Arbitrarily Large Planar Etsp Instances with Known Optimal Tours

Very recently, four diierent types of instances of the Euclidean Traveling Salesman Problem (ETSP) on the plane have been introduced. The coordinates of the cities have been deened by geometric iterative constructive processes. For each one of these instances, a unique optimal tour through the cities has been provided. Due to the nature of the constructive processes and the induction proofs of optimality, they provide us with a remarkable set of instances of the ETSP with arbitrarily many cities, and with known optimal tours of diierent fractal dimensions. In this paper we show how Lindenmayer's parallel rewriting systems, also known as L-Systems, can be used to encode the instances and the optimal tours. We present a general framework for the practical issues of the automatic generation of ETSP instances in TSPLIB format from L-Systems. no formato TSPLIB.