Table 4: Integer programming optimization test problems.

 Test problem Problem definition Problem 1 [51] FI1(x) = $||x|{|}_{1}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}|{x}_{1}|\text{\hspace{0.17em}}+\text{\hspace{0.17em}}.\text{\hspace{0.17em}}.\text{\hspace{0.17em}}.\text{\hspace{0.17em}}+\text{\hspace{0.17em}}|{x}_{n}|$ Problem 2 [51] FI2(x) = ${x}^{T}x$ = $\left[{x}_{1}\text{\hspace{0.17em}}.\text{\hspace{0.17em}}.\text{\hspace{0.17em}}.\text{\hspace{0.17em}}{x}_{n}\right]$ $\left[\begin{array}{l}{x}_{1}\\ ⋮\\ {x}_{n}\end{array}\right]$ Problem 3 [52] FI3(x) = $\left[15\text{\hspace{0.17em}}27\text{\hspace{0.17em}}36\text{\hspace{0.17em}}18\text{\hspace{0.17em}}12\right]\text{\hspace{0.17em}}x$ + ${x}^{T}$ $x$ Problem 4 [52] FI4(x) = ${\left(9{x}_{1}^{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}2{x}_{2}^{2}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}11\right)}^{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\left(3{x}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}4{x}_{2}^{2}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}7\right)}^{2}$ Problem 5 [52] FI5(x) = ${\left({x}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}10{x}_{2}\right)}^{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}5\text{\hspace{0.17em}}{\left({x}_{3\text{\hspace{0.17em}}}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{x}_{4}\right)}^{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\left({x}_{2}\text{\hspace{0.17em}}-2{x}_{3}\right)}^{4}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}10\text{\hspace{0.17em}}{\left({x}_{1}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}{x}_{4}\right)}^{4}$ Problem 6 [53] FI6(x) = $2{x}_{1}^{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}3{x}_{2}^{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}4{x}_{1}{x}_{2}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}6{x}_{1}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}3{x}_{2}$ Problem 7 [52] FI7(x) = $-3803.84\text{\hspace{0.17em}}-\text{\hspace{0.17em}}138.08{x}_{1}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}232.92{x}_{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}123.08{x}_{1}^{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}203.64{x}_{2}^{2}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}182.25{x}_{1}{x}_{2}$