This paper focuses on robust multi-criteria traffic network equilibrium problems with path capacity constraints. The concepts of robust vector equilibrium and robust vector equilibrium with respect to worst case are introduced, respectively. To generate a subset of robust vector equilibrium, an equivalent min-max optimization problem is constructed. In addition, a direct search algorithm, in which the step size without derivatives and redundant parameters, for solving this min-max problem is proposed. To find a subset of robust vector equilibrium with respect to worst case, an equivalent smoothing optimization problem based on a variant version of ReLU activation function is established. Numerical experiments are also presented to expound the advantages of the algorithms.