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Ackley function

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25: 67:. It was proposed by David Ackley in his 1987 PhD dissertation. The function is commonly used as a minimization function with global minimum value 0 at 0,.., 0 in the form due to Thomas Bäck. While Ackley gives the function as an example of "fine-textured broadly unimodal space" his thesis does not actually use the function as a test. 39: 272: 81: 319: 76: 400: 379: 330: 52: 349: 64: 267:{\displaystyle {\begin{aligned}f(x,y)=-20&{}\exp \left\\&{}-\exp \left+e+20\end{aligned}}} 283: 375: 367: 60: 371: 394: 16:
Function used as a performance test problem for optimization algorithms
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Bäck, Thomas (1996-02-15). "Artificial Landscapes".
352:", Kluwer Academic Publishers, Boston MA. p. 13-14 313: 266: 350:A connectionist machine for genetic hillclimbing 364:Evolutionary Algorithms in Theory and Practice 8: 70:On a 2-dimensional domain it is defined by: 44:Contour surfaces of Ackley's function in 3D 285: 181: 168: 157: 144: 132: 113: 80: 78: 366:. Oxford University Press. p. 142. 341: 63:used as a performance test problem for 7: 372:10.1093/oso/9780195099713.003.0008 14: 37: 30:Ackley function of two variables 23: 401:Test functions for optimization 331:Test functions for optimization 302: 290: 163: 137: 99: 87: 1: 277:Its global optimum point is 417: 314:{\displaystyle f(0,0)=0.} 53:mathematical optimization 65:optimization algorithms 348:Ackley, D. H. (1987) " 315: 268: 316: 269: 284: 77: 311: 264: 262: 381:978-0-19-509971-3 166: 408: 386: 385: 359: 353: 346: 320: 318: 317: 312: 273: 271: 270: 265: 263: 247: 243: 242: 238: 182: 177: 173: 169: 167: 162: 161: 149: 148: 133: 114: 41: 27: 416: 415: 411: 410: 409: 407: 406: 405: 391: 390: 389: 382: 361: 360: 356: 347: 343: 339: 327: 282: 281: 261: 260: 204: 200: 196: 192: 175: 174: 153: 140: 125: 121: 111: 75: 74: 61:convex function 57:Ackley function 49: 48: 47: 46: 45: 42: 33: 32: 31: 28: 17: 12: 11: 5: 414: 412: 404: 403: 393: 392: 388: 387: 380: 354: 340: 338: 335: 334: 333: 326: 323: 322: 321: 310: 307: 304: 301: 298: 295: 292: 289: 275: 274: 259: 256: 253: 250: 246: 241: 237: 234: 231: 228: 225: 222: 219: 216: 213: 210: 207: 203: 199: 195: 191: 188: 185: 180: 178: 176: 172: 165: 160: 156: 152: 147: 143: 139: 136: 131: 128: 124: 120: 117: 112: 110: 107: 104: 101: 98: 95: 92: 89: 86: 83: 82: 43: 36: 35: 34: 29: 22: 21: 20: 19: 18: 15: 13: 10: 9: 6: 4: 3: 2: 413: 402: 399: 398: 396: 383: 377: 373: 369: 365: 358: 355: 351: 345: 342: 336: 332: 329: 328: 324: 308: 305: 299: 296: 293: 287: 280: 279: 278: 257: 254: 251: 248: 244: 239: 235: 232: 229: 226: 223: 220: 217: 214: 211: 208: 205: 201: 197: 193: 189: 186: 183: 179: 170: 158: 154: 150: 145: 141: 134: 129: 126: 122: 118: 115: 108: 105: 102: 96: 93: 90: 84: 73: 72: 71: 68: 66: 62: 58: 54: 40: 26: 363: 357: 344: 276: 69: 56: 50: 233:π 227:⁡ 215:π 209:⁡ 190:⁡ 184:− 127:− 119:⁡ 106:− 59:is a non- 395:Category 325:See also 378:  55:, the 337:Notes 376:ISBN 368:doi 224:cos 206:cos 198:0.5 187:exp 135:0.5 130:0.2 116:exp 51:In 397:: 374:. 309:0. 258:20 109:20 384:. 370:: 306:= 303:) 300:0 297:, 294:0 291:( 288:f 255:+ 252:e 249:+ 245:] 240:) 236:y 230:2 221:+ 218:x 212:2 202:( 194:[ 171:] 164:) 159:2 155:y 151:+ 146:2 142:x 138:( 123:[ 103:= 100:) 97:y 94:, 91:x 88:( 85:f

Index



mathematical optimization
convex function
optimization algorithms
Test functions for optimization
A connectionist machine for genetic hillclimbing
doi
10.1093/oso/9780195099713.003.0008
ISBN
978-0-19-509971-3
Category
Test functions for optimization

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