Application of Particle Swarm Optimization and Genetic Algorithm Techniques to Solve Bi-level Congestion Pricing Problems

The solutions used to solve bi-level congestion pricing problems are usually based on heuristic network optimization methods which may not be able to find the best solution for these type of problems. The application of meta-heuristic methods can be seen as viable alternative solutions but so far, it has not received enough attention by researchers in this field. Therefore, the objective of this research was to compare the performance of two meta-heuristic algorithms namely, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), with each other and also with a conventional heuristic method in terms of degree of optimization, computation time and the level of imposed tolls. Hence, a bi-level congestion pricing problem formulation, for simultaneous optimization of toll locations and toll levels on a road network, using these two meta-heuristic methods, was developed. In the upper level of this bi-level problem, the objective was to maximize the variation in the Net Social Surplus (NSS) and in the lower level, the Frank-Wolfe user equilibrium method was used to assign traffic flow to the road network. PSO and GA techniques were used separately to determine the optimal toll locations and levels for a Sioux Falls network. The numerical results obtained for this network showed that GA and PSO demonstrated an almost similar performance in terms of variation in the NSS. However, the PSO technique showed 45% shorter run time and 24% lower mean toll level and consequently, a better overall performance than GA technique. Nevertheless, the number and location of toll links determined by these two methods were identical. Both algorithms also demonstrated a much better overall performance in comparison with a conventional heuristic algorithm. The results indicates the capability and superiority of these methods as viable solutions for application in congestion pricing problems.