Search results for "optimal"
showing 10 items of 706 documents
On necessary optimality conditions for optimal control problems governed by elliptic systems
2005
The article considers an optimal control problem for the linear elliptic system div for the case where the coefficient matrix A plays the role of control and belongs to a nonconvex set and the cost functional is a quadratic form with respect to . By transforming the original problem to a more suitable one and by using ideas from the homogenization theory a necessary optimality condition is derived.
A new preference handling technique for interactive multiobjective optimization without trading-off
2015
Because the purpose of multiobjective optimization methods is to optimize conflicting objectives simultaneously, they mainly focus on Pareto optimal solutions, where improvement with respect to some objective is only possible by allowing some other objective(s) to impair. Bringing this idea into practice requires the decision maker to think in terms of trading-off, which may limit the ability of effective problem solving. We outline some drawbacks of this and exploit another idea emphasizing the possibility of simultaneous improvement of all objectives. Based on this idea, we propose a technique for handling decision maker’s preferences, which eliminates the necessity to think in terms of t…
Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems
2015
This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed
Error Estimates for a Class of Elliptic Optimal Control Problems
2016
In this article, functional type a posteriori error estimates are presented for a certain class of optimal control problems with elliptic partial differential equation constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state equation. The functional a posteriori error estimates developed by Repin in the late 1990s are applied to estimate the cost function value from both sides without requiring the exact solution of the state equation. Moreover, a lower bound for the minimal cost functional value is derived. A meaningful error quantity coinciding with the gap between the cost functional values of an arbitrary admissible …
Shape optimization of elasto-plastic bodies under plane strains: Sensitivity analysis and numerical implementation
1992
Optimal shape design problems for an elastic body made from physically nonlinear material are presented. Sensitivity analysis is done by differentiating the discrete equations of equilibrium. Numerical examples are included.
A survey on handling computationally expensive multiobjective optimization problems using surrogates: non-nature inspired methods
2015
Computationally expensive multiobjective optimization problems arise, e.g. in many engineering applications, where several conflicting objectives are to be optimized simultaneously while satisfying constraints. In many cases, the lack of explicit mathematical formulas of the objectives and constraints may necessitate conducting computationally expensive and time-consuming experiments and/or simulations. As another challenge, these problems may have either convex or nonconvex or even disconnected Pareto frontier consisting of Pareto optimal solutions. Because of the existence of many such solutions, typically, a decision maker is required to select the most preferred one. In order to deal wi…
Applying the approximation method PAINT and the interactive method NIMBUS to the multiobjective optimization of operating a wastewater treatment plant
2014
Using an interactive multiobjective optimization method called NIMBUS and an approximation method called PAINT, preferable solutions to a five-objective problem of operating a wastewater treatment plant are found. The decision maker giving preference information is an expert in wastewater treatment plant design at the engineering company Pöyry Finland Ltd. The wastewater treatment problem is computationally expensive and requires running a simulator to evaluate the values of the objective functions. This often leads to problems with interactive methods as the decision maker may get frustrated while waiting for new solutions to be computed. Thus, a newly developed PAINT method is used to spe…
A NEW REPRESENTATION OF ENERGY STORAGE SYSTEMS OPERATION USING FOURIER THEORY IN OPTIMAL SMART GRIDS MANAGEMENT
2012
This paper investigates the possibility to use a new modeling of Energy Storage Systems based on zero integral functions. Such functions represent the course of the energy level stored in batteries during the solution of optimal management problems in smart-grids. Storage devices, such as all the other components that are required to meet an integral capacity constraint along the dispatch time, must show the same State of Charge at the start and at the end of the timeframe considered for operation. In this paper, a set of sinusoidal functions have been used for the synthesis of the charge and discharge course of energy Storage Systems. Such representation allows to eliminate the difficult c…
Voltage Regulation and Power Losses Minimization in Automated Distribution Networks by an Evolutionary Multiobjective Approach
2004
In this paper, the problem of voltage regulation and power losses minimization for automated distribution systems is dealt with. The classical formulation of the problem of optimal control of shunt capacitor banks and Under Load Tap Changers located at HV/MV substations has been coupled with the optimal control of tie-switches and capacitor banks on the feeders of a large radially operated meshed distribution system with the aim of attaining minimum power losses and the flattening of the voltage profile. The considered formulation requires the optimization of two different objectives; therefore the use of adequate multiobjective heuristic optimization methods is needed. The heuristic strate…
Wavelet-Based Optimal Control of a Wind Turbine System: A Computational Approach
2011
This paper deals with a computational optimization approach to the problem of state-feedback control design for a wind turbine system. The first step of the study is to develop a reduced order model for the system by considering the most important physical phenomena of aerodynamics and structural dynamics. Moreover, the behavior of the system can be influenced by the coupled dynamics between the tower motions and the blade pitch and turbine speed which can cause instabilities in the control loops in the worst case. By using a suitable wavelet funcation, called Haar functions, a recursive computational procedure is established for finding the system dynamics approximately by solving only alg…