%!PS-Adobe-3.0%%Title: Untitled Document%%Creator: Windows NT 3.5%%CreationDate: 0:44 5/15/1995%%Pages: (atend)%%BoundingBox: 17 22 577 819%%EndComments%%BeginProcSet: NTPSMar94% Copyright (c) 1991 - 1994 Microsoft Corporation/NTPSMar94 100 dict dup begin/bd{bind def}bind def/ld{load def}bd/ed{exch def}bd/a/currentpoint ld/c{curveto}bd/d/dup ld/e/eofill ld/f/fill ld/tr/translate ld/g/setgray ld/gr/grestore ld/gs/gsave ld/j/setlinejoin ld/L{lineto}bd/M{moveto}bd/n/newpath ld/cp/closepath ld/rlt/rlineto ld/rm/rmoveto ld/sl/setlinewidth ld/sd/setdash ld/r/setrgbcolor ld/s/stroke ld/t/show ld/aw/awidthshow ld/im/imagemask ld/SF{findfont exch scalefont setfont}bd/SM{cmtx setmatrix}bd/MF{findfont exch makefont setfont}bd/CM{/cmtx matrix currentmatrix def}bd/B {M exch dup 0 rlt exch 0 exch rlt neg 0 rlt} bd/CB {B cp eoclip} bd/h{/cbstr ed/lenstr ed/str ed lenstr str stringwidth pop sub cbstr div 0 str ashow}bd/v{{pop pop 3 -1 roll add M a} exch kshow pop pop}bd/H{{pop pop M d 0 rm a} exch kshow pop pop pop}bd/V{{pop pop M d 0 2 1 roll rm a}exch kshow pop pop pop}bd/EA {1 index 0 /G0 put 4 string 1 1 4 -1 roll {3 copy neg exch cvs dup 0 71 put cvn 3 -1 roll exch put} for pop} bd%%EndProcSet end def%%EndProlog%%BeginSetupmark {%%BeginFeature: *PageSize A4a4%%EndFeature} stopped cleartomark/#copies 1 def%%EndSetupNTPSMar94 begin%%Page: 1 1/PageSV save def17 819 translate 72 300 div dup neg scale0 0 transform .25 add round .25 sub exch .25 add round .25 sub exch itransform translate[125 0 0 -125 0 0] /Times-Roman MF470 574 M(Genetic Algorithm Toolbox) 1400 25 hn1398 5 470 589 Bf799 774 M(Test Functions) 742 14 hn741 5 799 789 Bf[50 0 0 -50 0 0] /Times-Roman MF987 992 M(Hartmut Pohlheim) 365 16 h576 1092 M(Department of Automatic Control and Systems Engineering) 1188 55 h947 1192 M(University of Sheffield) 446 23 h[67 0 0 -67 0 0] /Times-Bold MF284 1468 M(Table of Contents) 512 17 h[50 0 0 -50 0 0] /Times-Roman MF284 1596 M(1. Introduction) 299 15 h585 1596 M(................................) 416 32 h1001 1596 M(................................) 416 32 h1417 1596 M(................................) 416 32 h1833 1596 M(...............) 195 15 h2031 1596 M(3)t284 1671 M(2. Parametric Optimization) 536 26 h832 1671 M(................................) 416 32 h1248 1671 M(................................) 416 32 h1664 1671 M(............................) 364 28 h2031 1671 M(4)t402 1746 M(2.1. De Jong's function 1) 495 25 h897 1746 M(................................) 416 32 h1313 1746 M(................................) 416 32 h1729 1746 M(.......................) 299 23 h2031 1746 M(4)t402 1821 M(2.2. Axis parallel hyper-ellipsoid) 642 34 h1053 1821 M(................................) 416 32 h1469 1821 M(................................) 416 32 h1885 1821 M(...........) 143 11 h2031 1821 M(4)t402 1896 M(2.3. Rotated hyper-ellipsoid) 553 28 h962 1896 M(................................) 416 32 h1378 1896 M(................................) 416 32 h1794 1896 M(..................) 234 18 h2031 1896 M(4)t402 1971 M(2.4. Rosenbrock's valley \(De Jong's function 2\)) 935 47 h1339 1971 M(................................) 416 32 h1755 1971 M(.....................) 273 21 h2031 1971 M(4)t402 2046 M(2.5. Rastrigin's function 6) 509 27 h923 2046 M(................................) 416 32 h1339 2046 M(................................) 416 32 h1755 2046 M(.....................) 273 21 h2031 2046 M(5)t402 2121 M(2.6. Schwefel's function 7) 511 26 h923 2121 M(................................) 416 32 h1339 2121 M(................................) 416 32 h1755 2121 M(.....................) 273 21 h2031 2121 M(5)t402 2196 M(2.7. Griewangk's function 8) 549 27 h962 2196 M(................................) 416 32 h1378 2196 M(................................) 416 32 h1794 2196 M(..................) 234 18 h2031 2196 M(5)t402 2271 M(2.8. Sum of different Powers \(function 9\)) 822 41 h1235 2271 M(................................) 416 32 h1651 2271 M(.............................) 377 29 h2031 2271 M(6)t284 2346 M(3. Dynamic optimization) 488 23 h780 2346 M(................................) 416 32 h1196 2346 M(................................) 416 32 h1612 2346 M(................................) 416 32 h2031 2346 M(7)t402 2421 M(3.1. Double integrator) 442 22 h845 2421 M(................................) 416 32 h1261 2421 M(................................) 416 32 h1677 2421 M(...........................) 351 27 h2031 2421 M(7)t402 2496 M(3.2. Linear-quadratic system) 566 28 h975 2496 M(................................) 416 32 h1391 2496 M(................................) 416 32 h1807 2496 M(.................) 221 17 h2031 2496 M(8)t402 2571 M(3.3. Harvest system) 392 19 h806 2571 M(................................) 416 32 h1222 2571 M(................................) 416 32 h1638 2571 M(............................) 364 28 h2006 2571 M(10) 50 2 h402 2646 M(3.4. Push-cart system) 426 21 h832 2646 M(................................) 416 32 h1248 2646 M(................................) 416 32 h1664 2646 M(..........................) 338 26 h2006 2646 M(11) 50 2 h284 2721 M(4. References) 269 13 h559 2721 M(................................) 416 32 h975 2721 M(................................) 416 32 h1391 2721 M(................................) 416 32 h1807 2721 M(...............) 195 15 h2006 2721 M(12) 50 2 hPageSV restoreshowpage%%Page: 2 2/PageSV save def17 819 translate 72 300 div dup neg scale0 0 transform .25 add round .25 sub exch .25 add round .25 sub exch itransform translate[38 0 0 -38 0 0] /Times-Roman MF284 152 M(1. Introduction) 224 15 h1954 152 M(Page ) 83 5 h2037 152 M(2)tn1783 2 278 165 Bf284 3156 M(Genetic Algorithm Toolbox) 420 25 h1831 3156 M(Test Functions) 225 14 hn1783 2 278 3070 Bf[67 0 0 -67 0 0] /Times-Bold MF284 368 M(1. Introduction) 433 15 h[50 0 0 -50 0 0] /Times-Roman MF284 546 M(This document describes a number of test functions implemented for use with the) 1772 79 h284 621 M(Genetic Algorithm Toolbox for ) 647 30 h931 621 M(M)t[40 0 0 -40 0 0] /Times-Roman MF975 621 M(ATLAB) 130 5 h[50 0 0 -50 0 0] /Times-Roman MF1105 621 M(. These functions are drawn from the literature) 951 47 h284 696 M(on genetic algorithms, evolutionary strategies and global optimization. The first Section) 1772 89 h284 771 M(describes a set of common parametric test problems implemented as ) 1431 66 h1715 771 M(M)t[40 0 0 -40 0 0] /Times-Roman MF1759 771 M(ATLAB) 130 5 h[50 0 0 -50 0 0] /Times-Roman MF1889 771 M( m-files.) 167 9 h284 846 M(The second Section presents a number of dynamic optimization problems, implemented) 1772 82 h284 921 M(in ) 49 3 h333 921 M(S)t[40 0 0 -40 0 0] /Times-Roman MF361 921 M(IMULINK) 171 7 h[50 0 0 -50 0 0] /Times-Roman MF532 921 M(, as s-files and m-files as appropriate.) 735 40 hn5 5 257 1008 Bfn5 5 257 1008 Bfn195 5 263 1008 Bfn5 5 459 1008 Bfn466 5 465 1008 Bfn5 5 932 1008 Bfn1114 5 938 1008 Bfn5 5 2053 1008 Bfn5 5 2053 1008 Bfn5 74 257 1014 Bfn2 74 459 1014 Bfn2 74 932 1014 Bfn5 74 2053 1014 Bf305 1077 M(No.) 76 3 h557 1077 M(function name) 281 13 h1385 1077 M(description) 219 11 hn5 5 257 1089 Bfn195 5 263 1089 Bfn5 5 459 1089 Bfn466 5 465 1089 Bfn5 5 932 1089 Bfn1114 5 938 1089 Bfn5 5 2053 1089 Bfn5 74 257 1095 Bfn2 74 459 1095 Bfn2 74 932 1095 Bfn5 74 2053 1095 Bf377 1158 M(1)t[50 0 0 -50 0 0] /Courier MF485 1156 M(objfun1) 210 7 h[50 0 0 -50 0 0] /Times-Roman MF957 1158 M(De Jong's function 1) 406 20 hn5 2 257 1170 Bfn195 2 263 1170 Bfn2 2 459 1170 Bfn469 2 462 1170 Bfn2 2 932 1170 Bfn1117 2 935 1170 Bfn5 2 2053 1170 Bfn5 74 257 1173 Bfn2 74 459 1173 Bfn2 74 932 1173 Bfn5 74 2053 1173 Bf377 1236 M(2)t[50 0 0 -50 0 0] /Courier MF485 1234 M(objfun1a) 240 8 h[50 0 0 -50 0 0] /Times-Roman MF957 1236 M(axis parallel hyper-ellipsoid) 540 29 hn5 2 257 1248 Bfn195 2 263 1248 Bfn2 2 459 1248 Bfn469 2 462 1248 Bfn2 2 932 1248 Bfn1117 2 935 1248 Bfn5 2 2053 1248 Bfn5 74 257 1251 Bfn2 74 459 1251 Bfn2 74 932 1251 Bfn5 74 2053 1251 Bf377 1314 M(3)t[50 0 0 -50 0 0] /Courier MF485 1312 M(objfun1b) 240 8 h[50 0 0 -50 0 0] /Times-Roman MF957 1314 M(rotated hyper-ellipsoid) 448 23 hn5 2 257 1326 Bfn195 2 263 1326 Bfn2 2 459 1326 Bfn469 2 462 1326 Bfn2 2 932 1326 Bfn1117 2 935 1326 Bfn5 2 2053 1326 Bfn5 74 257 1329 Bfn2 74 459 1329 Bfn2 74 932 1329 Bfn5 74 2053 1329 Bf377 1392 M(4)t[50 0 0 -50 0 0] /Courier MF485 1390 M(objfun2) 210 7 h[50 0 0 -50 0 0] /Times-Roman MF957 1392 M(Rosenbrock's valley \(banana function\)) 754 37 hn5 2 257 1404 Bfn195 2 263 1404 Bfn2 2 459 1404 Bfn469 2 462 1404 Bfn2 2 932 1404 Bfn1117 2 935 1404 Bfn5 2 2053 1404 Bfn5 74 257 1407 Bfn2 74 459 1407 Bfn2 74 932 1407 Bfn5 74 2053 1407 Bf377 1470 M(5)t[50 0 0 -50 0 0] /Courier MF485 1468 M(objfun6) 210 7 h[50 0 0 -50 0 0] /Times-Roman MF957 1470 M(Rastrigins's function) 401 21 hn5 2 257 1482 Bfn195 2 263 1482 Bfn2 2 459 1482 Bfn469 2 462 1482 Bfn2 2 932 1482 Bfn1117 2 935 1482 Bf