Genetic Algorithm not returning "non-intersecting" routes

Question

So I have used a GA for TSP where the initial population is generated using Nearest Neighbor Method with different starting points. When my rate of mutation is >0, the initial best in the population remains the best when the rate of mutation is 0, the improvement happens but only in short bursts as shown in the following image:

I tried increasing the rate of mutation iteratively but that is not beneficial

here is my code for mutation:

def mutate(route,rate):
    for i in range(len(route)):
        #if (random.uniform(0,1) < rate):
        if (random.uniform(0,1) < rate):
            j=int(random.random()*len(route))
            
            cityA=route[i]
            cityB=route[j]
            
            route[i]=cityB
            route[j]=cityA
    return route 

here is my code for making children:

def make_babies(parent1, parent2):
    child = []
    child_1 = []
    half1_1=[]
    half1_2=[]
    child_2 = []
    half2_1=[]
    half2_2=[]
    
    splicepoint1 = int(random.random() * len(parent1))
    splicepoint2 = int(random.random() * len(parent1))
    
    startsplice = min(splicepoint1, splicepoint2)
    endsplice = max(splicepoint1, splicepoint2)

    for i in range(startsplice, endsplice):
        half1_1.append(parent1[i])
        #print(parent2)
        half2_1.append(parent2[i])
        
    half1_2 = [j for j in parent2 if j not in half1_1]
    half2_2 = [j for j in parent1 if j not in half2_1]

    child_1 = half1_1+half1_2
    child_2 = half2_1+half2_2
    return [child_1,child_2]

Even after this there are criss-crossing edges Please help me

EDIT1:- I have ensured eltism for best routes Here is my fitness function in case here lies an error:

    sum=0
    fitness_sum=0
    fitness=[]
    for i in range(len(sol)):
        fitness_sum=fitness_sum+(1/sol[i][1])**2
    for j in range(len(sol)):
        a=((1/(sol[j][1])**2)/(fitness_sum))
        fitness.append(a)
    return fitness

Answer 1

Your best is bound to improve depending on the size of the candidate population, but not necessarily on each iteration which explains the 'short bursts' (since the best may cross-over to a worse solution, while alternatives exhibit limited improvements).

Also, your mutation function is a cross-over function, as mutation typically introduces a new candidacy within a route's genotype from potentially unexplored candidacy within the phenotype.

Hence, you have 2 cross-over functions, and depending on your selection of candidates to the next iteration, are bound by a local optimum defined in your initial population.

Finally, criss-cross edges are irrelevant since graphs are not constrained to euclidian space, and edges are uni or bi-directional.