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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],2

Automated Design of Self-Assembly Wang Tiles ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],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 ,[object Object],[object Object],[object Object],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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],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) ,[object Object],8

1. COLLECT N_execution_threads 2. for EACH execution thread { 3. APPLY to a COP instance 4. } ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],12

References ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],13

Self-Assembling Hyper-heuristics: a proof of concept

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Self-Assembling Hyper-heuristics: a proof of concept