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

Outline Hyper-heuristics 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

Hyper-heuristics

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

Hyper-heuristics Definition: Search methodologies that select and combine low-level heuristics to solve hard computational problems Characteristics: domain-independent strategies, operate in space of heuristics Aim: manufacture unknown heuristics which are fast, well performing How it works: Hyper-heuristics Space of low-level heuristics Space of solutions selects & combines 1000 800 120 fast & well performing 3 Feedback Feedback Cooperative Entities Self-Assembly

Definition: Search methodologies that select and combine low-level heuristics to solve hard computational problems

Characteristics: domain-independent strategies, operate in space of heuristics

Aim: manufacture unknown heuristics which are fast, well performing

How it works:

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 4

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

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. 5

Self-Assembly Heuristics + 6 Execution threads (sequences of low level heuristics) by random walk (currently) Assembled heuristic

Q2: Would be 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) 7 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 8

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 ?

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 9

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)

Low level heuristics

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 IN IN IN OUT OUT OUT 10

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

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 #......... 11 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 12 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 13

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

References Automated Self-Assembling Programming . L. Li, P. Siepmann, J. Smaldon, G. Terrazas and N. Krasnogor. In N. Krasnogor, S. Gustafson, D. Pelta, and J. L. Verdegay, editors, Systems Self-Assembly: Multidisciplinary Snapshots. Elsevier, 2008. Evolving Tiles for Automated Self-Assembly Design . G. Terrazas, M. Gheorghe, G. Kendall and N.Krasnogor. In IEEE Congress on Evolutionary Computation, pages 2001–2008. IEEE Press, 2007. Memetic algorithms: The polynomial local search complexity theory perspective . N. Krasnogor and J.E. Smith. Journal of Mathematical Modelling and Algorithms , 7:3-24, 2008. A Domain-Specific Language for Programming in the Tile Assembly Model . D. Doty and M. J. Patitz, 2009. Electronic access at http://arxiv.org/abs/0903.0889 Solving NP-complete problems in the tile assembly model . Y. Brun. Theor. Comput. Sci., 395(1):31–46, 2008. Constant-Size Tileset for Solving an NP-Complete Problem in Nondeterministic Linear Time . Y. Brun. In 13th International Meeting on DNA Computing, volume 4848 of Lecture Notes in Computer Science, pages 26–35. Springer, 2008. Reducing Tileset Size: 3-SAT and Beyond . Y. Brun. In 14th International Meeting on DNA Computing, page 178, Prague, Czech Republic, June 2008. Sequence Alignment as a Method for Human Activity Analysis in Space and Time . N. Shoval and M. Isaacsonm. In Annals of the Association of American Geographers, 97(2) 282–297, 2007. Bioinformatics and handwriting/speech recognition: unconventional applications of similarity search tools . K. Jensen and G. Stephanopoulos. In Fourth Singapore-MIT Alliance Conference on Molecular Engineering of Biological and Chemical Systems, 2005. Activity pattern analysis by means of sequence-alignment methods . Wilson W. C. Environment and Planning A 30(6) 1017 – 1038, 1998. 14

Automated Self-Assembling Programming . L. Li, P. Siepmann, J. Smaldon, G. Terrazas and N. Krasnogor. In N. Krasnogor, S. Gustafson, D. Pelta, and J. L. Verdegay, editors, Systems Self-Assembly: Multidisciplinary Snapshots. Elsevier, 2008.

Evolving Tiles for Automated Self-Assembly Design . G. Terrazas, M. Gheorghe, G. Kendall and N.Krasnogor. In IEEE Congress on Evolutionary Computation, pages 2001–2008. IEEE Press, 2007.

Memetic algorithms: The polynomial local search complexity theory perspective . N. Krasnogor and J.E. Smith. Journal of Mathematical Modelling and Algorithms , 7:3-24, 2008.

A Domain-Specific Language for Programming in the Tile Assembly Model . D. Doty and M. J. Patitz, 2009. Electronic access at http://arxiv.org/abs/0903.0889

Solving NP-complete problems in the tile assembly model . Y. Brun. Theor. Comput. Sci., 395(1):31–46, 2008.

Constant-Size Tileset for Solving an NP-Complete Problem in Nondeterministic Linear Time . Y. Brun. In 13th International Meeting on DNA Computing, volume 4848 of Lecture Notes in Computer Science, pages 26–35. Springer, 2008.

Reducing Tileset Size: 3-SAT and Beyond . Y. Brun. In 14th International Meeting on DNA Computing, page 178, Prague, Czech Republic, June 2008.

Sequence Alignment as a Method for Human Activity Analysis in Space and Time . N. Shoval and M. Isaacsonm. In Annals of the Association of American Geographers, 97(2) 282–297, 2007.

Bioinformatics and handwriting/speech recognition: unconventional applications of similarity search tools . K. Jensen and G. Stephanopoulos. In Fourth Singapore-MIT Alliance Conference on Molecular Engineering of Biological and Chemical Systems, 2005.

Activity pattern analysis by means of sequence-alignment methods . Wilson W. C. Environment and Planning A 30(6) 1017 – 1038, 1998.

Thank you Low-level Heuristics A solution