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Matt Zykan

Matt Zykan. May 1, 2008. A Variety of Methods for Generating Mediocre TSCCDs. T ight, S ingle- C hange C overing D esign symbols total = V symbols per block = K. TSCCD. Why TSCCD? Difficult construction problem No known efficient, scalable algorithm Develop new EA techniques

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Matt Zykan

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  1. Matt Zykan May 1, 2008 A Variety of Methods for Generating Mediocre TSCCDs

  2. Tight, Single-Change Covering Design symbols total = V symbols per block = K TSCCD

  3. Why TSCCD? Difficult construction problem No known efficient, scalable algorithm Develop new EA techniques Complex space: many sub-optima Advance EA knowledge Motivation

  4. Preece et. al Non-genetic methods Produced a (5,20) at great expense Matt Johnson SNDL-MOEA Produced an 87% complete (5,20)‏ Previous Work

  5. Approach TSCCD as a puzzle Genome based on “move”s A move is defined by two integers Position [1,k] Symbol [1,v] Single-Change is guaranteed Tight / Cover must be solved Gene Design

  6. Data sequence of moves (primary genome)‏ leadin block Fitness eval. starts by building a full-length solution out of individuals Individual fitnesses are updated according to benefit/cost contributed to this composite solution Individual

  7. Fitness is based on “score” of moves Score = new pairs – dupl./invalid pairs Individual fitness is a running average of score per move contributed to construction Fitness

  8. Start with initial block, no moves Random for each construction Choose individual to append, repeat First, by predicted contribution Second, by general fitness Constructing Solutions

  9. Construction & Crossover individual full-length solution offspring

  10. K=4, V=12 16 clean moves out of 20 Results

  11. All genomes are full-length solutions Fitness = # of covers Uniform random initialization Fit. proportional parent selection 3-tournament survival selection Population 500, Children 200 Mutaterate 0.1, Crossrate 0.1 Benchmark MethodSimple EA

  12. Non-genetic stochastic optimization Data stored: weighted set of all moves for every possible block For K and V: KV possible moves VK possible blocks! Generate initial block Make weighted choice of next move given last block Update move weights according to result Strange MethodCollapser

  13. K=4, V=12 Results

  14. Error maps for (5, 20)‏ SNDL-MOEA [----------------------------------------_____] Collapser [------------------------------------334312422] Results

  15. TSCCD's solution space is a nightmarish hellscape Many, many local optima In the case of (5,20): 45 dimensions For generating suboptima: Collapser is very fast, uses infinite RAM Simple EA is kinda fast Complex EA is slow Conclusions

  16. Assembler Use Collapser/Simple to generate seeds Intelligently assemble seeds Essentially, replace population in Complex EA with random seeds Future Work

  17. Questions

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