Abstract: 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.
Abstract: 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.
Abstract: 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.
Abstract: 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.