As has been shown by Spiess (1984), the above problem can be solved by applying the successive linear approximation method (Frank and Wolfe, 1956). An important advantage of this method is the fact that only total volumes need to be computed and stored, since the destination dependent volumes
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are dealt with implicitly.
Optimal Strategy Equilibrium Transit Assignment:
Step 1:
(Subproblem)
Step 2:
(Line Search)
Step 3:
(Update)
The minimization in Step 2 is best implemented not by actual minimization, but by annulling the derivative, i.e. solving the equation
Note that the stopping criterion used in Step 3 of the above algorithm corresponds to the absolute gap, which is an upper bound for the difference between the objective function at the current solution and at the true optimum.
Implementation in EMME/2
In this section we describe how the transit equilibrium assignment can be implemented in the EMME/2 Transportation Pla
