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Ordinary differential equations usefully describe the behavior of a wide range of dynamic physical systems. The particle swarm optimization (PSO) method has been considered an effective tool for solving the engineering optimization problems for ordinary differential equations. This paper proposes a modified hybrid Nelder-Mead simplex search and particle swarm optimization (MNM- PSO) method for solving parameter estimation problems. The M-NM-PSO method improves the efficiency of the PSO method and the conventional NM-PSO method by rapid convergence and better objective function value. Studies are made for three well-known cases, and the solutions of the M-NM-PSO method are compared with those by other methods published in the literature. The results demonstrate that the proposed M-NM-PSO method yields better estimation results than those obtained by the genetic algorithm, the modified genetic algorithm (real-coded GA (RCGA), the conventional particle swarm optimization (PSO) method, and the conventional NMPSO method. [ABSTRACT FROM AUTHOR]

Abstract: Heuristic optimization provides a robust and efficient approach for solving complex real-world problems. The focus of this research is on a hybrid method combining two heuristic optimization techniques, genetic algorithms (GA) and particle swarm optimization (PSO), for the global optimization of multimodal functions. Denoted as GA-PSO, this hybrid technique incorporates concepts from GA and PSO and creates individuals in a new generation not only by crossover and mutation operations as found in GA but also by mechanisms of PSO. The results of various experimental studies using a suite of 17 multimodal test functions taken from the literature have demonstrated the superiority of the hybrid GA-PSO approach over the other four search techniques in terms of solution quality and convergence rates. [Copyright &y& Elsevier]