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.

传统调查的高昂成本促使研究人员开发方法，根据容易获得的交通计数来调整先前的出发地-目的地（OD）矩阵。梯度法是一种广泛用于 OD 矩阵调整问题 (ODMAP) 的数学规划方法。然而，由于问题的非凸性，该方法很容易陷入局部最优。此外，针对预定义目标矩阵的梯度解验证表明，该方法在估计 OD 矩阵元素之和方面存在相当大的困难。粒子群优化（PSO）是一种元启发式算法，因其全局搜索能力而受到广泛关注，但在局部搜索方面不太准确。所提出的算法将 PSO 与梯度方法混合，考虑到良好的局部收敛特性和有效的全局搜索的结合使得 ODMAP 成为一种优秀的算法。小型网络和现实网络的结果比较表明，与单独工作的组成部分相比，混合算法提供了更高的收敛性，并实现了更准确的解决方案。