Dataset of instances taken into account by the paper, together with solutions and achieved computational time. Manuscript submitted to 2022 IEEE-CBMS. ABSTRACT - Proton therapy is an oncological therapy that is more expensive than classical radiotherapy but that is considered the gold standard in several situations. Moreover, since there is still a limited amount of delivering facilities for this techniques, it is fundamental to increase the number of treated patients over time. The objective of this work is to offer an insight on the problem of the optimization of the part of the delivery time of a treatment plan that relates to the movements of the system. We denote it as the Nozzle Travel Time Problem (NTTP), in analogy with the Leaf Travel Time Problem (LTTP) in classical radiotherapy. In particular this work: (i) describes a mathematical model for the delivery system and formalize the optimization problem for finding the optimal sequence of movements of the system (nozzle and bed) that satisfies the covering of the prescribed irradiation directions; (ii) provides an optimization pipeline that solves the problem for instances with an amount of irradiation directions much greater than those usually employed in the clinical practice; (iii) reports preliminary results about the effects of employing two different resolution strategies within the aforementioned pipeline, that rely on an exact Traveling Salesmna Problem (TSP) solver (Concorde) and an efficient heuristic Vehicle Routing Open-source Optimization Machine (VROOM). For each combination of system features (SF1, SF2, SF3) and distance metric (L1 and Linf), 50 runs (5 session by 10 runs) with prescribed fields from 5 to 100 (step 5) have been executed. - 'grph' folder contains GTSP and ATSP instances in GraphML and txt format. - 'vrinst' folder contains ATSP instances, expressed as VRP instances, in json format, to be fed into VROOM - 'tsps' folder contains symmetric TSP instances in TSPLIB format to be fed into Concorde - 'ress' folder contains result of optimizzation obtained by Concorde (.sol and .res formats) and VROOM (.json) all the files in these folders is named as [SF#]_[distanceMetric][[prescribedFields#]_[subrun]][Session8charsCode], so that, for example "SF3_Linf[100_9]2e275d41" represents the 100 fields result of the 9th subrun of the session with code 2e275d41, where SF3 and Linf norm have been taken into account. - 'resultsNPY' folder contains .npy file about computation time and computed travel time for both solvers