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Table 3 Integer programming optimization testproblems

From: A hybrid cuckoo search algorithm with Nelder Mead method for solving global optimization problems

Test problem

Problem definition

Problem 1 (Rudolph 1994)

\(FI _{1}(x)=\Vert x\Vert _1=|x_1|+\cdots +|x_n|\)

Problem 2 (Rudolph 1994)

\(FI _{2}(x)=x^Tx= \left[ \begin{array}{ccc} x_1&\ldots&x_n\end{array}\right] \left[ \begin{array}{c} x_1\\ \vdots \\ x_n\end{array}\right]\)

Problem 3 (GlankwahmdeeL et al. 1979)

\(FI _{3}(x)= \left[ \begin{array}{ccccc} 15&\quad 27&\quad 36&\quad 18&\quad 12 \end{array}\right] x +x^T \left[ \begin{array}{ccccc} 35&{}\quad -20&{}\quad -10&{}\quad 32&{}\quad -10\\ -20&{}\quad 40&{}\quad -6&{}\quad -31&{}\quad 32\\ -10&{}\quad -6&{}\quad 11&{}\quad -6&{}\quad -10\\ 32&{}\quad -31&{}\quad -6&{}\quad 38&{}\quad -20\\ -10&{}\quad 32&{}\quad -10&{}\quad -20&{}\quad 31\\ \end{array}\right] x\)

Problem 4 (GlankwahmdeeL et al. 1979)

\(FI _{4}(x)=(9x_1^2+2x_2^2-11)^2+(3x_1+4x_2^2-7)^2\)

Problem 5 (GlankwahmdeeL et al. 1979)

\(FI _{5}(x)=(x_1+10x_2)^2+5(x_3-x_4)^2+(x_2-2x_3)^4+10(x_1-x_4)^4\)

Problem 6 (Rao 1994)

\(FI _{6}(x)=2x_1^2+3x_2^2+4x_1x_2-6x_1-3x_2\)

Problem 7 (GlankwahmdeeL et al. 1979)

\(FI _{7}(x)=-3803.84-138.08x_1-232.92x_2+123.08x_1^2+203.64x_2^2 + 182.25x_1x_2\)