Chad Barb committed May 07, 2002 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ``````/**** wanlinksolve - A Reasonably Effective Algorithm for Genetically Assigning Nodes. Chad Barb, May 3, 2002 applies a standard genetic algorithm (with crossover) to solve the problem of mapping a smaller "virtual" graph into a larger "physical" graph, such that the actual weights between acquired nodes are similar to desired weights. The penalty function is the sum of error square roots. For the application this was designed for, "weights" are values of latency time in milliseconds. `````` Chad Barb committed May 10, 2002 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 `````` switches: -v Extra verbosity. -2 Solve for bandwidth dimension; Penalty for error is sum of differences of natural logs, multiplied by . A good weight seems to be around 7, but the appropriate value is pretty much application-dependent. -r Specify the minimum number of rounds to go before stopping. Note that the algorithm won't actually stop until round 3n, where "n" is the round which found the best solution so far, or if it hits maxrounds. default: DEFAULT_ROUNDS -R Specify the absolute maximum number of rounds. default: -1 (infinite) `````` Chad Barb committed May 07, 2002 36 37 38 39 40 41 42 43 44 45 `````` takes input from stdin, outputs to stdout. input format: * One line containing a single number 'p'-- the number of physical nodes. * 'p' lines containing the name of each physical node * 'p' lines each containing 'p' space-delimited numbers; this is a P x P matrix of the _actual_ weight from pnodes to pnodes. For latencies, there are zeros along the diagonal. `````` Chad Barb committed May 10, 2002 46 47 `````` ? 'p' lines, a P x P matrix of actual bandwidth ('-2' switch only) `````` Chad Barb committed May 07, 2002 48 49 50 51 52 53 54 55 56 `````` * One line containing a single number 'v'-- the number of virtual nodes. * 'v' lines containing the name of each virtual node * 'v' lines each containing 'v' space delimited numbers; this is a V x V matrix of the _desired_ weight between vnodes. '-1's indicate "don't care"s.. (e.g. for the weight between two not-connected vnodes.) If link weights are symmetrical, this matrix will be its own transpose (symmetric over the diagonal.) `````` Chad Barb committed May 10, 2002 57 `````` ? 'v' lines, a V x V matrix of desired bandwidth ('-2' switch only) `````` Chad Barb committed May 07, 2002 58 59 60 61 62 63 64 65 66 67 68 `````` output format: Easily inferred. Note that the perl regexp: /(\S+)\smaps\sto\s(\S+)/ will grab vnode to pnode mappings (in \$1 and \$2, respectively.) ****/ #include #include `````` Chad Barb committed May 10, 2002 69 70 ``````#include #include `````` Chad Barb committed May 07, 2002 71 72 73 74 75 76 77 ``````#include // To keep things lightweight, // structures are statically sized to // accommodate up to MAX_NODES nodes. // These could be changed to STL vectors in the future. #define MAX_NODES 20 `````` Chad Barb committed May 10, 2002 78 79 80 ``````#define MAX_DIMENSIONS 2 #define DEFAULT_ROUNDS 160 `````` Chad Barb committed May 07, 2002 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 `````` // The size of our "population." // (100,000 seems to work well.) #define SOLUTIONS 100000 // The number of new children to produce each round. // (20,000 seems to work well.) #define CHILDREN_PER_ROUND 20000 // The probability a given child will NOT have a mutation. // (out of 1000). 990 means 1% of children will mutate. // (.01% will mutate twice, .0001% three times, etc.) // 500 means 50% of children will mutate (25% twice, 12% three times, etc.) // 500, incidentally, seems to be optimal. #define MUTATE_PROB 500 // A score below Epsilon means we've found a perfect solution, // so stop immediately. #define EPSILON 0.0001f // lets STL it up a notch. #include #include // BAM! using namespace std; // keep freebsd from mumbling about gets(3) being unsafe. #define gets( x ) fgets( x, sizeof( x ), stdin ) // keep track of user names for nodes. static map< int, string > pnodeNames; static map< int, string > vnodeNames; static int pnodes, vnodes; `````` Chad Barb committed May 10, 2002 117 118 119 120 121 122 123 124 125 ``````static int pLatency[MAX_DIMENSIONS][MAX_NODES][MAX_NODES]; static int vDesiredLatency[MAX_DIMENSIONS][MAX_NODES][MAX_NODES]; static int dimensions; static float d2weight; static int verbose = 0; static int minrounds, maxrounds; `````` Chad Barb committed May 07, 2002 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 `````` class Solution { public: int pnode_mapping[MAX_NODES]; // -1 means nothin' float error; }; static Solution pool[SOLUTIONS]; static inline int pickABest() { // a hacky (but damn fast) probibility curve to // favor mating better solutions. switch (rand() % 4) { case 0: return rand() % (SOLUTIONS / 32); case 1: return rand() % (SOLUTIONS / 16); case 2: return rand() % (SOLUTIONS / 4); case 3: return rand() % (SOLUTIONS / 2); default: return 0; // can't happen, but appease -Wall. } } static inline int pickAWorst() { return SOLUTIONS - pickABest(); } // uses templates to avoid massive numbers // of "if" choices.. compiler should generate two versions, // one with dump and one without. template static inline void calcError( Solution * t ) { float err = 0.0f; if (verbose) { printf("Error listing:\n"); } int vnode_mapping[MAX_NODES]; { for (int x = 0; x < pnodes; x++) { if (t->pnode_mapping[x] != -1) { vnode_mapping[ t->pnode_mapping[x] ] = x; } } } { `````` Chad Barb committed May 10, 2002 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 `````` for (int z = 0; z < dimensions; z++) { for (int x = 0; x < vnodes; x++) { for (int y = 0; y < vnodes; y++) { int should = vDesiredLatency[z][x][y]; if (should != -1) { int is = pLatency[z][ vnode_mapping[x] ][ vnode_mapping[y] ]; if (should != is) { float errDelta; if (z == 0) { errDelta = sqrtf((float)(abs(should - is))); } else { errDelta = d2weight * (float)(abs(should - is)); } if (verbose) { if (z == 0) { printf("%s -> %s latency (ms) should be %i; is %i (err [sqrt |a-b|] %4.3f)\n", vnodeNames[x].c_str(), vnodeNames[y].c_str(), should, is, errDelta ); } else { printf("%s -> %s bandwidth (kB/s) should be ~%i; is ~%i (err [wt * ln (a/b)] %4.3f)\n", vnodeNames[x].c_str(), vnodeNames[y].c_str(), (int)expf((float)should / 1000.0f), (int)expf((float)is / 1000.0f), errDelta ); } } err += errDelta; `````` Chad Barb committed May 07, 2002 207 208 209 210 211 212 213 `````` } } } } } } `````` Chad Barb committed May 10, 2002 214 `````` if (verbose) { printf("error of %4.3f\n", err ); } `````` Chad Barb committed May 07, 2002 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 `````` t->error = err; } static int compar( const void * a , const void * b ) { Solution * sa = (Solution *)a; Solution * sb = (Solution *)b; if (sa->error > sb->error) { return 1; } else if (sa->error < sb->error) { return -1; } else { return 0; } } static inline void sortByError() { // Ahh.. sweet, sweet qsort. qsort( pool, SOLUTIONS, sizeof( Solution ), compar ); } // "Mutating" is swapping what vnode a pnode maps to in // the solution with what vnode a different pnode maps to. // (if both are -1, e.g. not mapped to vnodes, nothing happens.) static inline void mutate( Solution * t ) { while(1) { // forecast calls for a 1% chance of mutation... if ((rand() % 1000) < MUTATE_PROB) { break; } int a = rand() % pnodes; int b = rand() % pnodes; int temp = t->pnode_mapping[a]; t->pnode_mapping[a] = t->pnode_mapping[b]; t->pnode_mapping[b] = temp; } } // TODO: make sure that failed matings don't happen too // often for difficult graphs. // (perhaps have a limited retry) static inline void splice( Solution * t, Solution * a, Solution * b) { int vnode_mapping_a[MAX_NODES]; int vnode_mapping_b[MAX_NODES]; int vnode_mapping_t[MAX_NODES]; int pnode_used[MAX_NODES]; bzero( pnode_used, sizeof( pnode_used ) ); { for (int x = 0; x < pnodes; x++) { if (a->pnode_mapping[x] != -1) { vnode_mapping_a[ a->pnode_mapping[x] ] = x; } if (b->pnode_mapping[x] != -1) { vnode_mapping_b[ b->pnode_mapping[x] ] = x; } } } // go through each mapping, and pick randomly // which one of the two parents' mappings the child // will inherit. // Inherit the one that makes sense if the other would // conflict with a previously chosen mapping. // If both would conflict with a previously chosen mapping. // its a failed mating, and we return. int pos = rand() % vnodes; for (int i = 0; i < vnodes; i++) { pos = (pos + 1) % vnodes; if (rand() % 2) { if (!pnode_used[ vnode_mapping_a[pos] ]) { vnode_mapping_t[pos] = vnode_mapping_a[pos]; pnode_used[ vnode_mapping_a[pos] ]= 1; } else { if (!pnode_used[ vnode_mapping_b[pos] ]) { vnode_mapping_t[pos] = vnode_mapping_b[pos]; pnode_used[ vnode_mapping_b[pos] ]= 1; } else { // failed mating. return; } } } else { if (!pnode_used[ vnode_mapping_b[pos] ]) { vnode_mapping_t[pos] = vnode_mapping_b[pos]; pnode_used[ vnode_mapping_b[pos] ]= 1; } else { if (!pnode_used[ vnode_mapping_a[pos] ]) { vnode_mapping_t[pos] = vnode_mapping_a[pos]; pnode_used[ vnode_mapping_a[pos] ]= 1; } else { // failed mating. return; } } } } // ok.. good one. for(int c = 0; c < pnodes; c++) { t->pnode_mapping[c] = -1; } for(int d = 0; d < vnodes; d++) { t->pnode_mapping[ vnode_mapping_t[d] ] = d; } // Mazeltov! mutate( t ); calcError( t ); } // Generate a random solution // for the initial population. static inline void generateRandomSolution( Solution * t ) { for (int i = 0; i < pnodes; i++) { t->pnode_mapping[i] = -1; } for (int j = 0; j < vnodes; j++) { while(1) { int r = rand() % pnodes; if (t->pnode_mapping[r] == -1) { t->pnode_mapping[r] = j; break; } } } calcError( t ); } `````` Chad Barb committed May 10, 2002 346 ``````void usage( char * appname ) `````` Chad Barb committed May 07, 2002 347 ``````{ `````` Chad Barb committed May 10, 2002 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 `````` fprintf(stderr, "Usage:\n" "%s [-v] [-2 ] [-r ] [-R ]\n\n" " -v extra verbosity\n" " -2 enable solving for bandwidth;\n" " multiply bandwidth penalties by .\n" " -r set minimum rounds (a.k.a. generations)\n" " default: %i\n" " -R set maximum rounds\n" " default: infinite (-1)\n\n", appname, DEFAULT_ROUNDS ); exit(-2); } int main( int argc, char ** argv ) { verbose = 0; dimensions = 1; d2weight = 1.0f / 1000.0f; minrounds = DEFAULT_ROUNDS; maxrounds = -1; int ch; while ((ch = getopt(argc, argv, "v2:r:R:")) != -1) { switch (ch) { case 'v': verbose++; break; case '2': dimensions = 2; d2weight = atof( optarg ) / 1000.0f; break; case 'r': minrounds = atoi( optarg ); break; case 'R': maxrounds = atoi( optarg ); break; default: usage( argv[0] ); } } `````` Chad Barb committed May 07, 2002 393 394 395 `````` char line[1024]; { `````` Chad Barb committed May 10, 2002 396 `````` if (verbose) { printf("How many physical nodes?\n"); } `````` Chad Barb committed May 07, 2002 397 398 399 `````` gets( line ); sscanf( line, "%i", &pnodes ); `````` Chad Barb committed May 10, 2002 400 `````` if (verbose) { printf("Okay, enter %i names for the physical nodes, one per line.\n", pnodes ); } `````` Chad Barb committed May 07, 2002 401 402 403 404 405 406 407 `````` for (int i = 0; i < pnodes; i++) { char name[1024]; gets( line ); sscanf( line, "%s", name ); pnodeNames[i] = string( name ); } `````` Chad Barb committed May 10, 2002 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 `````` for (int z = 0; z < dimensions; z++) { if (verbose) { printf("Enter %ix%i grid o' actual %s.\n", pnodes, pnodes, (z == 0) ? "latency" : "bandwidth"); } for (int y = 0; y < pnodes; y++) { char * linePos = line; gets( line ); while (*linePos == ' ') { linePos++; } // skip leading whitespace for (int x = 0; x < pnodes; x++) { sscanf( linePos, "%i", &pLatency[z][x][y] ); if (z == 1) { pLatency[z][x][y] = (int)( logf(pLatency[z][x][y]) * 1000.0f ); } while (*linePos != ' ' && *linePos != '\n') { linePos++; } while (*linePos == ' ') { linePos++; } } `````` Chad Barb committed May 07, 2002 423 424 425 426 427 `````` } } } { `````` Chad Barb committed May 10, 2002 428 `````` if (verbose) { printf("How many virtual nodes?\n"); } `````` Chad Barb committed May 07, 2002 429 430 431 `````` gets( line ); sscanf( line, "%i", &vnodes ); `````` Chad Barb committed May 10, 2002 432 `````` if (verbose) { printf("Okay, enter %i names for the virtual nodes, one per line.\n", vnodes ); } `````` Chad Barb committed May 07, 2002 433 434 435 436 437 438 439 `````` for (int i = 0; i < vnodes; i++) { char name[1024]; gets( line ); sscanf( line, "%s", name ); vnodeNames[i] = string( name ); } `````` Chad Barb committed May 10, 2002 440 441 442 443 `````` for (int z = 0; z < dimensions; z++) { if (verbose) { printf("Enter %ix%i grid o' desired %s (-1 is don't care.)\n", vnodes, vnodes, (z == 0) ? "latency" : "bandwidth"); `````` Chad Barb committed May 07, 2002 444 `````` } `````` Chad Barb committed May 10, 2002 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 `````` for (int y = 0; y < vnodes; y++) { char * linePos = line; gets( line ); while (*linePos == ' ') { linePos++; } // skip leading whitespace for (int x = 0; x < vnodes; x++) { sscanf( linePos, "%i", &vDesiredLatency[z][x][y] ); if (z == 1) { if (vDesiredLatency[z][x][y] != -1) { vDesiredLatency[z][x][y] = (int)(logf(vDesiredLatency[z][x][y]) * 1000.0f); } } while (*linePos != ' ' && *linePos != '\n') { linePos++; } while (*linePos == ' ') { linePos++; } } } } } `````` Chad Barb committed May 07, 2002 462 `````` `````` Chad Barb committed May 10, 2002 463 `````` if (verbose) { printf("Thanks.. now running...\n"); } `````` Chad Barb committed May 07, 2002 464 465 466 467 468 469 470 471 472 473 474 `````` { for (int i = 0; i < SOLUTIONS; i++) { generateRandomSolution( &(pool[i]) ); } sortByError(); } { int highestFoundRound = 0; float last = pool[0].error; `````` Chad Barb committed May 10, 2002 475 476 `````` for (int i = 0; i != maxrounds && (i < minrounds || i < highestFoundRound * 3); i++) { if (verbose && !(i % (minrounds / 10))) { `````` Chad Barb committed May 07, 2002 477 478 479 480 `````` printf("Round %i. (best %4.3f)\n", i, pool[0].error); } if (pool[0].error < last) { `````` Chad Barb committed May 10, 2002 481 482 `````` if (verbose) { printf("Better solution found in round %i (error %4.3f)\n", `````` Chad Barb committed May 07, 2002 483 `````` i, pool[0].error); `````` Chad Barb committed May 10, 2002 484 `````` } `````` Chad Barb committed May 07, 2002 485 486 487 488 489 490 491 492 493 494 495 496 `````` last = pool[0].error; highestFoundRound = i; } for (int j = 0; j < CHILDREN_PER_ROUND; j++) { // Overwrite a "bad" solution with the child of two "good" ones. splice( &(pool[pickAWorst()]), &(pool[pickABest()]), &(pool[pickABest()]) ); } sortByError(); if (pool[0].error < EPSILON) { `````` Chad Barb committed May 10, 2002 497 `````` if (verbose) { printf("Found perfect solution.\n"); } `````` Chad Barb committed May 07, 2002 498 499 500 501 502 503 `````` break; } } } { `````` Chad Barb committed May 10, 2002 504 `````` if (verbose) { printf("\nYour solution is as follows:\n"); } `````` Chad Barb committed May 07, 2002 505 506 `````` for (int x = 0; x < pnodes; x++) { if (pool[0].pnode_mapping[x] != -1) { `````` Chad Barb committed May 10, 2002 507 `````` printf("%s mapsTo %s\n", `````` Chad Barb committed May 07, 2002 508 509 510 511 512 513 514 `````` vnodeNames[pool[0].pnode_mapping[x]].c_str(), pnodeNames[x].c_str() ); } } printf("\n"); // dump a detailed report of the returned solution's errors. `````` Chad Barb committed May 10, 2002 515 `````` if (verbose) { calcError( &(pool[0]) ); } `````` Chad Barb committed May 07, 2002 516 517 `````` } `````` Chad Barb committed May 10, 2002 518 `````` if (verbose) { printf("Bye now.\n"); } `````` Chad Barb committed May 07, 2002 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 `````` return 0; } ``````