Efficient local search in traffic assignment

Gabriel de Oliveira Ramos, Ana L. C. Bazzan

Abstract: The traffic assignment problem (TAP) plays a key role in the context of efficient urban mobility. The TAP can be approached from various perspectives. One of the fundamental models to solve the TAP is the so-called User Equilibrium (UE), which assumes that drivers behave rationally aiming at minimising their travel costs. However, this is a complex optimisation problem. To this regard, in this paper we propose the use of the GRASP metaheuristic to provide approximate solutions to the UE. The path relinking mechanism is also used to increase the coverage of the solutions space. We advance the state-of-the-art by proposing a novel modelling for the TAP, through which one can adjust the granularity of the search space, thus making a more efficient, directed local search. We also devise an efficient assignment evaluation scheme that avoids redundant computations during the local search process. Additionally, we develop a novel greedy procedure for generating enhanced initial solutions for the GRASP algorithm. Based on experiments, we demonstrate that our approach outperforms classical algorithms, providing solutions that are significantly closer to the UE. Moreover, our empirical results show that the stability and fairness levels achieved by our approach are considerably better than those achieved by other methods.