A Cuckoo Search Algorithm for Multimodal Optimization

Table 3

Test functions used in the experimental study.

𝑓(𝑥)(𝑥={𝑥1,𝑥2})	𝑆	NO	Graph
𝑓𝐁𝐢𝐫𝐝1(𝐱)=sin(𝑥1)⋅𝑒^(1−cos(𝑥2))2+cos𝑥2⋅𝑒^(1−sin(𝑥1))2+(𝑥1−𝑥2)^2	[−2𝜋,2𝜋]	3
𝑓𝐂𝐫𝐨𝐬𝐬𝐢𝐧𝐭𝐫𝐚𝐲2(𝐱)=−0.0001⋅sin𝑥1⋅sin𝑥2⋅𝑒^|100−(𝑥12−𝑥22/𝜋)|+1^0.1	[−10,10]	12
𝑓𝐃𝐞𝐉𝐨𝐧𝐠𝐬𝟓3(𝐱)=0.002+∑^22𝑖=−2∑𝑗=−25(𝑖+1)+𝑗+3+𝑥1−16𝑗^6+𝑥2−16𝑖^6−1−1	[−40,40]	25
𝑓𝐄𝐠𝐠𝐡𝐨𝐥𝐝𝐞𝐫4(𝐱)=−𝑥2+47sin𝑥2+𝑥12+47−𝑥1sin𝑥1+𝑥22+47	[−512,512]	7
𝑓𝐕𝐢𝐧𝐜𝐞𝐧𝐭5(𝐱)=−∑^𝑛𝑖=1sin10⋅log𝑥𝑖	[0.25,10]	36
𝑓𝐑𝐨𝐨𝐭𝐬6(𝐱)=−1+(𝑥1+𝑥2𝑖)^6−1^−1	[−2,2]	6
𝑓𝐇𝐢𝐥𝐥𝐲7(𝐱)=10𝑒^−(|𝑥1|/50)61−cos100^3/4𝜋𝑥1^3/4+𝑒^−(|𝑥2|/250)61−cos100^3/4𝜋𝑥2^3/4+2𝑒^−((𝑏−𝑥1)2+(𝑏−𝑥2)2)/50; with𝑏=(5/6)⋅100^3/44/3	[−100,100]	48
𝑓𝐑𝐚𝐬𝐭𝐫𝐢𝐠𝐢𝐧8(𝐱)=∑^𝑛𝑖=1𝑥𝑖^2−10cos2𝜋𝑥𝑖	[−5.12,5.12]	25
𝑓𝐇𝐢𝐦𝐦𝐞𝐦𝐥𝐛𝐥𝐚𝐮9(𝐱)=−𝑥1^2+𝑥2−11^2−(𝑥1+𝑥2^2−7)^2	[−6,6]	5
𝑓𝐅𝐨𝐱𝐡𝐨𝐥𝐞𝐬10(𝐱)=−∑^30∑𝑖=1^𝑛𝑗=1𝑥𝑗−𝑎𝑖𝑗^2+𝑐𝑗^−1	[0,10]	8
𝑓𝐆𝐮𝐢𝐜𝐡𝐢_𝐟𝟒11(𝐱)=−𝑥1sin4𝜋𝑥1−𝑥2sin4𝜋𝑥2+𝜋	[−2,2]	12
𝑓𝐇𝐨𝐥𝐝𝐞𝐫𝐓𝐚𝐛𝐥𝐞12(𝐱)=−sin𝑥1cos𝑥2𝑒^|1−(𝑥12+𝑥22/𝜋)|	[−10,10]	12
𝑓𝐑𝐚𝐬𝐭𝐫𝐢𝐠𝐮𝐢𝐧_𝟒𝟗𝐦13(𝐱)=∑^𝑛𝑖=1𝑥𝑖^2−18cos2𝜋𝑥𝑖	[−1,1]	13
𝑓𝐒𝐜𝐡𝐰𝐞𝐟𝐞𝐥14(𝐱)=418.9829⋅𝑛+∑^𝑛𝑖=1−𝑥𝑖sin𝑥𝑖	[−500,500]	8