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A hybrid invasive weed optimization (HIWO) algorithm based on the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is proposed for the problems on parameter inversion of the nonlinear models of sun shadow with integer variables in the study. Our presented algorithm can take full advantage of the local search ability of BFGS algorithm and the global search ability of invasive weed optimization (IWO) algorithm. The HIWO algorithm can not only reverse the date of sun shadow model successfully, but also conquer the weaknesses that the classic mathematical methods are hard to address integer nonlinear optimization problems by utilizing integers in some random variables from algorithms. The results of numerical experiments demonstrate that the HIWO algorithm has not only high computing accuracy, but also fast convergence speed. It can effectively improve the accuracy and efficiency of the techniques of sun shadow location, and afford an effective and efficient technique to handle the issues of integer parameter inversion in engineering applications. [ABSTRACT FROM AUTHOR]

The purpose of the optimum designs is to determine the optimal experimental conditions in terms of minimum variance of the estimated vector of parameters, so that statistical inferences can be generated as accurate as possible. This theory presupposes knowledge of the function relating the explanatory variables with the response variable. In this situation, usually get designs with support points as parameters in the model. Since p-point designs assume that the model function is known, these could not be optimal in some practical situations because they do not allow to test the goodness of fit of the assumed model. In this paper we present a generalization of the methodology proposed by to increase the number of support points in D-optimality criterion. An expression for the variance of the predicted response in terms of a constant δ will be provided, which allow to determine the points to be added to the D-optimal design. We propose a strategy for choosing δ. Finally we provide a pseudo-optimal design with (p + s) support points. [ABSTRACT FROM AUTHOR]