Performance Analysis of MATLAB Solvers in the Case of a Quadratic Programming Generation Scheduling Optimization Problem

In the case of the proposed method, the problem is parallelized by considering multiple possible mode of operation profiles, which determine the range in which the generators operate in each period. For each of these profiles, the optimization is carried out independently, and the best resulting dispatch is chosen. For each such profile, the resulting problem is a quadratic programming (QP) problem with a potentially negative definite Q quadratic term, and constraints depending on the actual operation profile. In this paper we analyze the performance of available MATLAB optimization methods and solvers for the corresponding QP.

The Impact of Transaction Costs on Rebalancing an Investment Portfolio in Portfolio Optimization

Constructing a portfolio of investments is one of the most significant financial decisions facing individuals and institutions. In accordance with the modern portfolio theory maximization of return at minimal risk should be the investment goal of any successful investor. In addition, the costs incurred when setting up a new portfolio or rebalancing an existing portfolio must be included in any realistic analysis. In this paper rebalancing an investment portfolio in the presence of transaction costs on the Croatian capital market is analyzed. The model applied in the paper is an extension of the standard portfolio mean-variance optimization model in which transaction costs are incurred to rebalance an investment portfolio. This model allows different costs for different securities, and different costs for buying and selling. In order to find efficient portfolio, using this model, first, the solution of quadratic programming problem of similar size to the Markowitz model, and then the solution of a linear programming problem have to be found. Furthermore, in the paper the impact of transaction costs on the efficient frontier is investigated. Moreover, it is shown that global minimum variance portfolio on the efficient frontier always has the same level of the risk regardless of the amount of transaction costs. Although efficient frontier position depends of both transaction costs amount and initial portfolio it can be concluded that extreme right portfolio on the efficient frontier always contains only one stock with the highest expected return and the highest risk.

Method of Parameter Calibration for Error Term in Stochastic User Equilibrium Traffic Assignment Model

Stochastic User Equilibrium (SUE) model is a widely used traffic assignment model in transportation planning, which is regarded more advanced than Deterministic User Equilibrium (DUE) model. However, a problem exists that the performance of the SUE model depends on its error term parameter. The objective of this paper is to propose a systematic method of determining the appropriate error term parameter value for the SUE model. First, the significance of the parameter is explored through a numerical example. Second, the parameter calibration method is developed based on the Logit-based route choice model. The calibration process is realized through multiple nonlinear regression, using sequential quadratic programming combined with least square method. Finally, case analysis is conducted to demonstrate the application of the calibration process and validate the better performance of the SUE model calibrated by the proposed method compared to the SUE models under other parameter values and the DUE model.

Enhanced Particle Swarm Optimization Approach for Solving the Non-Convex Optimal Power Flow

An enhanced particle swarm optimization algorithm (PSO) is presented in this work to solve the non-convex OPF problem that has both discrete and continuous optimization variables. The objective functions considered are the conventional quadratic function and the augmented quadratic function. The latter model presents non-differentiable and non-convex regions that challenge most gradient-based optimization algorithms. The optimization variables to be optimized are the generator real power outputs and voltage magnitudes, discrete transformer tap settings, and discrete reactive power injections due to capacitor banks. The set of equality constraints taken into account are the power flow equations while the inequality ones are the limits of the real and reactive power of the generators, voltage magnitude at each bus, transformer tap settings, and capacitor banks reactive power injections. The proposed algorithm combines PSO with Newton-Raphson algorithm to minimize the fuel cost function. The IEEE 30-bus system with six generating units is used to test the proposed algorithm. Several cases were investigated to test and validate the consistency of detecting optimal or near optimal solution for each objective. Results are compared to solutions obtained using sequential quadratic programming and Genetic Algorithms.