Abstract
Heuristic search algorithms, which are characterized by faster convergence rates and can obtain better solutions than the traditional mathematical methods, are extensively used in engineering optimizations. In this paper, a newly developed elitist-mutated particle swarm optimization (EMPSO) technique and an improved gravitational search algorithm (IGSA) are successively applied to parameter estimation problems of Muskingum flood routing models. First, the global optimization performance of the EMPSO and IGSA are validated by nine standard benchmark functions. Then, to further analyse the applicability of the EMPSO and IGSA for various forms of Muskingum models, three typical structures are considered: the basic two-parameter linear Muskingum model (LMM), a three-parameter nonlinear Muskingum model (NLMM) and a four-parameter nonlinear Muskingum model which incorporates the lateral flow (NLMM-L). The problems are formulated as optimization procedures to minimize the sum of the squared deviations (SSQ) or the sum of the absolute deviations (SAD) between the observed and the estimated outflows. Comparative results of the selected numerical cases (Case 1–3) show that the EMPSO and IGSA not only rapidly converge but also obtain the same best optimal parameter vector in every run. The EMPSO and IGSA exhibit superior robustness and provide two efficient alternative approaches that can be confidently employed to estimate the parameters of both linear and nonlinear Muskingum models in engineering applications.
Highlights
Accurate forecasting of flood wave movement in natural river channels is extremely important for the real-time monitoring, alert and control of floods, which are effective non-engineering measures for preventing tremendous loss of lives and property
As shown in Table 5: (1) only the elitist-mutated particle swarm optimization algorithms (PSOs) (EMPSO) and improved gravitational search algorithm (IGSA) can steadily find the global optimal solution in every run, which is same to the reference; (2) the EMPSO still has the best performance in optimizing the nonlinear Muskingum model (NLMM)-L
The EMPSO algorithm and the IGSA were applied for solving the parameter estimation problems of three forms of linear or nonlinear Muskingum models (LMM, NLMM and NLMM-L)
Summary
Accurate forecasting of flood wave movement in natural river channels is extremely important for the real-time monitoring, alert and control of floods, which are effective non-engineering measures for preventing tremendous loss of lives and property. Two categories of approaches for flood routing exist: hydraulic and hydrologic methods [1]. EMPSO and IGSA for Estimating Muskingum Parameters numerically solving the famous Saint-Venant equations, which usually has strict requirements for the topographical data of the investigated stream channel (such as channel cross-section and roughness) and complicated computations [2]. The latter is based on the continuity and empirical storage equations and is more widely used in engineering applications due to its simplicity. The Muskingum flood routing model, developed by McCarthy [3], is the most frequently applied hydrologic technique
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