Search results for "optimal"
showing 10 items of 706 documents
Optimal Set Points Regulation of Distributed Generation Units in Micro-grids under Islanded Operation
2010
The present work studies the problem of optimizing the power production levels of dispersed generation units in islanded microgrids. The problem is intrinsically multi-objective with non linear objectives and constraints, thus the solution approach is based on evolutionary optimization and uses the Non dominated Sorting Genetic Algorithm II. The objectives are calculated based on the solution of the load flow problem. The latter problem is more complicated when in the considered system a physical node with a sufficiently large production capability is not available, because all the generation node of the systems have similar and limited generation capability. In this paper, the issue has be…
Frequency constrained optimal Power Flow based on Glow-worm Swarm Optimization in Islanded Microgrids
2015
This work presents an application of a swarm optimization method to solve the optimal power flow problem taking into account the constraints of frequency and line ampacity in three-phase islanded Microgrids. Each generation unit is equipped with a Power Electronics Interface. In the considered formulation, the droop control parameters are considered as variables to be adjusted by a higher control level, while the frequency is kept in rated bounds. Another typical constraint for OPF formulation, the max ampacity of each line, is also considered. Two case studies with different dimensions and electrical features have been considered and the obtained results show the efficiency of the proposed…
Geometric optimal control of the contrast problem in Magnetic Resonance Imaging
2012
Abstract The control of the dynamics of spin systems by magnetic fields has opened intriguing possibilities in quantum computing and in Nuclear Magnetic Resonance spectroscopy. In this framework, optimal control theory has been used to design control fields able to realize a given task while minimizing a prescribed cost such as the energy of the field or the duration of the process. However, some of the powerful tools of optimal control had not been used yet for NMR applications in medical imagery. Here, we show that the geometric control theory approach can be advantageously combined with NMR methods to crucially optimize the imaging contrast. This approach is applied to a benchmark proble…
Two-Sided Guaranteed Estimates of the Cost Functional for Optimal Control Problems with Elliptic State Equations
2014
In the paper, we discuss error estimation methods for optimal control problems with distributed control functions entering the right-hand side of the corresponding elliptic state equations. Our analysis is based on a posteriori error estimates of the functional type, which were derived in the last decade for many boundary value problems. They provide guaranteed two-sided bounds of approximation errors for any conforming approximation. If they are applied to approximate solutions of state equations, then we obtain new variational formulations of optimal control problems and guaranteed bounds of the cost functional. Moreover, for problems with linear state equations this procedure leads to gu…
NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point
2010
Most interactive methods developed for solving multiobjective optimization problems sequentially generate Pareto optimal or nondominated vectors and the decision maker must always allow impairment in at least one objective function to get a new solution. The NAUTILUS method proposed is based on the assumptions that past experiences affect decision makers’ hopes and that people do not react symmetrically to gains and losses. Therefore, some decision makers may prefer to start from the worst possible objective values and to improve every objective step by step according to their preferences. In NAUTILUS, starting from the nadir point, a solution is obtained at each iteration which dominates t…
Interactive Nonconvex Pareto Navigator for Multiobjective Optimization
2019
Abstract We introduce a new interactive multiobjective optimization method operating in the objective space called Nonconvex Pareto Navigator . It extends the Pareto Navigator method for nonconvex problems. An approximation of the Pareto optimal front in the objective space is first generated with the PAINT method using a relatively small set of Pareto optimal outcomes that is assumed to be given or computed prior to the interaction with the decision maker. The decision maker can then navigate on the approximation and direct the search for interesting regions in the objective space. In this way, the decision maker can conveniently learn about the interdependencies between the conflicting ob…
Modelling energy storage systems using Fourier analysis: An application for smart grids optimal management
2014
In this paper, a new and efficient model for variables representation, named F-coding, in optimal power dispatch problems for smart electrical distribution grids is proposed. In particular, an application devoted to optimal energy dispatch of Distributed Energy Resources including ideal storage devices is here considered. Electrical energy storage systems, such as any other component that must meet an integral capacity constraint in optimal dispatch problems, have to show the same energy level at the beginning and at the end of the considered timeframe for operation. The use of zero-integral functions, such as sinusoidal functions, for the synthesis of the charge and discharge course of bat…
Indirect Methods for Optimal Control Problems
2003
This chapter is dedicated to the numerical approximation of Optimal Control Problems. The algorithms are based on the necessary conditions for optimality which allow us to use a descent method for the minimization of the cost functional.
Multi-Start Methods
2006
Heuristic search procedures that aspire to find global optimal solutions to hard combinatorial optimization problems usually require some type of diversification to overcome local optimality. One way to achieve diversification is to re-start the procedure from a new solution once a region has been explored. In this chapter we describe the best known multi-start methods for solving optimization problems. We propose classifying these methods in terms of their use of randomization, memory and degree of rebuild. We also present a computational comparison of these methods on solving the linear ordering problem in terms of solution quality and diversification power.
An Interactive Evolutionary Multiobjective Optimization Method: Interactive WASF-GA
2015
In this paper, we describe an interactive evolutionary algorithm called Interactive WASF-GA to solve multiobjective optimization problems. This algorithm is based on a preference-based evolutionary multiobjective optimization algorithm called WASF-GA. In Interactive WASF-GA, a decision maker (DM) provides preference information at each iteration simple as a reference point consisting of desirable objective function values and the number of solutions to be compared. Using this information, the desired number of solutions are generated to represent the region of interest of the Pareto optimal front associated to the reference point given. Interactive WASF-GA implies a much lower computational…