Improved particle swarm algorithm for hydrological parameter optimization

In this paper, a new method named MSSE-PSO (master–slave swarms shuffling evolution algorithm based on particle swarm optimization) is proposed. Firstly, a population of points is sampled randomly from the feasible space, and then partitioned into several sub-swarms (one master swarm and other slave swarms). Each slave swarm independently executes PSO or its variants, including the update of particles' position and velocity. For the master swarm, the particles enhance themselves based on the social knowledge of master swarm and that of slave swarms. At periodic stage in the evolution, the master swarm and the whole slave swarms are forced to mix, and points are then reassigned to several sub-swarms to ensure the share of information. The process is repeated until a user-defined stopping criterion is reached. The tests of numerical simulation and the case study on hydrological model show that MSSE-PSO remarkably improves the accuracy of calibration, reduces the time of computation and enhances the performance of stability. Therefore, it is an effective and efficient global optimization method. Hydrological model has been widely applied in hydrology such as planning, design, operation, management, decision and so on. Normally, a hydrological model consists of some modules with a large number of parameters. The successful application of a hydrological model depends on how well the parameters are calibrated. Theoretically they can be assigned values from actual data, but actually it is almost impossible because of temporal and spacial variation of complicated hydrological process. Instead, an inverse problem is solved in which the parameters are optimized by fitting as closely as possible the simulation to the observation. However, affected by weather, climate, terrain, soil, vegetation and human activities, the parameter optimization of a hydrological model is in possession of some characters such as high-dimension, multi-peak values , nonlinear, discontinuous and non-convex and noisy etc., which makes it difficult to be calibrated exactly. The traditional methods to calibrate hydrological model include Rosenbrock method [1], simplex method [2], genetic algorithm (GA) [3–6] and SCE-UA [7–12]. Both Rosenbrock method and simplex method demand a lot on model structure, and they always converge to local optimal solution. GA is a highly parallel and adaptive optimization algorithm, but it also suffers from premature convergence and tends to get stuck into local optima, especially in complex multi-peak-search problems. SCE-UA has strong global search ability by introducing biologic evolvement to its numerical compute, but different 0096-3003/$-see front matter Ó 2010 Elsevier …