Search results for "optimal"
showing 10 items of 706 documents
A Simple Indicator Based Evolutionary Algorithm for Set-Based Minmax Robustness
2018
For multiobjective optimization problems with uncertain parameters in the objective functions, different variants of minmax robustness concepts have been defined in the literature. The idea of minmax robustness is to optimize in the worst case such that the solutions have the best objective function values even when the worst case happens. However, the computation of the minmax robust Pareto optimal solutions remains challenging. This paper proposes a simple indicator based evolutionary algorithm for robustness (SIBEA-R) to address this challenge by computing a set of non-dominated set-based minmax robust solutions. In SIBEA-R, we consider the set of objective function values in the worst c…
A Proximal Solution for a Class of Extended Minimax Location Problem
2005
We propose a proximal approach for solving a wide class of minimax location problems which in particular contains the round trip location problem. We show that a suitable reformulation of the problem allows to construct a Fenchel duality scheme the primal-dual optimality conditions of which can be solved by a proximal algorithm. This approach permits to solve problems for which distances are measured by mixed norms or gauges and to handle a large variety of convex constraints. Several numerical results are presented.
A fuzzy-logic based evolutionary multiobjective approach for automated distribution networks management
2004
In this paper, a methodology to treat constrained scheduling problems based on the repeated application of a fuzzy-logic-based multiobjective algorithm is presented. The application domain is that of automated distribution systems management. In particular, the problem of voltage regulation and power loses minimization is here considered. The classical formulation of the problem of optimal control of shunt capacitor banks and under load tap changers, ULTC, located at high voltage/medium voltage (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 mini…
Optimal control of option portfolios and applications
1999
We present an expected utility maximisation framework for optimally controlling a portfolio of options. By combining the replication approach to option pricing with ideas of the martingale approach to (stock) portfolio optimisation we arrive at an explicit solution of the option portfolio problem. Its characteristics are illustrated by some specific examples. As an application, we calculate an optimal option and consumption strategy for an investor who is obliged to hold a stock position until the time horizon.
Direct Numerical Methods for Optimal Control Problems
2003
Development of interior point methods for linear and quadratic programming problems occurred during the 1990’s. Because of their simplicity and their convergence properties, interior point methods are attractive solvers for such problems. Moreover, extensions have been made to more general convex programming problems.
Interactive multiobjective optimization with NIMBUS for decision making under uncertainty
2013
We propose an interactive method for decision making under uncertainty, where uncertainty is related to the lack of understanding about consequences of actions. Such situations are typical, for example, in design problems, where a decision maker has to make a decision about a design at a certain moment of time even though the actual consequences of this decision can be possibly seen only many years later. To overcome the difficulty of predicting future events when no probabilities of events are available, our method utilizes groupings of objectives or scenarios to capture different types of future events. Each scenario is modeled as a multiobjective optimization problem to represent differe…
A variational inequality approach to constrained control problems for parabolic equations
1988
A distributed optimal control problem for parabolic systems with constraints in state is considered. The problem is transformed to control problem without constraints but for systems governed by parabolic variational inequalities. The new formulation presented enables the efficient use of a standard gradient method for numerically solving the problem in question. Comparison with a standard penalty method as well as numerical examples are given.
Incremental heuristic approach for meter placement in radial distribution systems
2019
The evolution of modern power distribution systems into smart grids requires the development of dedicated state estimation (SE) algorithms for real-time identification of the overall system state variables. This paper proposes a strategy to evaluate the minimum number and best position of power injection meters in radial distribution systems for SE purposes. Measurement points are identified with the aim of reducing uncertainty in branch power flow estimations. An incremental heuristic meter placement (IHMP) approach is proposed to select the locations and total number of power measurements. The meter placement procedure was implemented for a backward/forward load flow algorithm proposed by…
Optimal Starting Conditions for the Rendezvous Maneuver, Part 2: Mathematical Programming Approach
2008
In a companion paper (Part 1, J. Optim. Theory Appl. 137(3), [2008]), we determined the optimal starting conditions for the rendezvous maneuver using an optimal control approach. In this paper, we study the same problem with a mathematical programming approach.
Necessary Optimality Conditions in Multiobjective Dynamic Optimization
2004
We consider a nonsmooth multiobjective optimal control problem related to a general preference. Both differential inclusion and endpoint constraints are involved. Necessary conditions and Hamiltonian necessary conditions expressed in terms of the limiting Frechet subdifferential are developed. Examples of useful preferences are given.