Binary or real-valued crossover and mutation, when applied naively to permutations, may produce duplicate or missing elements, such that the produced permutation is invalid. Specifically, a valid permutation must satisfy . This preserves the uniqueness of all elements.
Crossover
- Partially Matched Crossover
- Order Crossover: Preserves relative order
- Cycle Crossover: Preserves positions via cycles
- Edge Recombination Crossover: Preserves adjacency edges (good for TSP)
Mutation
For permutation mutation, we usually just swap two positions. This preserves permutation feasibility and injects diversity.