U prikladnij matematici testovi funkciyi dlya optimizaciyi shtuchni landshafti nelinijni funkciyi yaki vikoristovuyut dlya ocinki harakteristik algoritmiv optimizaciyi takih yak shvidkist zbizhnosti tochnist grubist zagalni harakteristiki Nizhche navedeni deyaki funkciyi testuvannya optimizacijnih algoritmiv sho dozvolyayut otrimati uyavlennya pro rizni harakterni situaciyi z yakimi stikayutsya algoritmi optimizaciyi pri virishenni zadach takogo rodu U pershij chastini navedeni funkciyi dlya testuvannya algoritmiv poshuku globalnogo minimumu maksimumu U drugij chastini funkciyi z vidpovidnimi frontami dlya algoritmiv bagatokriterialnoyi optimizaciyi Shtuchni landshafti navedeni dlya testuvannya optimizacijnih algoritmiv vzyati z dekilkoh dzherel div Posilannya Zagalnij viglyad rivnyannya grafik cilovoyi funkciyi mezhi zminnih ob yekta i koordinati globalnogo minimumu navedeni v tablici Zmist 1 Funkciyi dlya algoritmiv poshuku globalnogo minimumu 2 Funkciyi dlya algoritmiv bagatokriterialnoyi optimizaciyi 3 Primitki 4 Posilannya 5 DzherelaFunkciyi dlya algoritmiv poshuku globalnogo minimumu RedaguvatiNazva Risunok Formula Minimum Oblast poshukuAckley s function nbsp f x y 20 exp 0 2 0 5 x 2 y 2 displaystyle f x y 20 exp left 0 2 sqrt 0 5 left x 2 y 2 right right nbsp exp 0 5 cos 2 p x cos 2 p y e 20 displaystyle exp left 0 5 left cos left 2 pi x right cos left 2 pi y right right right e 20 nbsp f 0 0 0 displaystyle f 0 0 0 nbsp 5 x y 5 displaystyle 5 leq x y leq 5 nbsp Sphere function nbsp f x i 1 n x i 2 displaystyle f boldsymbol x sum i 1 n x i 2 nbsp f 0 0 0 displaystyle f 0 dots 0 0 nbsp x i displaystyle infty leq x i leq infty nbsp 1 i n displaystyle 1 leq i leq n nbsp Funkciya Rozenbroka nbsp f x i 1 n 1 100 x i 1 x i 2 2 x i 1 2 displaystyle f boldsymbol x sum i 1 n 1 left 100 left x i 1 x i 2 right 2 left x i 1 right 2 right nbsp Min n 2 f 1 1 0 n 3 f 1 1 1 0 n gt 3 f 1 1 n times 0 displaystyle text Min begin cases n 2 amp rightarrow quad f 1 1 0 n 3 amp rightarrow quad f 1 1 1 0 n gt 3 amp rightarrow quad f left underbrace 1 dots 1 n text times right 0 end cases nbsp x i displaystyle infty leq x i leq infty nbsp 1 i n displaystyle 1 leq i leq n nbsp Beale s function nbsp f x y 1 5 x x y 2 2 25 x x y 2 2 displaystyle f x y left 1 5 x xy right 2 left 2 25 x xy 2 right 2 nbsp 2 625 x x y 3 2 displaystyle left 2 625 x xy 3 right 2 nbsp f 3 0 5 0 displaystyle f 3 0 5 0 nbsp 4 5 x y 4 5 displaystyle 4 5 leq x y leq 4 5 nbsp Goldstein Price function nbsp f x y displaystyle f x y nbsp 1 x y 1 2 19 14 x 3 x 2 14 y 6 x y 3 y 2 displaystyle left 1 left x y 1 right 2 left 19 14x 3x 2 14y 6xy 3y 2 right right nbsp 30 2 x 3 y 2 18 32 x 12 x 2 48 y 36 x y 27 y 2 displaystyle left 30 left 2x 3y right 2 left 18 32x 12x 2 48y 36xy 27y 2 right right nbsp f 0 1 3 displaystyle f 0 1 3 nbsp 2 x y 2 displaystyle 2 leq x y leq 2 nbsp Booth s function nbsp f x y x 2 y 7 2 2 x y 5 2 displaystyle f x y left x 2y 7 right 2 left 2x y 5 right 2 nbsp f 1 3 0 displaystyle f 1 3 0 nbsp 10 x y 10 displaystyle 10 leq x y leq 10 nbsp Bukin function N 6 nbsp f x y 100 y 0 01 x 2 0 01 x 10 displaystyle f x y 100 sqrt left y 0 01x 2 right 0 01 left x 10 right quad nbsp f 10 1 0 displaystyle f 10 1 0 nbsp 15 x 5 displaystyle 15 leq x leq 5 nbsp 3 y 3 displaystyle 3 leq y leq 3 nbsp Matyas function nbsp f x y 0 26 x 2 y 2 0 48 x y displaystyle f x y 0 26 left x 2 y 2 right 0 48xy nbsp f 0 0 0 displaystyle f 0 0 0 nbsp 10 x y 10 displaystyle 10 leq x y leq 10 nbsp Levi function N 13 nbsp f x y sin 2 3 p x x 1 2 1 sin 2 3 p y displaystyle f x y sin 2 left 3 pi x right left x 1 right 2 left 1 sin 2 left 3 pi y right right nbsp y 1 2 1 sin 2 2 p y displaystyle left y 1 right 2 left 1 sin 2 left 2 pi y right right nbsp f 1 1 0 displaystyle f 1 1 0 nbsp 10 x y 10 displaystyle 10 leq x y leq 10 nbsp Three hump camel function nbsp f x y 2 x 2 1 05 x 4 x 6 6 x y y 2 displaystyle f x y 2x 2 1 05x 4 frac x 6 6 xy y 2 nbsp f 0 0 0 displaystyle f 0 0 0 nbsp 5 x y 5 displaystyle 5 leq x y leq 5 nbsp Easom function nbsp f x y cos x cos y displaystyle f x y cos left x right cos left y right nbsp exp x p 2 y p 2 displaystyle exp left left left x pi right 2 left y pi right 2 right right nbsp f p p 1 displaystyle f pi pi 1 nbsp 100 x y 100 displaystyle 100 leq x y leq 100 nbsp Cross in tray function nbsp f x y 0 0001 displaystyle f x y 0 0001 nbsp sin x sin y exp 100 x 2 y 2 p 1 0 1 displaystyle left left sin left x right sin left y right exp left left 100 frac sqrt x 2 y 2 pi right right right 1 right 0 1 nbsp Min f 1 34941 1 34941 2 06261 f 1 34941 1 34941 2 06261 f 1 34941 1 34941 2 06261 f 1 34941 1 34941 2 06261 displaystyle text Min begin cases f left 1 34941 1 34941 right amp 2 06261 f left 1 34941 1 34941 right amp 2 06261 f left 1 34941 1 34941 right amp 2 06261 f left 1 34941 1 34941 right amp 2 06261 end cases nbsp 10 x y 10 displaystyle 10 leq x y leq 10 nbsp Eggholder function nbsp f x y y 47 sin x 2 y 47 displaystyle f x y left y 47 right sin left sqrt left frac x 2 left y 47 right right right nbsp x sin x y 47 displaystyle x sin left sqrt left x left y 47 right right right nbsp f 512 404 2319 959 6407 displaystyle f 512 404 2319 959 6407 nbsp 512 x y 512 displaystyle 512 leq x y leq 512 nbsp Holder table function nbsp f x y sin x cos y exp 1 x 2 y 2 p displaystyle f x y left sin left x right cos left y right exp left left 1 frac sqrt x 2 y 2 pi right right right nbsp Min f 8 05502 9 66459 19 2085 f 8 05502 9 66459 19 2085 f 8 05502 9 66459 19 2085 f 8 05502 9 66459 19 2085 displaystyle text Min begin cases f left 8 05502 9 66459 right amp 19 2085 f left 8 05502 9 66459 right amp 19 2085 f left 8 05502 9 66459 right amp 19 2085 f left 8 05502 9 66459 right amp 19 2085 end cases nbsp 10 x y 10 displaystyle 10 leq x y leq 10 nbsp McCormick function nbsp f x y sin x y x y 2 1 5 x 2 5 y 1 displaystyle f x y sin left x y right left x y right 2 1 5x 2 5y 1 nbsp f 0 54719 1 54719 1 9133 displaystyle f 0 54719 1 54719 1 9133 nbsp 1 5 x 4 displaystyle 1 5 leq x leq 4 nbsp 3 y 4 displaystyle 3 leq y leq 4 nbsp Schaffer function N 2 nbsp f x y 0 5 sin 2 x 2 y 2 0 5 1 0 001 x 2 y 2 2 displaystyle f x y 0 5 frac sin 2 left x 2 y 2 right 0 5 left 1 0 001 left x 2 y 2 right right 2 nbsp f 0 0 0 displaystyle f 0 0 0 nbsp 100 x y 100 displaystyle 100 leq x y leq 100 nbsp Schaffer function N 4 nbsp f x y 0 5 cos 2 sin x 2 y 2 0 5 1 0 001 x 2 y 2 2 displaystyle f x y 0 5 frac cos 2 left sin left left x 2 y 2 right right right 0 5 left 1 0 001 left x 2 y 2 right right 2 nbsp f 0 1 25313 0 292579 displaystyle f 0 1 25313 0 292579 nbsp 100 x y 100 displaystyle 100 leq x y leq 100 nbsp Styblinski Tang function nbsp f x i 1 n x i 4 16 x i 2 5 x i 2 displaystyle f boldsymbol x frac sum i 1 n x i 4 16x i 2 5x i 2 nbsp X 2 903534 2 903534 n times displaystyle X underbrace 2 903534 ldots 2 903534 n text times nbsp 39 16617 n lt f X lt 39 16616 n displaystyle 39 16617n lt f X lt 39 16616n nbsp 5 x i 5 displaystyle 5 leq x i leq 5 nbsp 1 i n displaystyle 1 leq i leq n nbsp Simionescu function 1 nbsp f x y 0 1 x y displaystyle f x y 0 1xy nbsp subjected to x 2 y 2 r T r S cos n arctan x y 2 displaystyle text subjected to x 2 y 2 leq left r T r S cos left n arctan frac x y right right 2 nbsp where r T 1 r S 0 2 and n 8 displaystyle text where r T 1 r S 0 2 text and n 8 nbsp f 0 85586214 0 85586214 0 072625 displaystyle f pm 0 85586214 mp 0 85586214 0 072625 nbsp 1 25 x y 1 25 displaystyle 1 25 leq x y leq 1 25 nbsp Funkciyi dlya algoritmiv bagatokriterialnoyi optimizaciyi RedaguvatiNazva Risunok Formula Minimum Oblast poshukuBinh and Korn function nbsp Minimize f 1 x y 4 x 2 4 y 2 f 2 x y x 5 2 y 5 2 displaystyle text Minimize begin cases f 1 left x y right amp 4x 2 4y 2 f 2 left x y right amp left x 5 right 2 left y 5 right 2 end cases nbsp s t g 1 x y x 5 2 y 2 25 g 2 x y x 8 2 y 3 2 7 7 displaystyle text s t begin cases g 1 left x y right amp left x 5 right 2 y 2 leq 25 g 2 left x y right amp left x 8 right 2 left y 3 right 2 geq 7 7 end cases nbsp 0 x 5 displaystyle 0 leq x leq 5 nbsp 0 y 3 displaystyle 0 leq y leq 3 nbsp Chakong and Haimes function nbsp Minimize f 1 x y 2 x 2 2 y 1 2 f 2 x y 9 x y 1 2 displaystyle text Minimize begin cases f 1 left x y right amp 2 left x 2 right 2 left y 1 right 2 f 2 left x y right amp 9x left y 1 right 2 end cases nbsp s t g 1 x y x 2 y 2 225 g 2 x y x 3 y 10 0 displaystyle text s t begin cases g 1 left x y right amp x 2 y 2 leq 225 g 2 left x y right amp x 3y 10 leq 0 end cases nbsp 20 x y 20 displaystyle 20 leq x y leq 20 nbsp Fonseca and Fleming function nbsp Minimize f 1 x 1 exp i 1 n x i 1 n 2 f 2 x 1 exp i 1 n x i 1 n 2 displaystyle text Minimize begin cases f 1 left boldsymbol x right amp 1 exp left sum i 1 n left x i frac 1 sqrt n right 2 right f 2 left boldsymbol x right amp 1 exp left sum i 1 n left x i frac 1 sqrt n right 2 right end cases nbsp 4 x i 4 displaystyle 4 leq x i leq 4 nbsp 1 i n displaystyle 1 leq i leq n nbsp Test function 4 nbsp Minimize f 1 x y x 2 y f 2 x y 0 5 x y 1 displaystyle text Minimize begin cases f 1 left x y right amp x 2 y f 2 left x y right amp 0 5x y 1 end cases nbsp s t g 1 x y 6 5 x 6 y 0 g 2 x y 7 5 0 5 x y 0 g 3 x y 30 5 x y 0 displaystyle text s t begin cases g 1 left x y right amp 6 5 frac x 6 y geq 0 g 2 left x y right amp 7 5 0 5x y geq 0 g 3 left x y right amp 30 5x y geq 0 end cases nbsp 7 x y 4 displaystyle 7 leq x y leq 4 nbsp Kursawe function nbsp Minimize f 1 x i 1 2 10 exp 0 2 x i 2 x i 1 2 f 2 x i 1 3 x i 0 8 5 sin x i 3 displaystyle text Minimize begin cases f 1 left boldsymbol x right amp sum i 1 2 left 10 exp left 0 2 sqrt x i 2 x i 1 2 right right amp f 2 left boldsymbol x right amp sum i 1 3 left left x i right 0 8 5 sin left x i 3 right right end cases nbsp 5 x i 5 displaystyle 5 leq x i leq 5 nbsp 1 i 3 displaystyle 1 leq i leq 3 nbsp Schaffer function N 1 nbsp Minimize f 1 x x 2 f 2 x x 2 2 displaystyle text Minimize begin cases f 1 left x right amp x 2 f 2 left x right amp left x 2 right 2 end cases nbsp A x A displaystyle A leq x leq A nbsp Values of A displaystyle A nbsp form 10 displaystyle 10 nbsp to 10 5 displaystyle 10 5 nbsp have been used successfully Higher values of A displaystyle A nbsp increase the difficulty of the problem Schaffer function N 2 nbsp Minimize f 1 x x if x 1 x 2 if 1 lt x 3 4 x if 3 lt x 4 x 4 if x gt 4 f 2 x x 5 2 displaystyle text Minimize begin cases f 1 left x right amp begin cases x amp text if x leq 1 x 2 amp text if 1 lt x leq 3 4 x amp text if 3 lt x leq 4 x 4 amp text if x gt 4 end cases f 2 left x right amp left x 5 right 2 end cases nbsp 5 x 10 displaystyle 5 leq x leq 10 nbsp Poloni s two objective function nbsp Minimize f 1 x y 1 A 1 B 1 x y 2 A 2 B 2 x y 2 f 2 x y x 3 2 y 1 2 displaystyle text Minimize begin cases f 1 left x y right amp left 1 left A 1 B 1 left x y right right 2 left A 2 B 2 left x y right right 2 right f 2 left x y right amp left x 3 right 2 left y 1 right 2 end cases nbsp where A 1 0 5 sin 1 2 cos 1 sin 2 1 5 cos 2 A 2 1 5 sin 1 cos 1 2 sin 2 0 5 cos 2 B 1 x y 0 5 sin x 2 cos x sin y 1 5 cos y B 2 x y 1 5 sin x cos x 2 sin y 0 5 cos y displaystyle text where begin cases A 1 amp 0 5 sin left 1 right 2 cos left 1 right sin left 2 right 1 5 cos left 2 right A 2 amp 1 5 sin left 1 right cos left 1 right 2 sin left 2 right 0 5 cos left 2 right B 1 left x y right amp 0 5 sin left x right 2 cos left x right sin left y right 1 5 cos left y right B 2 left x y right amp 1 5 sin left x right cos left x right 2 sin left y right 0 5 cos left y right end cases nbsp p x y p displaystyle pi leq x y leq pi nbsp Zitzler Deb Thiele s function N 1 nbsp Minimize f 1 x x 1 f 2 x g x h f 1 x g x g x 1 9 29 i 2 30 x i h f 1 x g x 1 f 1 x g x displaystyle text Minimize begin cases f 1 left boldsymbol x right amp x 1 f 2 left boldsymbol x right amp g left boldsymbol x right h left f 1 left boldsymbol x right g left boldsymbol x right right g left boldsymbol x right amp 1 frac 9 29 sum i 2 30 x i h left f 1 left boldsymbol x right g left boldsymbol x right right amp 1 sqrt frac f 1 left boldsymbol x right g left boldsymbol x right end cases nbsp 0 x i 1 displaystyle 0 leq x i leq 1 nbsp 1 i 30 displaystyle 1 leq i leq 30 nbsp Zitzler Deb Thiele s function N 2 nbsp Minimize f 1 x x 1 f 2 x g x h f 1 x g x g x 1 9 29 i 2 30 x i h f 1 x g x 1 f 1 x g x 2 displaystyle text Minimize begin cases f 1 left boldsymbol x right amp x 1 f 2 left boldsymbol x right amp g left boldsymbol x right h left f 1 left boldsymbol x right g left boldsymbol x right right g left boldsymbol x right amp 1 frac 9 29 sum i 2 30 x i h left f 1 left boldsymbol x right g left boldsymbol x right right amp 1 left frac f 1 left boldsymbol x right g left boldsymbol x right right 2 end cases nbsp 0 x i 1 displaystyle 0 leq x i leq 1 nbsp 1 i 30 displaystyle 1 leq i leq 30 nbsp Zitzler Deb Thiele s function N 3 nbsp Minimize f 1 x x 1 f 2 x g x h f 1 x g x g x 1 9 29 i 2 30 x i h f 1 x g x 1 f 1 x g x f 1 x g x sin 10 p f 1 x displaystyle text Minimize begin cases f 1 left boldsymbol x right amp x 1 f 2 left boldsymbol x right amp g left boldsymbol x right h left f 1 left boldsymbol x right g left boldsymbol x right right g left boldsymbol x right amp 1 frac 9 29 sum i 2 30 x i h left f 1 left boldsymbol x right g left boldsymbol x right right amp 1 sqrt frac f 1 left boldsymbol x right g left boldsymbol x right left frac f 1 left boldsymbol x right g left boldsymbol x right right sin left 10 pi f 1 left boldsymbol x right right end cases nbsp 0 x i 1 displaystyle 0 leq x i leq 1 nbsp 1 i 30 displaystyle 1 leq i leq 30 nbsp Zitzler Deb Thiele s function N 4 nbsp Minimize f 1 x x 1 f 2 x g x h f 1 x g x g x 91 i 2 10 x i 2 10 cos 4 p x i h f 1 x g x 1 f 1 x g x displaystyle text Minimize begin cases f 1 left boldsymbol x right amp x 1 f 2 left boldsymbol x right amp g left boldsymbol x right h left f 1 left boldsymbol x right g left boldsymbol x right right g left boldsymbol x right amp 91 sum i 2 10 left x i 2 10 cos left 4 pi x i right right h left f 1 left boldsymbol x right g left boldsymbol x right right amp 1 sqrt frac f 1 left boldsymbol x right g left boldsymbol x right end cases nbsp 0 x 1 1 displaystyle 0 leq x 1 leq 1 nbsp 5 x i 5 displaystyle 5 leq x i leq 5 nbsp 2 i 10 displaystyle 2 leq i leq 10 nbsp Zitzler Deb Thiele s function N 6 nbsp Minimize f 1 x 1 exp 4 x 1 sin 6 6 p x 1 f 2 x g x h f 1 x g x g x 1 9 i 2 10 x i 9 0 25 h f 1 x g x 1 f 1 x g x 2 displaystyle text Minimize begin cases f 1 left boldsymbol x right amp 1 exp left 4x 1 right sin 6 left 6 pi x 1 right f 2 left boldsymbol x right amp g left boldsymbol x right h left f 1 left boldsymbol x right g left boldsymbol x right right g left boldsymbol x right amp 1 9 left frac sum i 2 10 x i 9 right 0 25 h left f 1 left boldsymbol x right g left boldsymbol x right right amp 1 left frac f 1 left boldsymbol x right g left boldsymbol x right right 2 end cases nbsp 0 x i 1 displaystyle 0 leq x i leq 1 nbsp 1 i 10 displaystyle 1 leq i leq 10 nbsp Viennet function nbsp Minimize f 1 x y 0 5 x 2 y 2 sin x 2 y 2 f 2 x y 3 x 2 y 4 2 8 x y 1 2 27 15 f 3 x y 1 x 2 y 2 1 1 1 exp x 2 y 2 displaystyle text Minimize begin cases f 1 left x y right amp 0 5 left x 2 y 2 right sin left x 2 y 2 right f 2 left x y right amp frac left 3x 2y 4 right 2 8 frac left x y 1 right 2 27 15 f 3 left x y right amp frac 1 x 2 y 2 1 1 1 exp left left x 2 y 2 right right end cases nbsp 3 x y 3 displaystyle 3 leq x y leq 3 nbsp Osyczka and Kundu function nbsp F 1 x 25 x 1 2 2 x 2 2 2 displaystyle F 1 x 25 left x 1 2 right 2 left x 2 2 right 2 nbsp x 3 1 2 x 4 4 2 x 5 1 2 displaystyle left x 3 1 right 2 left x 4 4 right 2 left x 5 1 right 2 nbsp Minimize f 1 x F 1 x f 2 x i 1 6 x i 2 displaystyle text Minimize begin cases f 1 left boldsymbol x right amp F 1 x f 2 left boldsymbol x right amp sum i 1 6 x i 2 end cases nbsp s t g 1 x x 1 x 2 2 0 g 2 x 6 x 1 x 2 0 g 3 x 2 x 2 x 1 0 g 4 x 2 x 1 3 x 2 0 g 5 x 4 x 3 3 2 x 4 0 g 6 x x 5 3 2 x 6 4 0 displaystyle text s t begin cases g 1 left boldsymbol x right amp x 1 x 2 2 geq 0 g 2 left boldsymbol x right amp 6 x 1 x 2 geq 0 g 3 left boldsymbol x right amp 2 x 2 x 1 geq 0 g 4 left boldsymbol x right amp 2 x 1 3x 2 geq 0 g 5 left boldsymbol x right amp 4 left x 3 3 right 2 x 4 geq 0 g 6 left boldsymbol x right amp left x 5 3 right 2 x 6 4 geq 0 end cases nbsp 0 x 1 x 2 x 6 10 displaystyle 0 leq x 1 x 2 x 6 leq 10 nbsp 1 x 3 x 5 5 displaystyle 1 leq x 3 x 5 leq 5 nbsp 0 x 4 6 displaystyle 0 leq x 4 leq 6 nbsp CTP1 function 2 variables nbsp Minimize f 1 x y x f 2 x y 1 y exp x 1 y displaystyle text Minimize begin cases f 1 left x y right amp x f 2 left x y right amp left 1 y right exp left frac x 1 y right end cases nbsp s t g 1 x y f 2 x y 0 858 exp 0 541 f 1 x y 1 g 1 x y f 2 x y 0 728 exp 0 295 f 1 x y 1 displaystyle text s t begin cases g 1 left x y right amp frac f 2 left x y right 0 858 exp left 0 541f 1 left x y right right geq 1 g 1 left x y right amp frac f 2 left x y right 0 728 exp left 0 295f 1 left x y right right geq 1 end cases nbsp 0 x y 1 displaystyle 0 leq x y leq 1 nbsp Constr Ex problem nbsp Minimize f 1 x y x f 2 x y 1 y x displaystyle text Minimize begin cases f 1 left x y right amp x f 2 left x y right amp frac 1 y x end cases nbsp s t g 1 x y y 9 x 6 g 1 x y y 9 x 1 displaystyle text s t begin cases g 1 left x y right amp y 9x geq 6 g 1 left x y right amp y 9x geq 1 end cases nbsp 0 1 x 1 displaystyle 0 1 leq x leq 1 nbsp 0 y 5 displaystyle 0 leq y leq 5 nbsp Primitki Redaguvati Simionescu P A 2014 Computer Aided Graphing and Simulation Tools for AutoCAD Users vid 1st Boca Raton FL CRC Press ISBN 9 781 48225290 3 Posilannya RedaguvatiOptimization Test Problems angl 3D Function Grapher angl Dzherela RedaguvatiBack Thomas Evolutionary algorithms in theory and practice evolution strategies evolutionary programming genetic algorithms Oxford Oxford University Press 1995 p 328 ISBN 0 19 509971 0 Deb Kalyanmoy 2002 Multiobjective optimization using evolutionary algorithms Repr ed Chichester u a Wiley ISBN 0 471 87339 X Binh T and Korn U MOBES A Multiobjective Evolution Strategy for Constrained Optimization Problems In Proceedings of the Third International Conference on Genetic Algorithms Czech Republic 1997 pp 176 182 Binh T A multiobjective evolutionary algorithm The study cases Technical report Institute for Automation and Communication Barleben Germany 1999 Otrimano z https uk wikipedia org w index php title Testovi funkciyi dlya optimizaciyi amp oldid 33369999
