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SET PARTITIONING
Denis Khryashchev
SET PARTITIONING Denis Khryashchev INTRODUCTION INTRODUCTION - - PowerPoint PPT Presentation
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
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INTRODUCTION
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PROBLEM STATEMENT
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NUMBER OF PARTITIONS
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MATHEMATICAL STATEMENT
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MATRIX REPRESENTATION
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MATRIX REPRESENTATION
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MATRIX REPRESENTATION
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MATRIX REPRESENTATION
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MATRIX REPRESENTATION
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MATRIX REPRESENTATION
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MATRIX REPRESENTATION
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PARTITION SOLUTION
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PARTITION SOLUTION
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GENETIC ALGORITHM
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GENETIC THINKING FOR PARTITIONS
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GENETIC EXAMPLE
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GENETIC EXAMPLE
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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.
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COMPUTATIONAL COMPLEXITY
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NAÏVE PARALLEL SOLUTION
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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.
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THE ISLAND MODEL EXAMPLE
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THE ISLAND MODEL EXAMPLE
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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.
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THE PARALLELIZATION
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COMPUTATIONAL COMPLEXITY
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COST OPTIMAL?
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