Hybrid gradient-swarm intelligence to improve quality of solutions for origin–destination matrix adjustment problem

The high cost of conventional surveys has motivated researchers to develop methods for adjusting a prior Origin–destination (OD) matrix from easily available traffic counts. The gradient method is a mathematical programming approach widely used for the OD matrix adjustment problem (ODMAP). However, this method easily gets trapped in local optima due to the non-convexity of the problem. Moreover, validation of the gradient solutions against predefined target matrices shows the method has considerable difficulty with estimating the sum of the OD matrix elements. Particle swarm optimization (PSO) is a metaheuristic which is getting lots of attention for its global search ability, but is less accurate in local search. The proposed algorithm hybridizes PSO with the gradient method, considering that the combination of good local convergence properties and effective global search makes an excellent algorithm for the ODMAP. Comparison of the results for a small and a real-life network demonstrates that the hybrid algorithm provides higher convergence properties and achieves more accurate solutions than its constituent parts working alone.