A New Path-Based Algorithm for Traffic Assignment with Nonadditive Path Cost

The traffic assignment problem (TAP) with nonadditive path cost can only be solved by path-based algorithms owing to the characteristics of its cost structure. These algorithms generally decompose the TAP into subproblems with path flow as the variable by OD pairs and solve them sequentially. In this paper, we present an innovative path-based algorithm that aims to overcome the limitations of existing approaches and significantly improve the solution efficiency of TAP with nonadditive path cost. In order to enhance the algorithm's performance, we utilize the Quasi-Newton and pattern search methods to improve the precision of the search direction and step size. Furthermore, the proposed algorithm is incorporated into the subnetwork decomposition framework of the bush-based algorithm. However, instead of visiting each subnetwork sequentially, our algorithm employs a self-adaptive scheme to determine the optimal allocation of computational resources in each inner loop. The subnetwork decomposition algorithm is more computationally energy-saving than the OD decomposition scheme in the traditional path-based algorithm. Numerical studies conducted using simple and practical networks with different path cost structures demonstrate the superior performance of the algorithm proposed in this paper compared to its competitors. In particular, the algorithm can handle TAP with diverse nonadditive and additive path costs, offering strong applicability in various traffic situations