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Transit assignment is an important problem in the literature of transportation. Almost all competitive algorithms in this area are strategy based. For uncongested transit networks, the problem may be formulated into an optimization problem for which good solution algorithms exist. A variational inequality formulation of the problem with several solution methods is also presented in the literature for congested networks. This paper is devoted to solving a transit assignment problem based on complementarity formulation using path flows. The solution algorithm exploits the three concepts of decomposition, path generation, and linearization. The procedure has been applied on a large-scale realcase transit network under fixed travel times as well as flow-dependent dwell times. Computational experiments show rapid convergence of the algorithm. Moreover, for the limited experiments performed, the computational time for the flow-dependent problem is only about twice that of the case for the fixed travel times, without an appreciable excess memory requirement.

Transportation network design problem (TNDP) aims to choose from among a set of alternatives (e.g., set of new arcs) which minimizes an objective (e.g., total travel time), while keeping consumption of resources (e.g., budget) within their limits. TNDP is formulated as a bilevel programming problem, which is difficult to solve on account of its combinatorial nature. Following a recent, heuristic by ant colony optimization (ACO), a hybridized ACO (HACO) has been devised and tested on the network of Sioux Falls, showing that the hybrid is more effective to solve the problem. In this paper, employing the heuristic of particle swarm optimization (PSO), an algorithm is designed to solve the TNDP. Application of the algorithm on the Sioux Falls test network shows that the performance of PSO algorithm is comparable with HACO.

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