A random search strategy for function optimization

Random seatlchmethods have been used for sometime either as xnetbds oflocating:functionxnhimaor 83 methodsof locating5&arting pointsfor other o@mization algorithms[l]. Thm random methods offer certain advantages: they can work if the function is discofitinuous or has discontinuous detivativ~;tSleycanbeusedto~da$~miniarrumrathertbanloca~ they wiU not be confused by difficult s&aces; and they can be used to locate s&Ming points for other te&@ues 121.On the other hark&they are not very efficient in many &cums&nces and do not take advantage of any useful featuresthe scion may have. However, they may be very useful in a new extent axon where littIe may be known about the axon to be optimized. They may be boy useful in identiffi~ ~ten~y ~~~ models Whenseveral choices are atile. The method suggested here proposes an ~p~vement on the random search method whkh is easy to implement and can give an idea of the feat~~ of &e fu,~ctionbig examit&. The author has fo-undthe method to be very useM in practice and has used it to solve problems which see are not intractable otherwise. As noted above, random search

. For an initial examination

possible

*wing other optimization

r. Step 2. Use a random number generatorto in the range xJ~wC1.

.nx

have been stod in eter thmtoseeifthe

-I

3

0.575 - 0.522

are very dosetogether, indicating

the duster centers.

that

a

m+kf+cli=f(t).

k = 0.5; vdnesi of f(t) were

3

pn c

P

m

2

m

0.

0.

0.876

0.880 0.046

f

3

8.084

0.533

0.828 0.007 0.164

0. 0.124 0.832

112

0.858

0.826

0.880

E

0.693' 1.938

0.004 1.425

0.189 2.170

m f

seen in the next example, however, this may not be an overwhelming tion in an actual exp&mental situation. This problem required ap1 hour of computer time for 10,000 random points.

will consider the application of the above ental dat* The experiment was an attempt to to impact, and the above equation was model. While the random search technique time, other methods failed completely. For PAR[5] failed to converge for all starting points find only positive values of the parameters. In ~~~~~t~ option t~~iques failed to find feeder-bead s~p~~~ method timates, but the r~dom search method initiaI s~~lex. The final results for one are shown in Table 4. s b&?&nfoz8Jnd for m been found for c. The results also tive to values of k or se resuits certainly be used in other

hS

1 2

3 4 5

L. E. !!hles, hdmduction to Non-km Statistical So-e,

Univ. Of CaliforniaPress,Berkeley,1983, pp. 325-326.