The paper presents the continuation of the author's research on Evolutionary Sets of Safe Ship Trajectories (ESoSST) methodology. In an earlier paper (Szlapczynski, 2011) the author described the foundations of this methodology, which used Evolutionary Algorithms (EA) to search for an optimal set of safe trajectories for all the ships involved in an encounter. The methodology was originally designed for open waters or restricted waters when only the standard Convention on the International Regulations for Preventing Collisions at Sea (COLREGS, 1972) rules apply. However, within Traffic Separation Schemes (TSS), where additionally Rule 10 of COLREGS applies, the problem is much more complex and a new solution is needed. This paper introduces the extended ESoSST methodology, with a focus on changes that have to be made to obey Rule 10 and fully support TSS. These changes include detecting and penalizing TSS violations, as well as the pre-processing phase (generating the initial population, which includes predefined TSS-compliant tracks). The methodology has been designed for possible application in Vessel Traffic Service (VTS) centres. Its new mechanisms are presented with details. The examples are included of the results of the computer simulation tests carried out for the Gulf of Gdansk TSS to illustrate the methodology's effectiveness and functional scope.