Dynamic penalty function method for the side constrained traffic assignment problem

The traffic assignment problem (TAP) is traditionally defined without side constraints. Although introducing side constraints into the TAP is used as a way of refining applied assignment models, it brings some computational difficulties that prevent the refined model from being applicable in real-case problems. In this paper an iterative solution algorithm is developed for TAP with linear side constraints. This method is based on implicitly considering the side constraints by means of adding a dynamic penalty function (DPF) to the link travel times. Each of the iterations of the algorithm is reduced to an unconstrained assignment followed by updating the penalty functions. The unconstrained assignment is carried out using the linearization method that has been derived from the complementarity formulation of TAP. The implementation of the algorithm and computational experiments on some well-known networks are also presented for two types of side constraint, i.e. link and node capacity constraints. For the link-type side constraint, compared to the reported results of the existing alternative approaches, a DPF algorithm finds feasible solutions with better Beckmann’s objective functions in less number of iterations. For the node-type constraints, the algorithm also shows good performance.