  The traffic assignment problem is one of the most important transportation
planning problems. The task faced by transportation planners, traffic
engineers, and computer scientists is to generate high quality, approximate
solutions of users equilibrium, that enable traffic scenario comparisons in a
reasonable CPU time. We introduce the k Paths Subtracting-Adding (k-PSA)
algorithm to approximate the user equilibrium of the traffic assignment
problem. The k-PSA algorithm consists of two alternating phases: (1)
enlargement of the set of attractive paths; (2) subtracting-adding trips
between generated attractive paths for each origin-destination pair of nodes.
The proposed algorithm performs the two phases iteratively until the number of
paths for each origin-destination pair is k. We tested the proposed algorithm
on four benchmark transportation networks from the literature. The performed
numerical tests show that the proposed approach generates, in short,
computation times, solutions that are, on average, very close to the user
equilibrium.
