حل مسئله ي تخصيص ترافيك با محدوديت ظرفيت كمان با استفاده از تابع جريمه

SOLVING TRAFFIC ASSIGNMENT PROBLEM WITH LINK CAPACITY CONSTRAINTS USING PENALTY FUNCTION

In traffic assignment problem (TAP) literature, methods like Frank-Wolfe have sufficient efficiency in solving the problem, assuming infinite capacities for the links, be¬cause, in these methods, each linearized sub-problem is equivalent to a shortest path problem between an origin and a destination fOD) pair. However, in reality, links have limited capacities and obtaining more realistic vol¬umes needs those capacities to be taken into account. Explicit consideration of this type of constraint in TAP causes each linearized sub-problem to be converted to a minimal cost, multi-commodity flow problem that is difficult to solve. Another method is to consider the con¬straints implicitly and use some penalty functions that are sensitive to capacities, so that, by adding them to travel time functions, the capacity constraints lead to being satisfied. In this paper, a suitable penalty func¬tion is suggested and itʹs usefulness is examined via some numerical examples. The results will be compared with the other methods of interest, such as: the inner penalty function (1PF) and the augmented Lagrangian multiplier (ALM). Also, the. results are presented by applying the suggested method to the network of Mashhad city, as a real case example, where the links approach to the signalized intersections are assumed capacitated.