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In this paper we develop a new hybrid algorithm incorporating the penalty function technique for solving nonlinear constrained optimization problems. The principle is based on converting the constrained optimization problem into an unconstrained optimization problem by the penalty function technique. Then, we have proposed a new penalty technique, called Big-M penalty that is different from the existing ones. Accordingly, a hybrid algorithm has been developed based on Split and Discard Strategy (SDS) and advanced real coded genetic algorithm (ARCGA), with tournament selection, multiparent whole arithmetical crossover, double mutation (boundary and whole nonuniform mutation) and elitism. In SDS technique, the entire search space is divided into two equal subregions. Then the one containing the feasible solution with better fitness value is selected. This process is repeated until the accepted subregion reduces to a very small region with negligible edges. Finally, to test the performance of the proposed method along with three different penalty function techniques, it is applied to several well-known benchmark test problems available in the literature.

We discuss two issues about risk measures: we first point out an alternative interpretation of the penalty function in the dual representation of a risk measure; then we analyze the continuity properties of comonotone convex risk measures. In particular, due to the loss of convexity, local and global continuity are no more equivalent and many implications true for convex risk measures do not hold any more.

The paper presents a modified differential quadrature (MDQ) method to investigate the dynamic response of perforated plates with elastically restrained edges under uniaxial impact compressive load. The perforated plate is divided into several separate plate elements that can be connected by using penalty function method (PFM) to ensure continuity along the shared edges. The in-plane stress distribution of the plate under the mechanical edge loading is determined by the pre-buckling analysis. To analyze the effect of elastically restrained edges on the dynamic response of perforated plates, artificial springs imposed for the edges are considered in the governing equilibrium equations. Verification analysis is carried out to demonstrate the efficiency and accuracy of the proposed method by comparing the results obtained with those available in the literature. Finally, the various effects of initial imperfection, rotational restrained stiffness, hole size and location, and shear load, on the dynamic response of perforated plates are investigated. The results show that the dynamic buckling load of perforated plates is significantly influenced by the rotational restraint stiffness, hole size and shear load as well as the initial geometric imperfection, whereas the effect of hole location can be neglected in the analysis of dynamic buckling of plates. Additionally, the results predicted by the proposed method can correlate well with the available numerical results.

Based on minimum the output energy (MOE) , this paper constructs a new object function from combining penalty function with Lagrange function, and proposed an improved blind multiuser detection algorithm based on Lagrange neural network. The theory analysis and simulation shows that the improved algorithm has lower computational complexity, faster convergence speed and lower bit error rate.

It has been noted that when fitting Coxian phase-type distributions to observed and simulated data by maximum likelihood, often a maximum corresponding to equality of two or more eigenvalues of the matrix of transition rates was found. Such equality of eigenvalues would contribute to the smoothness of the resulting probability density function. It is proposed to adjust the log-likelihood of the data by subtracting a quantity which penalises configurations that have disparate eigenvalues. The resulting penalised maximum likelihood estimation of the parameters specifying the transition rate matrix is discussed with reference to two example data-sets.

GAs are known to be capable of finding an optimal value with better probability than the descent-based nonlinear programming methods for optimization problems. As such, a GA-based optimization technique is adopted in the paper to obtain optimal future control inputs for predictive control systems. For reliable future predictions of a process, we identify the underlying process with an NNARX model structure that consists of a regressor vector and a set of parameters containing all the weights of the neural network. To reduce the volume of neural network, we determine the elements of the regresssor vector based on the Lipschitz index and a criterion. The Gauss-Newton based Levenberg-Marquardt method is used to estimate the parameters because of its robustness and superlinear rate of convergence. Since most industrial processes are subject to their constraints, we deal with the input-output constraints by modifying some genetic operators and/or using a penalty strategy in the GA-based predictive control. Furthermore, we extend the control scheme to multi-input, multi-output nonlinear dynamical systems. Some computer simulations are given to show the effectiveness of the GA-based predictive control method compared with the adaptive GPC algorithm.

We discuss two issues about risk measures: we first point out an alternative interpretation of the penalty function in the dual representation of a risk measure; then we analyze the continuity properties of comonotone convex risk measures. In particular, due to the loss of convexity, local and global continuity are no more equivalent and many implications true for convex risk measures do not hold any more.