Path Algorithm Find the shortest paths from A to all other nodes irn the following network using Dijkstra's algorithm. 15 a Credit Problems oints each Formulati blem and ombination Method wi on A simple transportation network has a single origin-destination pair which is connected by two parallel arcs. The total travel demand is 20 units of traffic between this origin-destination pair. Let t(.) be the arc travel time function, and x the traffic flow, we have. t, (x1) = 5 12 t2(x2)= 10 + 2x2 a. Formulale a non-linear programming model that is cqivalent to the UE traffic assignment problem on this simple network (hint: each arc is a path on this network, and arc flows are equivalent to path flows. This means you don't need to represent path flows separately in the formulation) b. Conduct ONE iteration of the Frank-Wolfe algorithm for the problem in part a A simple transportation network has a single origin-destination pair which is connected by two parallel arcs. The total travel demand is 20 units of traffic between this origin-destination pair. Let t(.) be the arc travel time function, and x the traffic flow, we have: 5 + x12 2x h(%) t2(x)-10 a. Formulate a non-linear programming model that is equivalent to the UF traffic assignment problem on this simple network (hint: each arc is a path on this network, and arc flows are equivalent to path flows. This means you don't need to represent path flows separately in the formulation). b. Conduct ONE iteration of the Frank-Wolfe algorithm for the problem in part a Be sure to: Specify an initial solution Formulate and solve the linear programming approximalion problem Determine the optimal step length, and Derive the new arc flows . . in Model Choi You are working with a pancl/longitudinal dataset which records mode choices made by the same individuals at several time poits. What assumptions of the multinomial logit model might be viated as you work with this dataset? Come up with as many advanced choice model types as possible that you can develop with this dataset without violating major assumptions it Network Assignm Review a recent paper on transit network assignment, and briefly summarize its methodology. Keep the summary to less than one page