This article recapitulates literature research solving transportation problems and these variants, notably the multimodal transportation problems variants. Moreover, the existing optimization methods critiqued and synthesized their efficiency to solve the transportation problem. This problem can be identified by various criteria and objectives functions that distinguished according to the case study. Based on the existing literature research, a taxonomy is proposed to distinguish different factors and criteria that perform and influence the multi-objective optimization on the transportation network planning problems. The transportation problems are cited according to these objective functions, and the variant of the problem by referring to the previous studies. In this article, the authors have focused their attention on a recent multi-objective mathematical model to solve the planning network of the multimodal transportation problem.