The multi-class dynamic user equilibrium (MDUE) model can be adopted in the lower level of a bi-level formulation of dynamic network design problems to predict heterogeneous travelers' path choices in response to transportation authority's decisions in the upper level. While a number of previous studies have devoted to the finite-dimensional MDUE (FMDUE) problem with a given number of user classes, the infinite-dimensional MDUE (IMDUE) problem was rarely addressed. This work proposes a column

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... neration-based algorithm that solves the IMDUE problem as a series of FMDUE sub-problems. Each sub-problem is formulated as a nonlinear minimization program via a gap function and solved by a feasible descent direction method that is able to circumvent the needs to calculate partial derivatives for determining search direction, while maintaining the mechanisms of searching along feasible descent directions. Numerical results show our approach is superior to the algorithm based on the method of successive averages.