## 1 Introduction
Taking into account the importance of shortest path and \(k\)-shortest path problems in this context, we pay special attention to these problems after reviewing basic concepts on multiobjective path problems. We present the main formulations of multiobjective path problems also including evidence-relevant theoretical results. Different categories of objective functions will be considered, namely linear and non-linear functions as well as some optimization path problems with an objective function composed of other functions and problems involving uncertainty. We outline the different types of resolution methods for these problems appearing in the scientific literature more relevant to this important application area, not forgetting the approximating approaches. Special emphasis will be given to exact resolution approaches, namely based on the shortest path, \(k\)-shortest path and dedicated multiobjective shortest path algorithms, having in mind that these algorithms can solve large instances of the problem in execution times compatible with the application context. Also, a classification and overview of relevant algorithms and related contributions concerning different types of problems and of resolution approaches, namely labeling, ranking, recursive and two-phase methods, as well as interactive approaches, will be put forward. Note that focusing this work on exact algorithms is not a severe limitation in many of the path problems because the available resolution approaches enable, in most cases, a fast resolution of large instances of the problems. It should be emphasized that when multiple and conflicting objectives are explicitly at stake in the path optimization problem, the global optimum does not exist. Thence, the optimal solution is substituted by the concept of an _efficient_ (also known as _Pareto optimal_) solution set corresponding to a nondominated point set in the objective function space. The designation 'efficient path' means a feasible path such that there are no other feasible paths capable of improving the value of one objective function without worsening the value of at least one of the other objective functions. A further distinction has to be made between supported and unsupported nondominated solutions as reviewed in the section on basic concepts. One of our main purposes in this work, developed in Section 2, is to provide insights into current research trends in the application of Operations Research techniques to solve multiobjective path problems and to outline possible future research directions. In particular, in the first part of this paper, we refer to articles that are focused on path problems and their resolution approaches. We considered works published in scientific journals, conference proceedings, and book chapters. We carried out a search in the following databases: Elsevier, Wiley, Springer, Scopus, IEEExplore, Research Gate, and Google Scholar; we used several keywords such as \"multiobjective paths\" or \"multicriteria paths\". We also present a summary of the main features of the problems in tables, which can help the researchers in comparing the works and exploring new possible configurations. In this paper, we consider three types of algorithms. Firstly, we consider the algorithms for which there is no articulation of preferences of the Decision Maker (DM) (this means that the aggregation of preferences is made a posteriori), so that the algorithms calculate the whole set of efficient solutions. Secondly, we consider those which are characterized by a progressive articulation of preferences of the DM, designated as interactive approaches; Thirdly, we consider those for which there is an a priori articulation of preferences, for instance by building a value/utility function. In the case of interactive approaches (see Figure 1), after each calculation phase leads to one (or several) efficient solution(s), there is a dialogue phase with the DM. This phase is carried out so that a new calculation phase is initiated, and so on.