The natural crossover for the 2D Euclidean TSP

For the traveling salesman problem various search algorithms have been suggested for decades. In the field of genetic algorithms, many genetic operators have been introduced for the problem. Most genetic encoding schemes have some restrictions that cause more-or-less loss of information contained in problem instances. We suggest a new encoding/crossover pair which pursues minimal information loss in chromosomal encoding and minimal restriction in recombination for the 2D Euclidean traveling salesman problem. The most notable feature of the suggested crossover is that it is based on a totally new concept of encoding. We also prove the theoretical validity of the new crossover by an equivalence-class analysis. The proposed encoding/crossover pair outperformed both distance-preserving crossover and edge-assembly crossover, two state-of-the-art crossovers in the literature.