Many portfolio Optimization problems deal with allocation of assets which carry a relatively high market price. Therefore, it is necessary to determine the integer value of assets when we deal with portfolio Optimization. In addition, one of the main concerns with most portfolio Optimization is associated with the type of constraints considered in different models. In many cases, the resulted problem formulations do not yield in practical solutions. Therefore, it is necessary to apply some managerial decisions in order to make the results more practical. This paper presents a portfolio Optimization based on an improved knapsack problem with the cardinality, floor and ceiling, budget, class, class limit and pre-assignment constraints for asset allocation. To handle the uncertainty associated with different parameters of the proposed model, we use robust Optimization techniques. The model is also applied using some realistic data from US stock market. Genetic algorithm is also provided to solve the problem for some instances.

One of the key issues for investors is the issue of creating an optimal stock portfolio. In the issue of choosing an portfolio, the decision maker faces different and sometimes conflicting goals such as rate of return, liquidity, dividend, and risk. In portfolio Optimization, the main issue is the optimal choice of assets and securities that can be made with a certain amount of capital, but on the one hand, the uncertainties associated with each share, and, on the other hand, the multiplicity of the optimal portfolio selection model, on the complexity of the problem increases. In this paper, the portfolio Optimization under uncertainty has been studied. A randomized approach to converting uncertainty into a state of definiteness and agreeing to plan for a single objective is used in combination. Information about 20 pharmaceutical companies from the Tehran Stock Exchange has been used and the validity of the model has been investigated. The results show that the stock portfolio offered has a high performance.

The present paper considers geometric shape Optimization of structures that are modelled by PDEs with random data. Random data appears in inputs and parameters of the PDE. Theoretical bases are presented, and the perturbation of the identity method is applied for transforming the shape Optimization problem into a fixed domain and then formulated as a stochastic optimal control problem. Random data is taken as random fields that are approximated by Karhunen-Loeve expansion. Uncertainty quantification is performed by applying non-intrusive techniques e.g., stochastic collocation method. Gradient method is applied for Optimization. Numerical result is represented in order to illustrate the applicability of the proposed method.

In this paper, an algorithm is proposed to improve the Constrained PID control design based on the convex-concave Optimization. The control system is designed by optimizing a performance cost function, taking into account the stability and efficiency constraints with frequency domain analysis in which the sensitivity and complementary sensitivity concepts are used. It is shown, using a counter example, the previous methods are not effective for some systems, the Optimization problem becomes unbounded and interrupted. To solve the problem, conditions where the Optimization problem fails to have a response are analyzed and the previous limitations are eliminated by representing a new designing method. The performance of the proposed scheme is shown by applying it to the counter example. Moreover, the control system is designed for an unstable system.

One of the main concerns in flight performance is to determine the highest level of capabilities for flying vehicles to perform the assigned missions. The objective of the current research is to utilize the maximum aerodynamic and propulsive capabilities of a flying robot. In this regard, the problem of optimal performance during all phases of a mission profile is proposed. By integrating a multi objective heuristic Optimization algorithm with Constrained Optimization approaches, all phases of a typical mission profile have been optimized. The major advantage of the proposed approach is that it provides the optimal time history for all state variables as well as the optimal flight path and the amount of required fuel.