A general algorithm for traffic assignment problems with continuously distributed user attributes

This paper presents a general-purpose algorithm for solving traffic assignment problems with continuously distributed user attributes. Traditional methods often rely on discretization, which introduces behavioral distortions and limits scalability. The proposed algorithm simulates a cumulative logit (CumLog) day-to-day adjustment process, in which travelers iteratively revise their route choices based on accumulated travel experience. Aggregate route choice probabilities are computed via numerical integration, eliminating the need for arbitrary user grouping, closed-form objective functions, or restrictive problem structures. Using the continuous bi-criteria traffic assignment problem as a test case, we establish convergence and detail implementation strategies. The algorithm is further extended to accommodate multiple continuous attributes, non-separable travel times, and non-additive cost functions. Unlike classical zero-order methods, which struggle with infinite user heterogeneity, the CumLog algorithm obviates intractable class-specific operations. Numerical experiments validate its convergence, efficiency, and generality across a range of problem settings.