Markowitz portfolio model still is the dominant approach in the investment profession and scientific approaches. Contrary to the growing use of portfolios and in spite of the rich literature on the subject, there are some problems and unanswered questions. How to select the stocks of a portfolio is a matter of controversy; besides, the approach to optimize the selected potfolio is a sub-group of this controversy. The aim of this work is to be a useful instrument for helping finance practitioners and researchers with the portfolio selection problem. While investigating major methods ever used in optimization, classics and heuristics, a hybridized algorithm, consisting of the combination of two heuristic algorithms, is applied to the portfolio selection problem in this paper. Portfolios are selected and optimized in Tehran stock exchange for the stocks of top 35 companies out of top 50 companies. The results indicate that the hybridized algorithm is adaptable to the portfolio selection problem, and in contrast to optimization via genetic algorithm, the hybridized algorithm holds a better convergence speed and owns a more reasonable risk-return performance. The research findings also show that in a comparison between the hybrid-based constructed portfolios, although the convergence speed and degree of diversification for the monthly selected portfolio outperforms the other one, the annual selected portfolio holds a better performance from risk-return point of view.

In this paper a hybrid algorithm based on exploration power of the Genetic algorithms and exploitation capability of Nelder Mead simplex is presented for global optimization of multivariable functions. Some modifications are imposed on genetic algorithm to improve its capability and efficiency while being hybridized with Simplex method. Benchmark test examples of structural optimization with a large number of variables and constraints are chosen to show the robustness of the algorithm.

In this paper, A innovative method designed to solving nonlinear optimization problems with convex object function and constrained. In this method, we define an cost function and we find variables to minimization of cost function. For create properly cost function we use K. K. T. optimal conditions. We used Nelder-Mead without derivative optimization method to minimization of cost function. When, dimensions of problem is about 10, application shows that efficiency of Nelder-Mead method is more than the other methods. Using new mathod is easier than the similar methods. By several examples efficiency of new method are verified.

Implementing spatial structures is common in real-world structures such as bridges, space structures, and ships. This topic has attracted researchers to propose more efficient and pristine methods to obtain more robust and cheaper solutions for spatial structure optimization problems. This paper presents a hybrid approach for simultaneous optimization of sizing and topology of spatial truss structures using genetic programming and local search methods. It aims to find the optimal cross-sectional areas and connectivities between the joints of the truss to achieve minimum structural weight subjected to static constraints. These constraints include structural kinematic stability, maximum allowable stress in elements and maximum nodal displacements in joints. First, this approach utilizes the tree-form representation of trusses and evolves to the optimal structure in search space; afterward, Nelder-Mead algorithm enhances the obtained solution in the final step. The proposed method has the capability of identifying redundant truss members and joints in the design space. Our method was applied to some numerical problems and compared with other existing popular and competent techniques in the literature. The findings provided lighter truss structures in comparison with other references.

In reverse engineering it may be required to perform multiple measurements due to the size and part complexity limitations of the physical equipment CMM/Optical Scanner and / or settings. To model the whole part it is required to bring different point sets obtained during different scans to a common coordinate system. Registration process for point clouds is to find the geometric transform between them in which all point clouds are transformed into a single absolute coordinate system. Theoretically, it is very straight forward to perform registration by finding the six components of transformation matrix (3 angles plus 3 displacements) and this can be mathematically determined if three non-linear points are known in both global and local coordinate systems. The process of registration is strongly affected by inaccurate data and may fail in the case of noisy data, hence other methods are usually sought to find the transformation matrix. This paper tries to solve the problem in practical applications. The Nelder-Mead method was employ for point clouds registration for the first time. The registration was also performed using Singular value decomposition and Genetic Algorithm methods. The three methods were compared in terms of convergence, accuracy and computation time.

The forces due to the unbalance in a system cause undesired vibration and noise, and reduce the system life. One of the new and efficient methods used to reduce the unbalance is the use of automatic dynamic ball balancer. The automatic dynamic ball balancer is a typical passive balancer which doesn't need control systems to balance the rotor. Because these devices are used in the systems which have variable unbalance according to the operating conditions and the system may be switched on and off several times a day, therefore reducing the balancing time becomes a necessary task. In practice, the gyroscopic effect is created for several reasons, e.g. when the rotor is located offset from the shaft midspan. Previous studies have not determined the optimum values of the damping ratio and mass of balls of the automatic dynamic ball balancer under the gyroscopic effect. In this study, the effect of damping ratio and the mass of balls of the automatic dynamic ball balancer on the stability and balancing of the system under the gyroscopic effect have been investigated and, using the Nelder-Mead simplex algorithm, the optimum values of these parameters to minimize the time of balancing and converging the Euler angles to zero are obtained.

The main objective of this research is to analyze optimization and the thermal performance of circular porous fins with four different profiles, rectangular, convex, triangular, and concave under fully wet conditions. In this research, a linear model was used for the relationship between humidity and temperature. Moreover, modeling was assumed one-dimensional and the temperature changed only in the direction of the radius of the fin. Moreover, the thermal conductivity and heat transfer coefficient were a function of porosity and temperature, respectively. The governing equations were solved using Galerkin’ s method, the finite difference method, and the Gauss-Seidel algorithm. In this study, the effects of different parameters including relative humidity, Darcy number, Rayleigh number and porosity on temperature distribution, fin efficiency, and fin effectiveness were investigated. The results showed that the efficiency and effectiveness and heat transfer rate to the base for the rectangular profile were higher than those of other profiles. In this research, the Nelder-Mead algorithm was used for optimization. The results showed that to maintain optimal conditions, the ratio of thickness to fin length should be increased by increasing relative humidity or decreasing the Darcy number, Rayleigh number, and porosity.

This study presents two mixed integer programming models for scheduling hybrid flow shops with sequence dependent setup times. In the first model, we assumed the machines at each stage are identical, but in the second model the machines at each stage are different. These models may be used to determine optimal solutions for hybrid flow shop problems of moderate size, and these problems could then be used as benchmarks for testing new sequencing heuristics.

Programming and designing the non-linear models cover a wide range of applications. Various scholars all around the world are engaged in taking this action and their main goal has been identified as providing efficient computational algorithms with the ability of evaluating the non-linear models. Nelder_Mead algorithm is among the most popular ones. Selecting a proper policy in energy concerns is dependent upon the estimation of the reserves and the expenditures incurred in negotiation of oil contracts. Those models capable of predicting the future supplies and their relative volume are valuable. However, traditional prediction models are not efficient enough and that’s why the researchers endeavor to find new methods for modeling the oil reserves. This paper aims to develop a new model to estimate the oil reserves by using exploratory and statistical data. It also tries to evaluate the model in one of famous the oil field by using Nelder_Mead algorithm.