1. 학습목표 공진화의 개념을 이해하고, sorting network에의 응용가능성을 점검한다
Lecture 2. Co-Evolution
학습목표
공진화의 개념을 이해하고, sorting network에의 응용가능성을 점검한다

2. Outline Review of the last lecture What is co-evolution
Co-evolving sorting networks (Hillis’s seminal work)
What is a sorting network
Simulated evolution on a Connection Machine
Co-evolving parasites improves simulated evolution
Summary

3. Review of Last Lecture
EAs can be regarded as population-based, stochastic generate-and-test algorithms
Two issues
How to generate offspring?
How to test (select) them?
Eas represent a whole family of algorithms, with different representation, search operators, etc
EC covers at least four major areas
EC is closely related to AI, CS, Operations Research, Machine Learning, Engineering, etc

4. Generate-and-Test Loop Generate a candidate solution
Test the candidate solution
Until a satisfactory solution is found or no more candidate solutions can be found
Candidate
Solutions
Generator
Tester …

5. What is Co-Evolution Without co-evolution
The fitness landscape is fixed
The same individual always gives the same fitness
Examples: TSPs
With co-evolution
The fitness landscape is not fixed
The fitness of an individual depends on other individuals
The same individual may not have the same fitness in different populations
In other words, co-evolution can be regarded as a kind of landscape coupling where adaptive moves by one individual will deform landscapes of others
Examples: pre-predator problems

6. Sorting Networks
is a sorting algorithm in essence, but can be represented graphically for the ease of understanding
Used widely in switching circuits, routing algorithms, and other areas in interconnection networks
Two issues
Number of comparators
Number of layers
Best known networks with 16 inputs
Year
1962
1964
1969
Designers
Bose, Nelson
Batcher, Knuth
Shapiro
Green
# comparators 65 63 62 60
still the best known today

7. Sorting Networks Comparators
Graphical representation of a sorting network
small
unsorted
input
sorted
output
large
input
element
unsorted
input
sorted
output
a layer

8. Problem Formulation
Search the space of sorting networks for the optimal one with the minimal number of comparators
Search the space of small networks for the optimal one that sorts all inputs correctly

9. Simulated Evolution without Co-Evolution
Genotypic representation
1 chromosome = 8 pairs of 4 bits
15 pairs
Genotype length = (2 * 15) * (4 * 8) = 960 (bits)
Phenotypic representation
An ordered sequence of ordered integer pairs
{(0, 1), (2, 3), ……}

10. Evolution (1) Fitness evaluation
2^16 different binary strings will be used as test cases
The fitness is proportional to the percentage of correctly sorted cases
Selection (reproduction)
Simple truncation that throws away the bottom 50%
Pick a pair at random in the neighborhood. The fitter individual is copied onto the less fit one
Connection Machine
Massively parallel (64K processors)
2-d grid with torroidal boundary conditions
One processor per individual

11. Evolution (2) The more repetitions you do, the better you’d
Approximate a Gaussian distribution (actually
It’s through the binomial distribution)
Recombination (crossover)
Two stages
Within individual crossover to generate the gamete pool
Between individual crossover to swap gametes
Choosing mates using a Gaussian distribution
Swap gametes between individuals
Choosing a mate
For each individual
1. Start with a pointer pointing to itself
2. Divide the grid into pairs of adjacent individuals
3. Flip a coin to decide whether a pair should exchange their addresses (pointers)
4. Repeat 2~3

12. Evolution (3) Mutation Point mutation
Very low rate, one per 1000 bits per generation
Experiments
64536 individuals for up to 5000 generations
The best found: 65 comparators
Problems
Local optima, i.e., the population stagnates at a sub-optimal solution and is unable to make further progress
Inefficiency in fitness evaluation. Often spent much time on some “easy” cases

13. Co-Evolution  Best network evolved: 61 comparators
Two separate populations
Host population: sorting networks
Parasite populations: test cases (10 to 20)
They co-locate at each node of the grid
They interact/co-evolve through fitness evaluation
For the host population, an individual is evaluated by the test cases at its site
For the parasite populations, an individual is evaluated by the number of cases that the network fails to sort
Co-evolution brings two benefits
It creates competition (“arms race”) between two populations and avoids early stagnation of a population
Saves time in fitness evaluation

14. Beyond Hillis’s Work
Basic concept and ideas about co-evolution: individuals interact There are a number of different ways of interacting fitness evaluations
Select a random individual in another population in fitness evaluation
Select the best
Select a group (even the whole population)
Inter-population versus intra-population
Competitive co-evolution versus cooperative co-evolution
Population 1
Population 2

15. Summary
Basic concept and ideas about co-evolution: individuals interact with each other through changing each other’s fitness landscapes
Parallel evolutionary algorithms: fine-grained model
Diploid representation, special operators
Co-evolution creates “arms race”
References
W. Daniel Hillis, “Co-evolving parasites improve simulated evolution as an optimization procedure,” Artificial Life II, SFI Studies in the Science of Complexity, vol. X, edited by C.G. Langton, C. Taylor, J.D. Farmer and S. Rasmussen, Addison-Wesley, pp , 1991.