT MATRIX REPRESENTATION MATRIX REPRESENTATION MATRIX REPRESENTATION MATRIX REPRESENTATION MATRIX REPRESENTATION


  1. SET PARTITIONING Denis Khryashchev

  2. INTRODUCTION

  3. INTRODUCTION

  4. PROBLEM STATEMENT

  5. NUMBER OF PARTITIONS

  6. MATHEMATICAL STATEMENT

  7. MATRIX REPRESENTATION

  8. MATRIX REPRESENTATION

  9. MATRIX REPRESENTATION

  10. MATRIX REPRESENTATION

  11. MATRIX REPRESENTATION

  12. MATRIX REPRESENTATION

  13. MATRIX REPRESENTATION

  14. PARTITION SOLUTION

  15. PARTITION SOLUTION

  16. GENETIC ALGORITHM

  17. GENETIC THINKING FOR PARTITIONS

  18. GENETIC EXAMPLE

  19. GENETIC EXAMPLE

  20. SEQUENTIAL GENETIC ALGORITHM 1. Initialization creates a starting population of a given size. 2. Evaluation assesses if the current population is “solution - like”. 3. Local search heuristics improves convergence of solution by selecting better candidates. 4. Mutation modifies the species of the population randomizing them. 5. Crossover combines two parents exchanging and scrambling their bits together to create a new species.

  21. COMPUTATIONAL COMPLEXITY

  22. NAÏVE PARALLEL SOLUTION

  23. THE ISLAND MODEL ALGORITHM Separate and isolated subpopulations evolve independently in parallel. Occasionally, fit species (strings) migrate between subpopulations. The algorithm is programmed using a single-program multiple data (SPMD) model. The processors “synchronize” exchanging fit strings. The path to parallelism is the expansion of the original algorithm with a migration of the species between the islands.

  24. THE ISLAND MODEL EXAMPLE

  25. THE ISLAND MODEL EXAMPLE

  26. THE ALGORITHM 1. When a fit species appeared or enough time passed since the last migration it’s time to migrate. 2. The top species migrate to the neighboring populations with send_string(). 3. At the same time the current population welcomes new migrants with recv_string(). 4. The less fit species replaced with the new ones.

  27. THE PARALLELIZATION

  28. COMPUTATIONAL COMPLEXITY

  29. COST OPTIMAL?

  30. THANK YOU ! Questions ?

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