Crossover operator for permutations

Question

i\'m trying to solve the problem of crossover in genetic algorithm on my permutations. Let\'s say I have two permutations of 20 integers. I want to crossover them to get two

Answer 1

According to my research and implementations of genetic operators. Many types of crossover operators exist for the order coding (i.e. repetition of genes not allowed, like in TSP). In general, I like to think that there are two main families:

The ERX-family

A list of neighborhood is used to store the neighbors of each node in both parents. Then, The child is generated using only the list. ERX is known to be more respectful and alleles transmitting, which basically means that the links between genes are not likely to be broken.

Examples of ERX-like operators include: Edge Recombination (ERX), Edge-2, Edge-3, Edge-4, and Generalized Partition Crossover (GPX).

OX-like crossovers

Two crossover points are chosen. Then, the genes between the points are swapped between the two parents. Since repetitions are not allowed, each crossover proposes a technique to avoid/eliminate repetitions. These crossover operators are more disruptive than ERX.

Example of OX-like crossovers: Order crossover (OX), Maximal Preservative Crossover (MPX), and Partial-Mapped Crossover (PMX).

The first family (ERX) performs better in plain genetic algorithms. While the second family is more suited in a hybrid genetic algorithm or memetic algorithm (use of local search). This paper explains it in details.