Solving Double Digest Problem by Genetic Algorithm Marek Kukačka & Zdeněk Pátek

Double Digest Problem (DDP) Input: ΔA – fragment lengths from the complete digest with enzyme A ΔB – fragment lengths from the complete digest with enzyme B ΔAB – fragment lengths from the complete digest with both A and B Output: A – location of the cuts in the restriction map for the enzyme A B – location of the cuts in the restriction map for the enzyme B Double Digest Problem is NP - complete

Genetic Algorithm (GA)

Mutation Swap mutation Insert mutation

Crossover One-point crossover

Selection Inverse Tournament Selection while (populationSize > N) do select individuals X1, X2 from population randomly if fitness(X1) > fitness(X2) remove X2 from population else remove X1 from population

Results – Random DDPs (1)

Results – Random DDPs (2)

Results – Random DDPs (3)

Results – Random DDPs (4)

Results – Random DDPs (5)

Custom DDPs (1) 1. Custom DDP (moderate) 2. Custom DDP (easy) B: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 AB: 1, 2, 3, 4, 5, 4, 2, 6, 1, 6, 2, 4, 5, 4, 3, 2, 1 2. Custom DDP (easy) B: 1, 10, 1, 10, 1, 10, 1, 10, 1, 10 AB: 1, 10, 1, 1, 9, 1, 2, 8, 1, 3, 7, 1, 4, 6

Custom DDPs (2) 3. Custom DDP (hard) 4. Custom DDP (weird) B: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 AB: 1, 2, 3, 4, 2, 3, 6, 2, 5, 5, 3, 6, 3, 5, 5, 2, 6, 3, 2, 4, 3, 2, 1 4. Custom DDP (weird) A: (1, 3) 100 B: (2, 2) 100 AB: (1, 1, 2) 100

Results – 1. Custom DDP NO_EXP NO_FAILS POP_SIZE MUT_PROB MUT_RATIO CRS_PROB AVG_GEN BEST_GEN AVG_MRS BEST_MRS 20 167 100 0.5 0.1 466 74 93479 14634 44 500 176 100111 34963 50 0.9 366 39 73356 7833 47 310 68 39691 8661 12 322 63 41253 7988 252 40 32233 5156 45 1 292 53 29224 5300 14 351 108 35193 10799 17 342 59 34233 5900 300 494 160 296817 95966 38 475 96 285085 57797 41 258 155408 24636 11 346 60 133189 23174 4 278 65 107046 24861 5 271 104279 20279 24 77502 13499 3 175 54 52618 16199 8 274 46 82377 13800 66 536 241 536578 241216 353 106 353710 105502 67 271012 67416 365 56 233966 35731 153 98060 24225 254 48 162812 30849 10 371 58 185819 28997 6 152 75997 32497 13 76572 23499

Results – 2. Custom DDP NO_EXP NO_FAILS POP_SIZE MUT_PROB MUT_RATIO CRS_PROB AVG_GEN BEST_GEN AVG_MRS BEST_MRS 20 27 100 0.5 0.1 449 51 89878 10241 39 428 63 85575 12454 28 0.9 394 18 78904 3533 9 365 49 46757 6336 14 317 40 40647 5082 11 271 30 34842 3788 6 1 321 56 32164 5600 4 398 33 39883 3300 200 36 20044 3600 10 300 378 60 227068 35700 21 356 214179 29489 12 239 43 143611 25985 3 155 34 59652 13112 37 77161 14169 2 134 51464 10347 121 36568 6000 133 48 40153 14399 8 232 22 69717 6600 500 272 272415 55772 67 300331 67080 228 50 228515 49822 163 104541 13191 91 58355 25586 5 81 52147 21092 115 57923 5499 113 19 56698 9499 140 70272 9000

Results – 3. Custom DDP NO_EXP NO_FAILS POP_SIZE MUT_PROB MUT_RATIO CRS_PROB AVG_GEN BEST_GEN AVG_MRS BEST_MRS 20 200 100 0.5 0.1   UNSOLVABLE 0.9 126 558 112 71456 14164 178 365 46973 14407 1 300 161 724 439 278213 169016 54 491 188838 38022 199 466 179 178930 68642 123 481 185 144537 55499 152 372 89 111836 26699 500 82 541 261 541227 261369 110 533 189 533523 189694 86 338 109 216641 69882 26 345 221109 69757 16 343 90 219688 57656 139 564 228 282066 113995 50 182769 54498 76 371 130 185519 64999