In this paper, a multi-objective scenario based mathematical model is presented for the capacitated hub location problem in public transportation considering economic and investment aspects. Three objective functions are regarded in the presented mathematical model. The first one aims to minimise the total costs considering the possibility of investing the unused budget at each period. The second one aims to minimise the total processing time in the hub network at each period. The last one aims to minimise the maximum distance between each pair of origin-destination nodes in the network. To solve the model, three multi-objective meta-heuristic algorithms are developed, namely S metric selection evolutionary multi-objective optimisation algorithm (SMS-EMOA), multi-objective imperialist competitive algorithm (MOICA) and non-dominated sorting genetic algorithm (NSGA-II). Finally, developed algorithms are compared to each other based on several comparison measures using a relatively novel statistical approach.