Simultaneous Optimization of Signal Timing and Capacity Improvement in Urban Transportation Networks Using Simulated Annealing

Capacity expansions as well as its reduction have been widely anticipated as important countermeasures for traffic congestion. Although capacity expansion had been traditionally well noticed as a congestion mitigation measure, but it was not until recently that capacity reduction measures such as; congestion pricing, road diet and other such capacity reduction measures were noticed as congestion mitigation measures. Measures such as signal optimization, metering and congestion pricing are intended to affect the travel pattern and assignment behavior of travelers to make the results of the User Equilibrium (UE) traffic assignment, followed by the travelers, closer to the System Optimal (SO) outcomes, intended by the planners. As such, a bi-level optimization model was formulated for the simultaneous optimization of capacity improvement/expansion and signal timing in an urban transportation network. The model takes into account both the effect of higher demand, induced by the capacity expansion, and the rerouting potential effect of traffic signals. The solution algorithm developed here consists of two major components; the gradient projection algorithm (GP) to solve the lower level traffic assignment problem and the Simulated Annealing (SA) algorithm to solve the master problem. In order to illustrate the method a case study was examined. The analysis and application of the proposed algorithm shows that the performance function gradually converged along the simulation run, and no divergence problem is observed. By applying the developed algorithm, the total network travel time reduced by 13.42%, in which 5.76% is reached by only optimizing the signal times. Using the GP algorithm and taking advantages of dynamic memory in the process of simulation, the whole simulation acquired from computer time is 13.63 seconds with a convergence rate of 0.001.