Mathematical Problems in Engineering

Research Article

Genetic Algorithm for Combinatorial Path Planning: The Subtour Problem

Figure 13

In this example the effects of the application of the 2-opt method are illustrated. In (a) chromosome 𝐬 2 = ( 𝑎 , 𝑡 1 , 𝑡 2 , 𝑡 3 , 𝑡 4 , 𝑡 5 , 𝑡 6 , 𝑡 7 ) is shown. Since edge ( 𝑡 1 , 𝑡 2 ) crosses ( 𝑡 5 , 𝑡 6 ) , (6.1) is satisfied and (b) shows chromosome 𝐬 2 = ( 𝑎 , 𝑡 1 , 𝑡 5 , 𝑡 4 , 𝑡 3 , 𝑡 2 , 𝑡 6 , 𝑡 7 ) after edges ( 𝑡 1 , 𝑡 5 ) and ( 𝑡 2 , 𝑡 6 ) have been replaced by edges ( 𝑡 1 , 𝑡 2 ) and ( 𝑡 5 , 𝑡 6 ) , respectively.
483643.fig.0013a
(a) Before the application of the 2-opt method
483643.fig.0013b
(b) After the application of the 2-opt method