A bridge vibration measurement method by Unmanned Aerial Vehicles (UAVs) based on a Convolutional Neural Network (CNN) and Bayesian Optimization (BO) is proposed. In the proposed method, the video of the bridge structure is collected by a UAV, then the reference points in the background of the bridge and the target points on the bridge in the video are tracked by the Kanade-Lucas-Tomasi (KLT) optical flow method, so that their coordinates can be obtained. The BO is used to find the optimal hyper-parameter combination of a CNN, and the CNN based on BO is used to correct the bridge displacement signal collected by the UAV. Finally, the natural frequency of the bridge is extracted by processing the corrected displacement signals with Operational Modal Analysis (OMA). Moreover, a steel truss is used as the experimental model. The number of reference points and the shooting time of the UAV with the optimal correction effect of the BO-based CNN are obtained by two groups of comparative experiments, and the influence of the distance between structure and reference points on the correction effect of the BO-based CNN is determined by another group of comparative experiment. The static reference points are not required for the proposed method, which evidently enhances the applicability of UAVs; the conclusion of this paper has great guiding significance for the actual bridge vibration measurement.

The aim of this paper is to investigates the existence of the dispersion of SH-wave in a heterogeneous orthotropic layer lying over a heterogeneous elastic half-space and underlying an inhomogeneous Semi-Infinite medium. Hyperbolic variation in upper Semi-Infinite associated with directional rigidities and density has been considered while linear variation in the intermediate layer associated with initial stress, density, shear moduli and lower half-space associated with rigidity and density has been considered. The dispersion equation of SH-wave has been obtained in a closed form by using variable separation method. The effects of inhomogeneities of the assumed media are illustrated by figures using MATLAB programming. The Earth's composition is heterogeneous that incorporates extremely hard layers. The propagation of SH-wave across crustal layer of the Earth very much depends upon heterogeneity and orthotropic properties. In fact, the observation reveals that the phase velocity of SH-wave is directly proportionate to inhomogeneity parameter, orthotropic parameter and heterogeneity parameter. That means as inhomogeneity parameter and heterogeneity orthotropic parameter increases, the phase velocity of SH-wave increases proportionately. Moreover, the obtained dispersion equation of SH-wave coincides with the classical result of Love wave as initial stress, inhomogeneities, and the upper semiinfinite medium is neglected. This analysis may be helpful to expound the nature of the dispersion of seismic waves in elastic media.

Cardinality constrained portfolio optimization problems are widely used portfolio optimization models which incorporate restriction on the number of assets in the portfolio. Being mixed-integer programming problems make them NP-hard thus computationally challenging, specially for large number of assets. In this paper, we consider cardinality constrained mean-variance (CCMV) and cardinality constrained mean-CVaR (CCMCVaR) models and propose a hybrid algorithm to solve them. At first, it solves the relaxed model by replacing L_0-norm, which bounds the number of assets, by L_1-norm. Then it removes those assets that do not significantly contribute on the portfolio and apply the original CCMV or CCMCVaR model to the remaining subset of assets. To deal with the large number of scenarios in the CCMCVaR model, conditional scenario reduction technique is applied. Computational experiments on 3 large data sets show that the proposed approach is competitive with the original models from risk, return and Sharpe ratio perspective while being significantly faster.

While many real-world optimization problems typically involve multiple constraints, unconstrained problems hold practical and fundamental significance. They can arise directly in specific applications or as transformed versions of constrained optimization problems.‎ ‎Newton's method‎, ‎a notable numerical technique within the category of line search algorithms, is widely used for function optimization‎. The search direction and step length play crucial roles in this algorithm. ‎This paper introduces an algorithm aimed at enhancing the step length within the Broyden quasi-Newton process‎. ‎Additionally‎, ‎numerical examples are provided to compare the effectiveness of this new method with another approach‎.

The two requirements of impartiality and equitability expressed with the principle of transfers are fulfilled by all objective functions in equitable multi-objective optimization. However, in some practical situations, the decision-maker believes these requirements should only be satisfied by a subset of objective functions. To solve the problem in this paper, we first divide the set of objective functions into two subsets, the subset given by the decision maker and its complement. Then, we apply the concepts of equitable efficiency and efficiency for these two subsets, respectively. Furthermore, we apply the mean and inequality measures for these subsets of objective functions and present the new mean-equity models for solving the location problem. We investigate the relationship between $2$-efficient solutions of the new mean-equity models and efficient solutions of the location problem.

Fractional programming is a significant nonlinear planning tool within operation research‎. ‎It finds applications in diverse domains such as resource allocation‎, ‎transportation‎, ‎production programming‎, ‎performance evaluation‎, ‎and finance‎. ‎In practical scenarios‎, ‎uncertainties often make it challenging to determine precise coefficients for mathematical models‎. ‎Consequently‎, ‎utilizing indefinite coefficients instead of definite ones is recommended in such cases‎. ‎Grey systems theory‎, ‎along with probability theory‎, ‎randomness‎, ‎fuzzy logic‎, ‎and rough sets‎, ‎is an approach that addresses uncertainty‎. ‎In this study‎, ‎we address the problem of linear fractional programming with grey coefficients in the objective function‎. ‎To tackle this problem‎, ‎a novel approach based on the variable change technique proposed by Charnes and Cooper‎, ‎along with the convex combination of intervals‎, ‎is employed‎. ‎The article presents an algorithm that determines the solution to the grey fractional programming problem using grey numbers‎, ‎thus capturing the uncertainty inherent in the objective function‎. ‎To demonstrate the effectiveness of the proposed method‎, ‎an example is solved using the suggested approach‎. ‎The result is compared with solutions obtained using the whitening method‎, ‎employing Hu and Wong's technique and the Center and Greyness Degree Ranking method‎. ‎The comparison confirms the superiority of the proposed method over the whitening method‎, ‎thus suggesting adopting the grey system approach in such situations‎.