Numerous algorithms have recently been invented with varying strengths and weaknesses, none of which is the best for all cases. Herein, a hybrid optimization method known as a PSOHHO optimization algorithm is presented. There are two methods for combining algorithms: parallel and sequential. We adopted the parallel method and optimized the algorithm's performance. We cover the weaknesses of one algorithm with the strengths of another algorithm using a new method of combination. In this method, using several formulas, the top populations are exchanged between the two algorithms, and a new population is created. With this ability, the strengths of an algorithm can be used to compensate for the weaknesses of the other algorithm. In this method, no changes are made to the algorithms. The main goal is to use existing algorithms. This method aims to attain the optimal solution in the shortest time possible. Two algorithms of particle swarm optimization (PSO) and Harris Hawks optimization (HHO) were used to present this method and five truss samples were considered to confirm the performance of this method. Based on the results, this method has rapid convergence speed and acceptable results compared to the other methods. It also yields better results than its basic algorithms.

The Markowitz’s optimization problem is considered as a standard quadratic programming problem that has exact mathematical solutions. Considering real world limits and conditions، the portfolio optimization problem is a mixed quadratic and integer programming problem for which efficient algorithms do not exist. Therefore، the use of meta-heuristic methods such as neural networks and evolutionary algorithms has been an important issue in the literature of portfolio optimization. This study considers the problem of finding the efficient frontier associated with the standard mean-variance portfolio optimization model and presents a heuristic algorithm based upon particle swarm optimization for finding the cardinality constrained efficient frontier. The test data set is the daily prices of 20 companies from March 2006 to September 2008 from the TEPIX in Iran. The results show that PSO is successful in constrained portfolio optimization to find the optimum solutions in all levels of risk and return.

Metaheuristic optimization algorithms are a relatively new class of optimization algorithms that are widely used for difficult optimization problems in which classic methods cannot be applied and are considered as known and very broad methods for crucial optimization problems. In this study, a new metaheuristic optimization algorithm is presented, the main idea of which is inspired by models in kinematics. This algorithm obtains better results compared to other optimization algorithms in this field and is able to explore new paths in its search for desirable points. Hence, after introducing the projectiles optimization (PRO) algorithm, in the first experiment, it is evaluated by the determined test functions of the IEEE congress on evolutionary computation (CEC) and compared with the known and powerful algorithms of this field. In the second try out, the performance of the PRO algorithm is measured in two practical applications, one for the training of the multi-layer perceptron (MLP) neural networks and the other for pattern recognition by Gaussian mixture modeling (GMM). The results of these comparisons are presented in various tables and figures. Based on the presented results, the accuracy and performance of the PRO algorithm are much higher than other existing methods.