The strong network orientation problem

This study presents models and heuristics for solving the strong network orientation problem (SNOP), which can model several tactical optimization problems of setting directions in urban networks. The objective is to set an orientation for each edge in an undirected graph such that the resulting digraph is strongly connected and the total travel distance between any pair of nodes is minimized (or maximized). Investigating tactical optimization problems such as SNOP is motivated by several challenges in urban networks due to the growth of population in urban areas, large number of daily trips, increasing price of maintaining urban networks, and the need to reduce air pollution and passive noise. Thus, a new trend is to utilize the urban networks better. In this context, we first use a multicommodity flow formulation to model the minimization problem. The maximization version is modeled by using the dual formulation of the shortest path problem. Then, scalable heuristic strategies for solving SNOP are investigated. For such purpose, we first propose basic components such as constructive heuristics, perturbations and local searches. They are combined into several metaheuristics based on local searches, multi-start and evolutionary schemes, i.e. Multistart Local Search, Iterated Local Search (ILS), Relaxed ILS, Evolutionary Local Search (ELS), Relaxed ELS, and Variable Neighborhood Search. Computational experiments have been performed to analyze the proposed methods in terms of efficiency and quality of solutions, using grid instances and a graph from downtown Clermont-Ferrand in France.