Coding TSP tours as permutations via an insertion heuristic

An insertion heuristic for the traveling salesman problem builds a tour one city at a time by inserting each city into the tour at a position that increases the tour’s length the least. Permutations can encode TSP tours for genetic search via this heuristic. Decoding such a chromosome consists of inserting the cities into a tour in the order the chromosome lists them. The chromosome specifies when each city is inserted into the tour rather than where; this scheme enlists the heuristic’s power in the genetic search. This paper describes a genetic algorithm for TSP that encodes candidate tours as permutations via the insertion heuristic, as well as two crossover operators appropriate to the coding. Tests on thirteen TSP instances indicate that the algorithm is effective on instances of moderate size, often identifying optimal tours, and that it continues to find tours that are short, though not optimal, as the number of cities increases and the search space grows.