Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Simplification of Models
2016
In practical applications the “complete” model, i.e., a model that contains all features that the experts in the application domain consider important, is often quite complicated and difficult to analyse mathematically. A straightforward numerical realization is often costly and may give very little qualitative understanding of the situation. It is therefore important to study if the model can be systematically simplified in order to enhance a qualitative analysis/understanding.
SIOPRED performance in a Forecasting Blind Competition
2012
In this paper we present the results obtained by applying our automatic forecasting support system, named SIOPRED, over a data set of time series in a Forecasting Blind Competition. In order to apply our procedure for providing point forecasts it has been necessary to develop an interactive strategy for the choice of the suitable length of the seasonal cycle and the seasonality form for a generalized exponential smoothing method, which have been obtained using SIOPRED. For the choice of those essential characteristics of forecasting methods, also a certain multi-objective formulation which minimizes several measures of fitting is used. Once these specifications are established, the model pa…
Soft Computing Techniques for Portfolio Selection: Combining SRI with Mean-Variance Goals
2014
A fuzzy portfolio selection model is presented incorporating a socially responsible goal without discarding a priori financially good portfolios or weakening a priori the financial goals. Hence, the optimal portfolios it provides could be either efficient from the strictly financial point of view or non-efficient if leaving the efficient frontier substantially improves the degree of social responsibility. The model can be used to direct heuristic procedures in order to select a reduced number of various alternatives from which the investor can directly make a final decision.
Unfolding dynamics of small peptides biased by constant mechanical forces
2018
We show how multi-ensemble Markov state models can be combined with constant-force equilibrium simulations. Besides obtaining the unfolding/folding rates, Markov state models allow gaining detailed insights into the folding dynamics and pathways through identifying folding intermediates and misfolded structures. For two specific peptides, we demonstrate that the end-to-end distance is an insufficient reaction coordinate. This problem is alleviated through constructing models with multiple collective variables, for which we employ the time-lagged independent component analysis requiring only minimal prior knowledge. Our results show that combining Markov state models with constant-force simu…
A comparison of simplex and simulated annealing for optimization of a new rear underrun protective device
2012
In this paper, two optimization approaches to improve the product design process have been analysed. Through the analysis of a case study, concerning the designing of a new High Energy Absorption Rear Underrun Protective Device (HEARUPD), two different optimization approaches (simplex and simulated annealing) have been compared. In the implemented optimization processes, the crash between an economy car and the rear part of a truck has been simulated by dynamic numerical (FEM) analyses. Moreover, authors have proposed the use of a suitable linear function of four variables with the purpose of reducing the multi-objective optimization processes to mono-objective ones. That has been made to s…
Analysis of multi degree of freedom systems with fractional derivative elements of rational order
2014
In this paper a novel method based on complex eigenanalysis in the state variables domain is proposed to uncouple the set of rational order fractional differential equations governing the dynamics of multi-degree-of-freedom system. The traditional complex eigenanalysis is appropriately modified to be applicable to the coupled fractional differential equations. This is done by expanding the dimension of the problem and solving the system in the state variable domain. Examples of applications are given pertaining to multi-degree-of-freedom systems under both deterministic and stochastic loads.
Solving some optimal control problems using the barrier penalty function method
2005
In this paper we present a new approach to solve the two-level optimization problem arising from an approximation by means of the finite element method of optimal control problems governed by unilateral boundary value problems. The minimized functional depends on control variables and state variables x. The latter are the optimal solution of an auxiliary quadratic programming problem, whose parameters depend on u.
Separatrix reconstruction to identify tipping points in an eco-epidemiological model
2018
Many ecological systems exhibit tipping points such that they suddenly shift from one state to another. These shifts can be devastating from an ecological point of view, and additionally have severe implications for the socio-economic system. They can be caused by overcritical perturbations of the state variables such as external shocks, disease emergence, or species removal. It is therefore important to be able to quantify the tipping points. Here we present a study of the tipping points by considering the basins of attraction of the stable equilibrium points. We address the question of finding the tipping points that lie on the separatrix surface, which partitions the space of system traj…
Observer-based control design for a class of nonlinear systems subject to unknown inputs: LMI approach
2015
This paper deals with the problem of observer-based controller design for a class of nonlinear systems subject to unknown inputs. A novel method is presented to design a controller using estimated state variables which guarantees all the state variables of the closed-loop system converge to the vicinity of the origin and stay there forever. This is done via satisfying several sufficient conditions in terms of nonlinear matrix inequalities. In light of linear algebra, particularly matrix decompositions, the achieved conditions will be converted to a Linear Matrix Inequality (LMI) problem to facilitate the procedure of computing the observer and controller gains. Finally, the effectiveness of…
Transitions between imperfectly ordered crystalline structures: A phase switch Monte Carlo study
2012
A model for two-dimensional colloids confined laterally by ``structured boundaries'' (i.e., ones that impose a periodicity along the slit) is studied by Monte Carlo simulations. When the distance $D$ between the confining walls is reduced at constant particle number from an initial value ${D}_{0}$, for which a crystalline structure commensurate with the imposed periodicity fits, to smaller values, a succession of phase transitions to imperfectly ordered structures occur. These structures have a reduced number of rows parallel to the boundaries (from $n$ to $n\ensuremath{-}1$ to $n\ensuremath{-}2$, etc.) and are accompanied by an almost periodic strain pattern, due to ``soliton staircases'' …