Toward minimal restriction of genetic encoding and crossovers for the two-dimensional Euclidean TSP

In the field of evolutionary algorithms (EAs), many operators have been introduced for the traveling salesman problem (TSP). Most encoding schemes have various restrictions that often result in a loss of information contained in problem instances. We suggest a new chromosomal encoding scheme that pursues minimal information loss and a crossover scheme with minimal restriction for the two-dimensional (2D) Euclidean TSP. The most notable feature of the suggested crossover is that it uses the 2D tour images themselves for chromosomal cutting. We 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, which represent two state-of-the-art crossovers in the literature. We also tested its performance on a mixed framework that incorporates a large-step Markov chain technique into the framework of a traditional EA.