Mathematical Problems in Engineering

Research Article

Electromagnetic Problems Solving by Conformal Mapping: A Mathematical Operator for Optimization

Table 9

Relation between vertices, slopes, and prevertices.
Polygon vertices (Figure 15)Slopes 𝛼 𝑛 Prevertices (Genetic Algorithm)
𝑤 1 = − 1 . 9 9 + 3 . 0 0 𝑖 𝛼 1 = 0 . 5 0 0 0 𝑥 1 = 1 . 0 0 0 0 0 0
𝑤 2 = − 1 . 9 9 + 6 . 0 0 𝑖 𝛼 2 = − 0 . 5 0 0 0 𝑥 2 = 1 . 7 6 8 6 4 0
𝑤 3 = − 4 . 0 0 + 6 . 0 0 𝑖 𝛼 3 = − 0 . 5 0 0 0 𝑥 3 = 1 . 8 5 3 6 9 5
𝑤 4 = − 4 . 0 0 + 3 . 0 0 𝑖 𝛼 4 = 0 . 5 0 0 0 𝑥 4 = 1 . 8 5 3 6 9 6
𝑤 5 = − 6 . 0 0 + 3 . 0 0 𝑖 𝛼 5 = − 0 . 5 0 0 0 𝑥 5 = 1 . 8 5 3 7 7 7
𝑤 6 = − 6 . 0 0 + 1 . 9 0 𝑖 𝛼 6 = − 0 . 5 0 0 0 𝑥 6 = 1 . 8 5 4 0 8 2
𝑤 7 = − 1 . 0 0 + 1 . 9 0 𝑖 𝛼 7 = 0 . 6 4 7 6 𝑥 7 = 1 . 8 5 4 1 0 1
𝑤 8 = − 2 . 0 0 + 0 . 0 0 𝑖 𝛼 8 = − 0 . 6 4 7 6 𝑥 8 = 1 . 8 5 5 5 5 5
𝑤 9 = 2 . 0 0 + 0 . 0 0 𝑖 𝛼 9 = − 0 . 6 4 7 6 𝑥 9 = 2 . 1 4 1 7 6 2
𝑤 1 0 = 1 . 0 0 + 1 . 9 0 𝑖 𝛼 1 0 = 0 . 6 4 7 6 𝑥 1 0 = 2 . 1 4 3 2 1 1
𝑤 1 1 = 6 . 0 0 + 1 . 9 0 𝑖 𝛼 1 1 = − 0 . 5 0 0 0 𝑥 1 1 = 2 . 1 4 3 2 3 0
𝑤 1 2 = 6 . 0 0 + 3 . 0 0 𝑖 𝛼 1 2 = − 0 . 5 0 0 0 𝑥 1 2 = 2 . 1 4 3 5 3 5
𝑤 1 3 = 4 . 0 0 + 3 . 0 0 𝑖 𝛼 1 3 = 0 . 5 0 0 0 𝑥 1 3 = 2 . 1 4 3 6 1 6
𝑤 1 4 = 4 . 0 0 + 6 . 0 0 𝑖 𝛼 1 4 = − 0 . 5 0 0 0 𝑥 1 4 = 2 . 1 4 3 6 1 7
𝑤 1 5 = 1 . 9 9 + 6 . 0 0 𝑖 𝛼 1 5 = − 0 . 5 0 0 0 𝑥 1 5 = 2 . 2 2 8 6 9 8
𝑤 1 6 = 1 . 9 9 + 3 . 0 0 𝑖 𝛼 1 6 = 0 . 5 0 0 0 𝑥 1 6 = 2 . 9 9 7 3 1 2