Different algorithms for solving elastic demand traffic assignment problems and mode split-assignment problems are discussed. We note that there are different ways to implement the Frank-Wolfe technique to solve these problems and give the most efficient implementation. We then discuss Evans' procedure and compare it with the Frank-Wolfe technique. Computational results indicate that the Frank-Wolfe algorithm is unstable for the elastic assignment problem—its rate of convergence is very sensitive to values used for upper bounds on trips, which are purely artificial “tuning parameters.” Evans' algorithm is found to be more robust and to converge consistently faster than the Frank-Wolfe technique for both classes of problems studied.

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A theoretical and computational investigation is made of the performance of a dynamic-programming-based algorithm for nonlinear integer problems with various types of constraints. We include linear constraints, aggregated linear constraints, separable nonlinear constraints and constraints involving maxima and minima. Separability of the objective function is assumed. The new feature of the algorithm is that two types of fathoming or pruning are used to reduce the size of tables and number of computations: fathoming by bounds and fathoming by infeasibility.

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