Two-phase algorithm for solving the preference-based multicriteria optimal path problem with reference points

The shortest path problem arises in several contexts like transportation, telecommunication or data analysis. New requirements in solving practical problems (e.g., efficient content delivery for information-centric networks, urban passenger transport system or social network) impose that more than one criterion should be considered. Since the objectives are in conflict, the solution is not unique, rather a set of (efficient) paths is defined as optimal. The most satisfactory path should be selected considering additional preference information. Generally, computing the entire set of efficient solutions is time consuming. In this paper, we apply the reference point method for finding the best path. In a reference point-based approach, non-additive scalarizing function is applied. In this case, the classical optimality principle for the shortest path problem is not valid. To overcome this issue, we propose an equivalent formulation dealing with the constrained shortest path (CSP) problem. The idea is to define a set of constraints guaranteeing that an optimal solution to the problem at hand lies in the feasible region of the defined CSP problem. We propose a two-phase method where, in the first phase, a bound on the optimal solution is computed and used to define the constraints, whereas, in the second phase a labelling algorithm is applied to search for an optimal solution to the defined CSP problem. The method is tested on instances generated from random and grid networks, considering several scenarios. The computational results show that, on average, the proposed solution strategy is competitive with the state-of-the-art approaches and behaves the best on grid networks.