A Travelling Salesman Problem (TSP) is an NPhard combinatorial problem that is very important for many real-world applications. In this paper, it is shown, that proposed approach solves multi-objective TSP (mTSP) more effectively than other investigated methods, i.e. Non-dominated Sorting Genetic Algorithm II (NSGA-II). The proposed methods use rank and crowding distance (well-known from NSGA-II), combining those mechanisms in a novel, unique way: competing and coevolving in the evolution process. The proposed modifications are investigated and verified by the benchmark mTSP instances, and results are compared to other methods.