Self-Assembling Hyper-heuristics: a proof of concept

Self-Assembling Hyper-heuristics: a proof of concept German Terrazas [email_address] Dario Landa-Silva and Natalio Krasnogor submitted to the 9th international conference on Artificial Evolution (EA'09)

Outline

Automated design of self-assembly Wang tiles

Self-assembly Heuristics

Model

Hypothesis

Methodology

Execution threads analysis

Test case

Travelling Salesman Problem

Execution threads analysis

Conclusions

2

Automated Design of Self-Assembly Wang Tiles

Self-Assembly (SA): complex structures are formed from many autonomous components interacting with one another. There is no master plan nor external influences.

Self-assembly Wang Tiles System

Set of tiles square in shape and coloured edges

2D square lattice

Matrix M and temperature T

Random walk, edge-to-edge (local) interactions:

if M[ci, cj] > T

then Stick

else Bounce off

M = colour-colour strength matrix Wang tiles 3

Wang tiles system Target structure Fixed T , Fixed M Q1: Is it possible to make an automated design of tiles capable of obtaining a particular supra-structure by means of SA? A1: Yes. 4

Self-Assembly Heuristics + 5 Execution threads (sequences of low level heuristics) by random walk (currently) Assembled heuristic

Q2: Is it possible to automatically design the correct assembly of a heuristic, the execution threads of which optimise a given problem instance ? Q3: If Q2 is yes, is it possible to apply the same methodology to a different problem ? Execution threads analysis + Assembled heuristics characterisation + Evolutionary design Methodology Solving NP-complete problems in the tile assembly model . Y. Brun (SubsetSum) Constant-Size Tileset for Solving an NP-Complete Problem in Nondeterministic Linear Time . Y. Brun (SubsetSum) Reducing Tileset Size: 3-SAT and Beyond . Y. Brun (3-SAT) 6 Combinatorial Optimisation Problems Self-assembly Heuristics Low Level Heuristic Assembled heuristics

Execution Threads Analysis

Execution thread analysis sheds light on patterns of low level heuristics inherent to an emergent assembled heuristic

Q: are there “common” combinations of heuristics among the execution threads ?

Q: If yes, how reliable are these combinations ?

1. COLLECT N_execution_threads 2. for EACH execution thread { 3. APPLY to a COP instance 4. } 5. FILTER BEST_execution_threads 6. APPLY MSA (e.g. Muscle) 7. ANALYSE patterns of heuristics 8. GEN TEMPLATE_execution_threads 9. GEN RND_execution_threads 10. for EACH execution thread { 11. APPLY to a COP instance 12. } 13. TEMPLATE vs. RND 7

Test Case: TSP

Problem instances: (easy to solve symmetric TSP instances)

Geographical distance

Groetschel 16-city (ulysses16)

Groetschel 22-city (ulysses22)

2D Euclidean distance

Eilon 51-city (eil51)

Eilon 76-city (eil76)

Krolak 100-city (kroA100)

n-city insertion : selects sub-tour of size n and inserts randomly between two consecutive cities (n=1) n-exchange : selects n links for removal and insertion (n=2)

Low level heuristics

8

1. COLLECT N_execution_threads 2. for EACH execution thread { 3. APPLY to a COP instance 4. }

way to generated different lengths systematically

generate structures similar to the ones of SA tiles sim

percolation cluster on 2D square lattice

P in (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9)

heuristics uniformly distributed

Execution threads

9 IN IN IN OUT OUT OUT

5. FILTER BEST_execution_threads 6. APPLY MSA (e.g. Muscle) 7. ANALYSE patterns of heuristics 2-exchange A T 1-city insertion e76_ 0.72490706 _T1 ATTTAATTTATTATATTTATTTTTTTTTATATTATATAATTTAATATAAAAAAATA e76_ 0.88475836 _T2 ATTATTTATATTTATATATAAAATAATTTTTTTTAATATTTAATATA e76_ 0.96840148 _T3 TATATTTAAAATATATAAATTAATATTAAA e76_ 1.03159851 _T4 TATAAAAAAAATATTTATTTTTTTTTTATAAA e76_ 1.13197026 _T5 TATATATATTATAAAATATATTATAAAAAAATAA Q: Are there “common” combinations of heuristics among the execution threads ? A: Yes, there are common combinations  template execution thread 0-11# TATA #7-12# TATA #3-8# TTT #4-4# TAAA #1-10# AAAA #6-7# TATA #......... 10 TATA TATA TTT TAAA AAAA TATA AAA

Q: How reliable are these combinations ? Generate 300 Template-based execution thread RND execution thread evaluate 100 times RND ET length N evaluated 100 times Template-based ET length N evaluated 100 times 11 8. GEN TEMPLATE_execution_threads 9. GEN RND_execution_threads 10. for EACH execution thread { 11. APPLY to a COP instance 12. } 13. TEMPLATE vs. RND

Conclusions

Three components of stochasticity

Random distribution of low level heuristics across the lattice

Random walk for execution threads collection

Stochastic nature of low level heuristics

Computational expensive, parallelisation needed

Yes it is possible to visualise patterns of heuristics (MSA)

Best execution threads are not totally reliable compared to randomly generated execution threads (due to stochastic application of heuristics)

Individual assessment of patterns of heuristics

Increase the diversity of low level heuristics

Reduce the number of stochastic components

Fix the distribution of low level heuristics

Fix the way execution threads are collected

Multiple evaluations of collected execution threads

Try different instance problems, e.g. asymmetric TSP, knapsack

12

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