A metaheuristic-based framework for index tracking with practical constraints

Recently, numerous investors have shifted from active strategies to passive strategies because the passive strategy approach affords stable returns over the long term. Index tracking is a popular passive strategy. Over the preceding year, most researchers handled this problem via a two-step procedure. However, such a method is a suboptimal global-local optimization technique that frequently results in uncertainty and poor performance. This paper introduces a framework to address the comprehensive index tracking problem (IPT) with a joint approach based on metaheuristics. The purpose of this approach is to globally optimize this problem, where optimization is measured by the tracking error and excess return. Sparsity, weights, assets under management, transaction fees, the full share restriction, and investment risk diversification are considered in this problem. However, these restrictions increase the complexity of the problem and make it a nondeterministic polynomial-time-hard problem. Metaheuristics compose the principal process of the proposed framework, as they balance a desirable tradeoff between the computational resource utilization and the quality of the obtained solution. This framework enables the constructed model to fit future data and facilitates the application of various metaheuristics. Competitive results are achieved by the proposed metaheuristic-based framework in the presented simulation

Neurodynamic approaches to model predictive control.

Pan, Yunpeng.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (p. 98-107).Abstract also in Chinese.Abstract --- p.ip.iiiAcknowledgement --- p.ivChapter 1 --- Introduction --- p.2Chapter 1.1 --- Model Predictive Control --- p.2Chapter 1.2 --- Neural Networks --- p.3Chapter 1.3 --- Existing studies --- p.6Chapter 1.4 --- Thesis structure --- p.7Chapter 2 --- Two Recurrent Neural Networks Approaches to Linear Model Predictive Control --- p.9Chapter 2.1 --- Problem Formulation --- p.9Chapter 2.1.1 --- Quadratic Programming Formulation --- p.10Chapter 2.1.2 --- Linear Programming Formulation --- p.13Chapter 2.2 --- Neural Network Approaches --- p.15Chapter 2.2.1 --- Neural Network Model 1 --- p.15Chapter 2.2.2 --- Neural Network Model 2 --- p.16Chapter 2.2.3 --- Control Scheme --- p.17Chapter 2.3 --- Simulation Results --- p.18Chapter 3 --- Model Predictive Control for Nonlinear Affine Systems Based on the Simplified Dual Neural Network --- p.22Chapter 3.1 --- Problem Formulation --- p.22Chapter 3.2 --- A Neural Network Approach --- p.25Chapter 3.2.1 --- The Simplified Dual Network --- p.26Chapter 3.2.2 --- RNN-based MPC Scheme --- p.28Chapter 3.3 --- Simulation Results --- p.28Chapter 3.3.1 --- Example 1 --- p.28Chapter 3.3.2 --- Example 2 --- p.29Chapter 3.3.3 --- Example 3 --- p.33Chapter 4 --- Nonlinear Model Predictive Control Using a Recurrent Neural Network --- p.36Chapter 4.1 --- Problem Formulation --- p.36Chapter 4.2 --- A Recurrent Neural Network Approach --- p.40Chapter 4.2.1 --- Neural Network Model --- p.40Chapter 4.2.2 --- Learning Algorithm --- p.41Chapter 4.2.3 --- Control Scheme --- p.41Chapter 4.3 --- Application to Mobile Robot Tracking --- p.42Chapter 4.3.1 --- Example 1 --- p.44Chapter 4.3/2 --- Example 2 --- p.44Chapter 4.3.3 --- Example 3 --- p.46Chapter 4.3.4 --- Example 4 --- p.48Chapter 5 --- Model Predictive Control of Unknown Nonlinear Dynamic Sys- tems Based on Recurrent Neural Networks --- p.50Chapter 5.1 --- MPC System Description --- p.51Chapter 5.1.1 --- Model Predictive Control --- p.51Chapter 5.1.2 --- Dynamical System Identification --- p.52Chapter 5.2 --- Problem Formulation --- p.54Chapter 5.3 --- Dynamic Optimization --- p.58Chapter 5.3.1 --- The Simplified Dual Neural Network --- p.59Chapter 5.3.2 --- A Recursive Learning Algorithm --- p.60Chapter 5.3.3 --- Convergence Analysis --- p.61Chapter 5.4 --- RNN-based MPC Scheme --- p.65Chapter 5.5 --- Simulation Results --- p.67Chapter 5.5.1 --- Example 1 --- p.67Chapter 5.5.2 --- Example 2 --- p.68Chapter 5.5.3 --- Example 3 --- p.76Chapter 6 --- Model Predictive Control for Systems With Bounded Uncertainties Using a Discrete-Time Recurrent Neural Network --- p.81Chapter 6.1 --- Problem Formulation --- p.82Chapter 6.1.1 --- Process Model --- p.82Chapter 6.1.2 --- Robust. MPC Design --- p.82Chapter 6.2 --- Recurrent Neural Network Approach --- p.86Chapter 6.2.1 --- Neural Network Model --- p.86Chapter 6.2.2 --- Convergence Analysis --- p.88Chapter 6.2.3 --- Control Scheme --- p.90Chapter 6.3 --- Simulation Results --- p.91Chapter 7 --- Summary and future works --- p.95Chapter 7.1 --- Summary --- p.95Chapter 7.2 --- Future works --- p.96Bibliography --- p.9

A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization

In this paper, we propose a new tractable framework for dealing with linear dynamical systems affected by uncertainty, applicable to multistage robust optimization and stochastic programming. We introduce a hierarchy of near-optimal polynomial disturbance-feedback control policies, and show how these can be computed by solving a single semidefinite programming problem. The approach yields a hierarchy parameterized by a single variable (the degree of the polynomial policies), which controls the trade-off between the optimality gap and the computational requirements. We evaluate our framework in the context of three classical applications-two in inventory management, and one in robust regulation of an active suspension system-in which very strong numerical performance is exhibited, at relatively modest computational expense.National Science Foundation (U.S.) (Grant EFRI-0735905)National Science Foundation (U.S.) (Grant DMI-0556106)United States. Air Force Office of Scientific Research (Grant FA9550-06-1-0303

Minimizing the Adverse Effects of Electric Fields in Magnetic Resonance Imaging using Optimized Gradient Encoding and Peripheral Nerve Models

Magnetic Resonance Imaging (MRI) is an important imaging modality in both the clinic and in research. MRI technology has been trending toward increasing field strengths to improve the signal-to-noise ratio of the MR signal and fast excitation/encoding strategies to more flexible target anatomical regions during excitation to reduce the total imaging time. While largely successful, both strategies rely on the application of increasingly strong and rapidly switched magnetic fields: the radio frequency (RF) field for excitation and the gradient field for encoding. The technology for generating these fields (and rapidly switching them) has advanced to the point that we are limited by biological responses to the switching fields. For the gradient field, the electric field generated in the tissue causes peripheral nerve stimulation (PNS) causing mild but bothersome sensations at low levels, up to pain or cardiac malfunction at higher levels. The electric fields created by the much faster time-varying RF cause heat deposition, ultimately denaturing proteins and causing tissue damage. In this thesis, methods are presented to characterize and minimize these two problems associated with the switched magnetic fields in MRI. The deposited RF energy (Specific Absorption Rate, SAR) incurred during shaped excitations can be significantly reduced by optimizing gradient and RF waveforms for inner-volume excitations that allow imaging of a sub-volume of the body without wrapping artifacts. The adverse effects of the switching gradient fields are addressed by designing time-optimal gradient encoding waveforms and by developing a method to predict and characterize PNS using field simulations and a full-body nerve model allowing these critical effects to be addressed at the gradient coil design stage. In the first part, time-optimal gradient trajectories are demonstrated that use the gradient hardware at the maximum available performance. The skeleton of the trajectory is defined by a set of k-space control points. The method optimizes gradient waveforms that traverse the k-space control points in the minimum possible amount of time. By using an analytic representation of the gradients (piece-wise linear), the design process is fast and numerically robust. The resulting trajectories sample k-space efficiently while using the gradient system at maximum performance. Compared to the leading Optimal Control method, the proposed method generates gradient waveforms that are 9.2% shorter. The computation process is ∼100x faster and does not suffer from numerical instabilities such as oscillations. In the second part, a method is developed that jointly optimizes parallel transmission RF and gradient waveforms for fast and robust 3-D inner-volume excitation of the MRI signal in minimal time and with minimal energy deposition. The optimization of the k-space trajectories is based on a small number of shape parameters that are well-suited for joint optimization with the RF waveforms. Within each iteration of the trajectory optimization, a small tip-angle least-squares RF pulse design problem is solved. Using optimized 3-D cross (shells) trajectories, a cube shape (brain shape) region was excited with 3.4% (6.2%) NRMSE in less than 5 ms using a 7 T scanner with 8 Tx channels and a clinical gradient system (Gmax = 40 mT/m, Smax = 150 T/m/s). Incorporation of off-resonance robustness in the pulse design significantly altered the k-space trajectory solutions and improved the practical performance of the pulses. In the final part, a framework is presented that simulates PNS thresholds for realistic gradient coil geometries and thus allows, for the first time, to directly address PNS in the coil design process. The PNS framework consists of an accurate body model for simulation of the induced electric fields, an atlas of peripheral nerves, and a neurodynamic model to predict the nerve responses to imposed electric fields. With this model, measured PNS thresholds of two leg/arm solenoid coils and three commercial actively-shielded MR gradient coils could be reproduced with good accuracy. The proposed method can be used to assess the PNS capability of gradient coils during the design phase, without building expensive prototype coils

A portfolio stock selection model based on expected utility, entropy and variance

In the context of investment decision-making, the selection of stocks is important for a successful construction of portfolios. In this paper the expected utility, entropy and variance (EU-EV) model is applied for stock selection, which can be used as preselection model for mean-variance portfolio optimization problems. Based on the EU-EV risk, stocks are ranked and the best ranked stocks with lower risk are selected in order to form subsets of stocks, which are then used to construct portfolios. The EU-EV model is applied to the PSI 20 index, to the Euro Stoxx 50 index and to the Nasdaq 100 index. Subsets of selected stocks are analysed and their portfolios' efficiencies are compared with those of the portfolios obtained from the whole set of stocks using the mean-variance model. The results reveal that the EU-EV model is an adequate stock selection model for building up efficient portfolios with a lower number of stocks.The author thanks the reviewers for helpful comments. The author thanks support from FCT (“Fundação para a Ciência e a Tecnologia”) through the Projects UIDB/00013/2020 and UIDP/00013/2020