algorithm - How to deal with crossover when sequence matters? -

how 1 go crossing on 2 parents when children must have particular ordering?

for example, when applying genetic algorithms travelling salesman problem on fixed graph of vertices / edges, must contend fact not vertices can travel other vertices. makes crossover more difficult because unlike tsp in vertices may travel other vertices, when crossover performed must done @ point produces legal path. alternative crossover anyway , reject illegal paths, risk great computational expensive , few no legal paths.

i've read permutation crossover i'm not entirely sure how solves issue. can point me in right direction or advise?

ordering should, far possible, not constraint in genetic programming. maybe should contemplate pick format solutions. example, in tsp, consider codon a->b.

instead of meaning 'take edge b', consider 'take shortest path b'. way, solutions feasible. have pre-compute shortest path matrix pre-processing.

now, not guarantee candidates feasible solutions after crossover. crossover should tuned in order guarantee solution still feasible. example, tsp, consider sequences :

1 : b c d e f g h

2 : d e g c b f h

choose pivot randomly (e in our example). leads following sequences completed :

1' : b c d e . . .

2' : d e . . . . .

all vertices have visited in order have valid solution. in 1', f, g , h have visited. order them in sequence 2. in 2', g, c, b, f , h re-ordered in 1 :

1' : b c d e g f h

2' : d e b c f g h

hope helps.