Evolutionary Computation on the Connex Architecture

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Evolutionary Computation on the Connex
Architecture

• István Lorentz1 Mihaela Malita2
  Razvan Andonie3
• (presenter)
• 1Electronics and Computers Department,
  Transylvania University of Brasov, Romania
• 2Computer Science Department, Saint Anselm
  College Manchester, NH,
• 3Computer Science Department, Central Washington
  University Ellensburg, WA, USA

MAICS 2011 The 22nd Midwest Artificial
Intelligence and Cognitive Science Conference
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Presentation Outline

• The Connex Architecture
• (more in Prof. Gheorghe M. Stefan)
• Evolutionary Algorithms (EA)
• Parallelizing EA on Connex
• Example problems
• Results
• Conclusions

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The Connex Chip

• The Connex Array
• Many-core data parallel area of 1024 Processing
  Cells (PC)
• Area 50 mm2 of the 1024-PC array, including
  1Mbyte of memory and the two controllers
• Clock speed 400 MHz
• Also on the chip
• Multi-core area 4 MIPS cores
• Speculative parallel pipe of 8 PE
• Interfaces
• DDR, PCI
• Video and Audio interfaces for 2 HDTV channels
• Total Power 5 Watts
• Total Area 82 mm2
• 65nm implementation

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The Connex Array

• Sequencer
• Issues in each cycle (on a 2-stage pipe) one
  instruction for Connex Array and one instruction
  for itself
• I/O Controller
• Controls a 6.4 GB/s I/O channel
• Works in parallel with code running on the Connex
  Array
• Processing Cell
• Integer unit
• Data memory
• Boolean (predicate) unit

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Genetic Algorithms (GA)
Initialize population randomly

• Chromosomes represented as vectors of integer
  components in Connex
• Maximum chromosome length 1024 elements
• Population forms a matrix
• Processing blocks are parallelized

Crossover
Mutation
Evaluation
Select new generation
Convergence or limit ?
No
Yes
STOP
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Evolution strategy (ES)
Initialize population randomly

• Similar algorithm to GA
• Population and mutation parameters encoded in
  vectors
• Recombination forms a new individual from
  multiple parents
• Mutation adds a gaussian-distributed random
  variable to each vector component
• Deterministic selection of new generation, based
  of fitness ranking

Recombination
Mutation
Evaluation
Select new parent generation
Convergence or limit ?
No
Yes
STOP
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Parallel Crossover

• Combines genes of two individuals (parents)
• Example 1-point crossover at a random position
  in Vector-C
• vector crossover (vector X, vector Y)
• int position rand( VECTORSIZE )
• where ( i lt position)
• C X
• elsewhere
• C Y
• return C
• Uses Connex's parallel-if construct where(cond)
  elsewhere ...

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Parallel Mutation

• A single position is selected, randomly
• vector mutate(vector X)
• int pos rand(VECTOR_SIZE)
• float amount rand11()
• where (i pos)
• X amount
• return X
• The operation will affect only the selected
  position

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Evaluation of fitness function

• The class of fitness functions that can be
  evaluated efficiently on Connex are those
  composed by
• 1. data-parallel stage (local computation on each
  PC), followed by
• 2. parallel reduction (sum)
• For example
• - Sum of squared differences
• - Knapsack problem sum of weighted items
• - Travelling salesman problem sum of distances
  between cities in a route

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Example 1. The Rosenbrock function

• Benchmark problem for optimizations
• Vector-C implementation
• where ( iltN )
• Xsh rotateLeft(X, 1)
• where( ilt(N-1) )
• X2 X X
• Xsh - X2
• Xsh Xsh 100
• X2 1 - X
• X2 X2 X2
• X2 Xsh
• return sumv(X2)

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Example 2 The molecular distance geometry
problem (MDGP)

• The problem given a set of distance measurements
  between atoms, determine their cartesian
  coordonates
• Formulated as a global optimization problem,
  minimize
• Not all distances are known
• Some distances can be given as upper and lower
  bounds

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Representing MDGP on Connex

• Each given distance d(i,j) is mapped to a
  processing element
• Some PC share vertices
• Shared vertices share also random generator seeds
• No interprocessor communication (except parallel
  reduction)

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Running MDGP On Connex

• Evaluate distances
• Xi,Yi vertices
• D vector of known distances
• void evaluateDist(vector Xi,Yi,D)
• vector Dx, Dy
• DxXik-Xjk
• DyYik-Yjk
• Dx dx Dy dy
• Dx dy
• return sumAbsDiff(Dx,D)

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Results
Results
Operation Tpar Tseq Speedup
AB 1 1024 N
xorshift 128 13 13312 N
sumAbsDiffs 7 4096 0.5 N
1-Point Crossover 3 2048 0.6 N
Uniform Crossover 15 14350 0.9 N
Uniform Mutation 33 21172 0.6 N
HS Mutation 107 71506 0.6 N
Rosenbrock 14 14325 N
evaluateDist 13 10240 0.7 N
Summary of operations parallel instruction
counts, sequential instructions and speedups,
where N1024, the vector size.
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Conclusions

• - The Connex chip is suitable to parallelize
  evolutionary algorithms, by vectorization
• - By horizontal data mapping, we can benefit of
  the parallel reduction, for a certain class of
  optimization problems