Application of optimization methods to vibration control of stretched strings

In this paper, non-linear programming techniques are applied to the problem of controlling the vibration pattern of a stretched string. First, the problem of finding the magnitudes of two control forces applied at two points l1 and l2 on the string to reduce the energy of vibration over the interval (l1, l2) relative to the energy outside the interval (l1, l2) is considered. For this problem the relative merits of various methods of non-linear programming are compared. The more complicated problem of finding the positions and magnitudes of two control forces to obtain the desired energy pattern is then solved by using the slack unconstrained minimization technique with the Fletcher-Powell search. In the discussion of the results it is shown that the position of the control force is very important in controlling the energy pattern of the string.

Geometric optimization methods for the analysis of gene expression data

DNA microarrays provide such a huge amount of data that unsupervised methods are required to reduce the dimension of the data set and to extract meaningful biological information. This work shows that Independent Component Analysis (ICA) is a promising approach for the analysis of genome-wide transcriptomic data. The paper first presents an overview of the most popular algorithms to perform ICA. These algorithms are then applied on a microarray breast-cancer data set. Some issues about the application of ICA and the evaluation of biological relevance of the results are discussed. This study indicates that ICA significantly outperforms Principal Component Analysis (PCA).

Geometric optimization methods for independent component analysis applied on gene expression data

DNA microarrays provide a huge amount of data and require therefore dimensionality reduction methods to extract meaningful biological information. Independent Component Analysis (ICA) was proposed by several authors as an interesting means. Unfortunately, experimental data are usually of poor quality- because of noise, outliers and lack of samples. Robustness to these hurdles will thus be a key feature for an ICA algorithm. This paper identifies a robust contrast function and proposes a new ICA algorithm. © 2007 IEEE.

Technical and economic resources management in smart grids using heuristic optimization methods

Intensive use of Distributed Generation (DG) represents a change in the paradigm of power systems operation making small-scale energy generation and storage decision making relevant for the whole system. This paradigm led to the concept of smart grid for which an efficient management, both in technical and economic terms, should be assured. This paper presents a new approach to solve the economic dispatch in smart grids. The proposed methodology for resource management involves two stages. The first one considers fuzzy set theory to define the natural resources range forecast as well as the load forecast. The second stage uses heuristic optimization to determine the economic dispatch considering the generation forecast, storage management and demand response

Extremum estimators and stochastic optimization methods

Submitted in partial fulfillment for the Requirements for the Degree of PhD in Mathematics, in the Speciality of Statistics in the Faculdade de Ciências e Tecnologia

Non-smooth optimization methods for computation of the conditional value-at-risk and portfolio optimization

We examine numerical performance of various methods of calculation of the Conditional Value-at-risk (CVaR), and portfolio optimization with respect to this risk measure. We concentrate on the method proposed by Rockafellar and Uryasev in (Rockafellar, R.T. and Uryasev, S., 2000, Optimization of conditional value-at-risk. Journal of Risk, 2, 21-41), which converts this problem to that of convex optimization. We compare the use of linear programming techniques against a non-smooth optimization method of the discrete gradient, and establish the supremacy of the latter. We show that non-smooth optimization can be used efficiently for large portfolio optimization, and also examine parallel execution of this method on computer clusters.

Comparative studies on non-convex optimization methods for transmission network expansion planning

We have investigated and extensively tested three families of non-convex optimization approaches for solving the transmission network expansion planning problem: simulated annealing (SA), genetic algorithms (GA), and tabu search algorithms (TS). The paper compares the main features of the three approaches and presents an integrated view of these methodologies. A hybrid approach is then proposed which presents performances which are far better than the ones obtained with any of these approaches individually. Results obtained in tests performed with large scale real-life networks are summarized.

Comparative studies on non-convex optimization methods for transmission network expansion planning

We have investigated and extensively tested three families of non-convex optimization approaches for solving the transmission network expansion planning problem: simulated annealing (SA), genetic algorithms (GA), and tabu search algorithms (TS). The paper compares the main features of the three approaches and presents an integrated view of these methodologies. A hybrid approach is then proposed which presents performances which are far better than the ones obtained with any of these approaches individually. Results obtained in tests performed with large scale real-life networks are summarized.

Noisy kriging-based optimization methods: A unified implementation within the DiceOptim package

Kriging-based optimization relying on noisy evaluations of complex systems has recently motivated contributions from various research communities. Five strategies have been implemented in the DiceOptim package. The corresponding functions constitute a user-friendly tool for solving expensive noisy optimization problems in a sequential framework, while offering some flexibility for advanced users. Besides, the implementation is done in a unified environment, making this package a useful device for studying the relative performances of existing approaches depending on the experimental setup. An overview of the package structure and interface is provided, as well as a description of the strategies and some insight about the implementation challenges and the proposed solutions. The strategies are compared to some existing optimization packages on analytical test functions and show promising performances.

Optimization methods for the operating room management under uncertainty: stochastic programming vs. decomposition approach

The operating theatres are the engine of the hospitals; proper management of the operating rooms and its staff represents a great challenge for managers and its results impact directly in the budget of the hospital. This work presents a MILP model for the efficient schedule of multiple surgeries in Operating Rooms (ORs) during a working day. This model considers multiple surgeons and ORs and different types of surgeries. Stochastic strategies are also implemented for taking into account the uncertain in surgery durations (pre-incision, incision, post-incision times). In addition, a heuristic-based methods and a MILP decomposition approach is proposed for solving large-scale ORs scheduling problems in computational efficient way. All these computer-aided strategies has been implemented in AIMMS, as an advanced modeling and optimization software, developing a user friendly solution tool for the operating room management under uncertainty.

A theoretical comparison of two optimization methods for radiofrequency drive schemes in high frequency MRI resonators

In this paper, numerical simulations are used in an attempt to find optimal Source profiles for high frequency radiofrequency (RF) volume coils. Biologically loaded, shielded/unshielded circular and elliptical birdcage coils operating at 170 MHz, 300 MHz and 470 MHz are modelled using the FDTD method for both 2D and 3D cases. Taking advantage of the fact that some aspects of the electromagnetic system are linear, two approaches have been proposed for the determination of the drives for individual elements in the RF resonator. The first method is an iterative optimization technique with a kernel for the evaluation of RF fields inside an imaging plane of a human head model using pre-characterized sensitivity profiles of the individual rungs of a resonator; the second method is a regularization-based technique. In the second approach, a sensitivity matrix is explicitly constructed and a regularization procedure is employed to solve the ill-posed problem. Test simulations show that both methods can improve the B-1-field homogeneity in both focused and non-focused scenarios. While the regularization-based method is more efficient, the first optimization method is more flexible as it can take into account other issues such as controlling SAR or reshaping the resonator structures. It is hoped that these schemes and their extensions will be useful for the determination of multi-element RF drives in a variety of applications.

Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.