From: A hybrid cuckoo search algorithm with Nelder Mead method for solving global optimization problems
Test problem | Problem defination |
---|---|
Problem 1 (Yang 2010b) | \(FM _{1}(x)=\text {max}\;{f_i(x)},\; i=1,2,3,\) |
\(f_1(x)=x_1^2+x_2^4,\) | |
\(f_2(x)=(2-x1)^2+(2-x_2)^2,\) | |
\(f_3(x)=2exp(-x_1+x_2)\) | |
Problem 2 (Yang 2010b) | \(FM _{2}(x)=\text {max}\;{f_i(x)}, \;i=1,2,3,\) |
\(f_1(x)=x_1^4+x_2^2\) | |
\(f_2(x)=(2-x1)^2+(2-x_2)^2,\) | |
\(f_3(x)=2exp(-x_1+x_2)\) | |
Problem 3 (Yang 2010B) | \(FM _{3}(x)=x_1^2+x_2^2+2x_3^2+x_4^2-5x_1-5x_2-21x_3+7x_4,\) |
\(g_2(x)=-x_1^2-x_2^2-x_3^3-x_4^2-x_1+x_2-x_3+x_4+8,\) | |
\(g_3(x)=-x_1^2-2x_2^2-x_3^2-2x_4+x_1+x_4+10,\) | |
\(g_4(x)=-x_1^2-x_2^2-x_3^2-2x_1+x_2+x_4+5\) | |
Problem 4 (Yang 2010B) | \(FM _{4}(x)=\text {max}\;{f_i(x)}\;i=1,\ldots ,5\) |
\(f_{1}(x)=(x_1-10)^2+5(x_2-12)^2+x_3^4+3(x_4-11)^2 +10x_5^6+7x_6^2+x_7^4-4x_6x_7-10x_6-8x_7,\) | |
\(f_2(x)=f_1(x)+10(2x_1^2+3x_2^4+x_3+4x_4^2+5x_5-127),\) | |
\(f_3(x)=f_1(x)+10(7x_1+3x_2+10x_3^2+x_4-x_5-282),\) | |
\(f_4(x)=f_1(x)+10(23x_1+x_2^2+6x_6^2-8x_7-196),\) | |
\(f_5(x)=f_1(x)+10(4x_1^2+x_2^2-3x_1x_2+2x_3^2+5x_6-11x_7\) | |
Problem 5 (Schwefel 1995) | \(FM _{5}(x)=\text {max}\;{f_i(x)},\;i=1,2,\) |
\(f_1(x)=|x_1+2x_2-7|\), | |
\(f_2(x)=|2x_1+x_2-5|\) | |
Problem 6 (Schwefel 1995) | \(FM _{6}(x)=\text {max}\;{f_i(x)},\) |
\(f_i(x)=|x_i|,\;i= 1,\ldots ,10\) | |
Problem 7 (Lukšan and Vlcek 2000) | \(FM _{7}(x)= \text {max}\;{f_i(x)},\;i=1,2,\) |
\(f_1(x)=(x_1-\sqrt{(x_1^2+x_2^2)}cos\sqrt{x_1^2+x_2^2})^2+0.005(x_1^2+x_2^2)^2,\) | |
\(f_2(x)=(x_2-\sqrt{(x_1^2+x_2^2)}sin\sqrt{x_1^2+x_2^2})^2+0.005(x_1^2+x_2^2)^2\) | |
Problem 8 (Lukšan and Vlcek 2000) | \(FM _{8}(x)= \text {max}\;{f_i(x)},\;i=1,\ldots ,4,\) |
\(f_1(x)=(x_1-(x_4+1)^4)^2+(x_2-(x_1-(x_4+1)^4)^4)^2 +2x_3^2+x_4^2-5(x_1-(x_4+1)^4)-5(x_2-(x1-(x_4+1)^4)^4)-21x_3+7x_4,\) | |
\(f_2(x)=f_1(x)+10[(x_1-(x_4+1)^4)^2+(x_2-(x_1-(x_4+1)^4)^4)^2 +x_3^2+x_4^2+(x_1-(x_4+1)^4)-(x_2-(x_1-(x_4+1)^4)^4)+x_3-x_4-8],\) | |
\(f_3(x)=f_1(x)+10[(x_1-(x_4+1)^4)^2+2(x_2-(x_1 -(x_4+1)^4)^4)^2+x_3^2+2x_4^2-(x_1-(x_4+1)^4)-x_4-10]\) | |
\(f_4(x)=f_1(x)+10[(x_1-(x_4+1)^4)^2+(x_2-(x_1 -(x_4+1)^4)^4)^2+x_3^2+2(x_1-(x_4+1)^4)-(x_2-(x_1-(x_4+1)^4)^4)-x_4-5]\) | |
Problem 9 (Lukšan and Vlcek 2000) | \(FM _{9}(x)= \text {max}\;{f_i(x)},\;i=1,\ldots ,5,\) |
\(f_1(x)=(x_1-10)^2+5(x_2-12)^2+x_3^4+3(x_4-11)^2+10x_5^6+7x_6^2+x_7^4-4x_6x_7-10x_6-8x_7\), | |
\(f_2(x)=-2x_1^2-2x_3^4-x_3-4x_4^2-5x_5+127\), | |
\(f_3(x)=-7x_1-3x_2-10x_3^2-x_4+x_5+282\), | |
\(f_4(x)=-23x_1-x_2^2-6x_6^2+8x_7+196\), | |
\(f_5(x)=-4x_1^2-x_2^2+3x_1x_2-2x_3^2-5x_6+11x_7\) | |
Problem 10 (Lukšan and Vlcek 2000) | \(FM _{10}(x)=\text {max}\;{|f_i(x)|}, \;i=1,\ldots ,21,\) |
\(f_i(x)=x_1exp(x_3t_i)+x_2exp(x_4t_i)-\frac{1}{1+t_i},\) | |
\(t_i=-0.5+\frac{i-1}{20}\) |