SET PARTITIONING Denis Khryashchev INTRODUCTION INTRODUCTION PROBLEM STATEMENT

SET PARTITIONING Denis Khryashchev

INTRODUCTION

PROBLEM STATEMENT

NUMBER OF PARTITIONS

MATHEMATICAL STATEMENT

MATRIX REPRESENTATION

PARTITION SOLUTION

GENETIC ALGORITHM

GENETIC THINKING FOR PARTITIONS

GENETIC EXAMPLE

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

COMPUTATIONAL COMPLEXITY

NAÏVE PARALLEL SOLUTION

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.

THE ISLAND MODEL EXAMPLE

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

THE PARALLELIZATION

COMPUTATIONAL COMPLEXITY

COST OPTIMAL?

THANK YOU ! Questions ?