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
38:
24:
286:
79:
362:
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
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.