Journal of Applied Mathematics

Research Article

A Fuzzy Genetic Algorithm Based on Binary Encoding for Solving Multidimensional Knapsack Problems

Table 2

Test functions (source: [22]).
Test FunctionConstraints
𝑓 1 ( 𝑥 ) = { 1 + ( 𝑥 1 + 𝑥 2 + 1 ) 2 ⋅ ( 1 9 − 1 4 𝑥 1 + 3 𝑥 2 1 − 1 4 𝑥 2 + 6 𝑥 1 𝑥 2 + 3 𝑥 2 2 ) } ⋅
{ 3 0 + ( 2 𝑥 1 − 3 𝑥 2 ) 2 ⋅ ( 1 8 − 3 2 𝑥 1 + 1 2 𝑥 2 1 + 4 8 𝑥 2 − 3 6 𝑥 1 𝑥 2 + 2 7 𝑥 2 2 ) } 		− 1 0 ≤ 𝑥 𝑖 ≤ 1 0
𝑓 2 ( 𝑥 ) = ( 4 − 2 . 1 𝑥 2 1 + 𝑥 4 1 / 3 ) 𝑥 2 1 + 𝑥 1 𝑥 2 + ( − 4 + 4 𝑥 2 2 ) 𝑥 2 2 − 3 ≤ 𝑥 1 ≤ 3
− 2 ≤ 𝑥 2 ≤ 2
𝑓 3 ∑ ( 𝑥 ) = { 5 𝑖 = 1 𝑖 c o s ( ( 𝑖 + 1 ) 𝑥 1 ∑ + 𝑖 ) } ⋅ { 5 𝑖 = 1 𝑖 c o s ( ( 𝑖 + 1 ) 𝑥 2 + 𝑖 ) } − 1 0 ≤ 𝑥 𝑖 ≤ 1 0
𝑓 4 ( 𝑥 ) = ( 𝑥 2 − ( 5 . 1 / 4 𝜋 2 ) 𝑥 2 1 + ( 5 / 𝜋 ) 𝑥 1 − 6 ) 2 + 1 0 ( 1 − 1 / 8 𝜋 ) c o s ( 𝑥 1 ) + 1 0 − 5 ≤ 𝑥 1 ≤ 1 0
0 ≤ 𝑥 2 ≤ 1 5