Constrained Objective Function Research Articles

One-Step Image Reconstruction for Cine MRI with a Quadratic Constraint

Motivation: In cine MRI, the measurements within each timeframe alone are too noisy for image reconstruction. Some information must be ‘borrowed’ from other time frames and the reconstruction algorithm is a slow iterative procedure. Goals: We set up a constrained objective function, which uses the measurements at other time frames to regularize the image reconstruction. We derive a non-iterative algorithm to minimize this objective function. Approach: The derivation of the algorithm is based on the calculus of variations. The resultant algorithm is in the form of filtered backprojection. Results: The feasibility of the proposed algorithm is demonstrated with a clinical patient brain study. Impact: Non-iterative reconstruction that minimizes a constrained objective function significantly increases the throughput in healthcare institutions. This may translate to reduced healthcare costs. The new reconstruction formula has a closed form that gives an explicit expression of how to incorporate the reference image in dynamic reconstruction.

An improved stochastic inversion method for 3D elastic impedance under the prior constraints of random medium parameters

Three-dimensional (3D) elastic impedance inversion is widely used in oil and gas exploration with its excellent identification of reservoirs and noise immunity. However, modifying the prior information directly in inversion will undoubtedly destroy the spatial autocorrelation structure of the elastic impedance. Maintaining the elastic impedance spatial autocorrelation structure in seismic inversion is of great significance for guiding the reservoir identification and prediction. The 3D prior information construction method is proposed under the constraint of random medium parameters. This method establishes an intrinsic connection between random medium parameters and elastic impedance based on seismic data and well data, which provides a theoretical basis for simulating prior information satisfying the spatial correlation of the subsurface medium. To ensure the invariance of the spatial structure term in the inversion process, the random term and the spatial structure term in the simulation process are separated by the gradual deformation method (GDM), and the priori constrained objective function is further constructed to reduce the inversion uncertainty. Numerical example shows that the relative error of the proposed simulation method is smaller than that of conventional sequential Gaussian simulation, and the details are more accurately depicted based on the priori inversion results in this study. In addition, the elastic impedance equation based on the p-wave modulus is derived by combining with the reservoir sensitive parameters in field data. The field examples document that this method can effectively perform high-resolution geophysical prediction of underground thin-layer reservoirs.

An improved model predictive control method for path tracking of autonomous vehicle considering longitudinal velocity

In order to increase the accuracy of the path tracking, an improved model predictive control (IMPC) is proposed for autonomous vehicle under road conditions of large curvature, which can enhance the performances of the driving stability and safety. The controller design is implemented in four steps. First, the curvature of road ahead is derived and applied to determine the longitudinal velocity. Thus, the longitudinal velocity is not assumed to be constant, which is the salient feature of the proposed control. Second, the kinematic model of vehicle is established by the Ackermann steering principle. Third, the predictive model is constructed by linearization and discretization of the kinematic model. Fourth, the longitudinal velocity and the front steering angle are imposed on hard constraints, and the constrained objective function is designed and composed of the position deviation and the control increment. Then, we can obtain the optimal results of the longitudinal velocity and the front steering angle. Furthermore, experiment and simulation on the path tracking of an autonomous vehicle are presented. The results show that the proposed control can realize excellent tracking performance under the road conditions of large curvature.

Distribution preserving-based deep semi-NMF for data representation

The semi-nonnegative matrix factorization (Semi-NMF) is a promising soft K-means clustering technique. Deep Semi-NMF, which stacks one-layer Semi-NMF into multi-layer, is able to learn the hierarchical projections and can obtain the deep hidden representations according to the unknown attributes of the given data. On the other hand, the inherent structure of the each data cluster can be described by the distribution of the intraclass data. Then one hopes to learn the new deep hidden representations which can preserve the intrinsic structures embedded in the original data space perfectly. Here seamlessly integrating the benefits of the Deep Semi-NMF and the distribution preserving strategy, we propose a novel distribution preserving-based deep semi-nonnegative matrix factorization method (DPNMF) to achieve this goal. In DPNMF, by maintaining the consistency of two distributions that can approximate the manifold structures, we can seek the deep hidden features which reveal the original intrinsic structures. As a result, the manifold structures in the raw data are well preserved in the new feature space. We also devise an adaptive projected Barzilai-Borwein method to optimize the proposed constrained objective function efficiently. The experimental results on the several real-world datasets show that the proposed DPNMF can achieve advantageous clustering performance in terms of accuracy (ACC), normalized mutual information (NMI), and adjusted rand index (ARI).

Seismic inversion with L2,0-norm joint-sparse constraint on multi-trace impedance model

Impedance inversion of post-stack seismic data is a key technology in reservoir prediction and characterization. Compared to the common used single-trace impedance inversion, multi-trace impedance simultaneous inversion has many advantages. For example, it can take lateral regularization constraint to improve the lateral stability and resolution. We propose to use the L2,0-norm of multi-trace impedance model as a regularization constraint in multi-trace impedance inversion in this paper. L2,0-norm is a joint-sparse measure, which can not only measure the conventional vertical sparsity with L0-norm in vertical direction, but also measure the lateral continuity with L2-norm in lateral direction. Then, we use a split Bregman iteration strategy to solve the L2,0-norm joint-sparse constrained objective function. Next, we use a 2D numerical model and a real seismic data section to test the efficacy of the proposed method. The results show that the inverted impedance from the L2,0-norm constraint inversion has higher lateral stability and resolution compared to the inverted impedance from the conventional sparse constraint impedance inversion.

Active control of structures using genetic algorithm with dynamic weighting factors using in the constrained objective function

Active control method by improving specification of well-known intelligent numerical search method i.e. genetic algorithm is developed here. This method reduces displacement of the structure by optimizing the control forces at each time step. The efficiency of the genetic algorithm as a part of nature-inspired metaheuristic methods is highly dependent on the constrained objective function. The constrained objective function is achieved by combining the constraints of the optimization problem. There are several methods to numerically combine these constraints. Using appropriate weighting factors to generate this function has been suggested by many researchers. In previous studies, the selection of these factors has been based on experimental or try and error methods and were constant throughout the control period. Proper selection of weighting factors increases the efficiency of the control method. Presenting a new genetic algorithm method in a way selecting weighting factors dynamically over the structural control period is the aim of this paper. Here, weighting factors are non-static in nature and are dynamically selected at each time step according to the memory of the previous step. Numerical results clearly prove the accuracy and efficiency of the proposed control process in comparison with Constant weighting factors methods.

Mitigating the Effect of Electric Vehicle integration in Distribution Grid using Slime Mould Algorithm

The effects of electric vehicle (EV) integration in three different urban residential neighborhoods of Bangladesh are assessed in this work. A Monte Carlo simulation-based stochastic load flow algorithm is developed to analyze system parameters such as aggregated power demand, voltage profile, energy losses, and voltage stability margin (VSMsys). Two scenarios for EV penetration (20% and 30%) were investigated, and the implications of seasonal load variation were assessed. The Monte Carlo results indicate that one of the areas is susceptible to sustaining EVs in the present system due to the potential of voltage collapse. The results also suggest that the other two areas would be able to accommodate EVs in the future. Finally, a slime mould algorithm (SMA)-based optimization approach is developed and applied to the relevant networks to identify their optimal charging strategies based on the outcomes of the Monte-Carlo simulation. A constrained objective function with an optimal amount of load, (VSMsys) index, and total active power loss was formulated to complete the assessment. The results indicate that the proposed optimal charging approach improves the grid’s capacity to accommodate a more significant proportion of the EV load while maintaining ideal system voltage and reducing power loss.

Multiobjective Evolutionary Interpretable Type-2 Fuzzy Systems With Structure and Parameter Learning for Hexapod Robot Control

This article proposes a data-driven multiobjective evolutionary interval type-2 fuzzy-logic system (IT2FLS) learning approach that considers both system performance and rule interpretability. One characteristic of the evolutionary learning framework is that the IT2FLS structure is incrementally generated instead of searching from an initially huge grid-type rule base, which significantly reduces the parameter search space. Another one is that a new constrained objective function is proposed to improve the distinguishability of the generated interval type-2 fuzzy sets (FSs) without restricting them to be evenly distributed. Because of the tradeoff between system performance and interpretability, a new multiobjective ant colony optimization (ACO) algorithm is proposed to optimize the IT2FLS parameters and improve optimization performance. The evolutionary IT2FLS learning approach is applied to control a real wall-following hexapod robot. The approach shows the advantages of model-free design and interpretability and robustness to noise in the evolved type-2 fuzzy rules. Simulations with performance comparisons and experiments in controlling a real robot show the advantages of the learning approach.

A compact spline-enhanced monopole antenna for broadband/multi-band and beyond UWB applications

In this work, a compact monopole antenna for broadband/multi-band and beyond ultra-wideband (UWB) communication has been proposed. The structure is based on a spline-enhanced radiator with a broadband feed and a modified ground plane. Rigorous design optimization of the radiator has been performed in a two-stage framework where optimization of the structure with respect to electrical performance is followed by explicit miniaturization using a constrained objective function. Two compact radiators characterized by footprints of 404 mm2 and 322 mm2, as well as frequency ranges from 2.8 GHz to 34.9 GHz and from 2.9 GHz to 33.9 GHz have been designed. Except for a relatively narrow frequency range in Ka band (from 34.9 GHz to 37.8 GHz), the larger structure is capable of operating for up to 80 GHz. Owing to a simple topology, small size and broadband operation, the presented antennas are of potential use in mobile terminals dedicated to support various wireless technologies including Internet of Things, WiFi, or UWB-based localization services. The proposed radiators have been benchmarked against other broadband/beyond UWB antennas from the literature. Electrical and field characteristics of the proposed structures have been confirmed through measurements of the fabricated prototypes.

Tensor factorization-based particle swarm optimization for large-scale many-objective problems

• A tensor factorization-based particle swarm optimization is proposed to directly dived large-scale decision space into small-scale sub-spaces, alleviating the dimensionality cures of large-scale problems. • An circular algorithm of sub-population is designed to asymptotically push the whole population to the true Pareto front. • The proposed tensor factorization-based model can be applied to other large-scale and multi-objective evolutionary algorithms. In this paper, a tensor factorization-based circular optimization algorithm of subpopulations is proposed to solve multi- and many-objective optimization problems with large-scale decision variables. Various intermediated procedures, such as variable analysis, clustering, and grouping, to divide large-scale decision variables are needed by most existing algorithms, seriously affecting the optimization performance. The tensor factorization, which is excellent in decomposition and dimensionality reduction of tensors, is originally introduced to the proposed algorithm to decompose the large-scale decision space into small-scale sub-spaces. Then an evolutionary strategy is designed to optimize these sub-populations by speed-constrained multi-objective particle swarm optimization circularly, searching for ideal solutions in each newly constructed lower-scale sub-space. Finally, tensor factorization is used to reconstruct the whole population for asymptotically optimizing the population by all the subpopulations. Using the proposed algorithm on some well-known multi-objective and many-objective benchmarks with 1000 decision variables, it outperformed other state-of-the-art algorithms both in solution quality and convergence rate. The main weakness of the proposed algorithm is the reconstruction error caused by the tensor factorization, which slows down the convergence rate of optimization. Hence our future work is to construct a constrained objective function with the restricted condition of the sparsity of the tensor, which affects the reconstruction error, and seek the solving algorithm.

Physical Model-Inspired Deep Unrolling Network for Solving Nonlinear Inverse Scattering Problems

In this article, to bridge the gap between the traditional model-based methods and data-driven deep learning schemes, we propose a physical model-inspired deep unrolling network for solving nonlinear inverse scattering problems, termed PM-Net. The proposed end-to-end network is formed by two consequent steps. First, an augmented Lagrangian method is introduced to transform a constrained objective function to be an unconstrained optimization. In addition, it is further decomposed into four quasi-linear subproblems. Second, we unfold the iterative scheme into a layer-wise deep neural network. Each subproblem is mapped into a module of the deep unrolling network. In PM-Net, these variables including the weight, the regularization of contrast, and other parameters are learned and updated alternately by corresponding network layers. PM-Net effectively combines neural networks with the knowledge of underlying physics as well as traditional techniques. Unlike existing networks, PM-Net explicitly exploits contrast source and contrast modules. Compared to traditional iterative methods, the performance of PM-Net is comparable or even better than subspace-based optimization method in the high noise-level circumstance. Compared to the state-of-the-art learning approaches, not only less network parameters need to be learned, but also better performance is achieved by PM-Net.

Abdominal T2-Weighted Imaging and T2 Mapping Using a Variable Flip Angle Radial Turbo Spin-Echo Technique.

T2 mapping is of great interest in abdominal imaging but current methods are limited by low resolution, slice coverage, motion sensitivity, or lengthy acquisitions. Develop a radial turbo spin-echo technique with refocusing variable flip angles (RADTSE-VFA) for high spatiotemporal T2 mapping and efficient slice coverage within a breath-hold and compare to the constant flip angle counterpart (RADTSE-CFA). Prospective technical efficacy. Testing performed on agarose phantoms and 12 patients. Focal liver lesion classification tested on malignant (N=24) and benign (N=11) lesions. 1.5 T/RADTSE-VFA, RADTSE-CFA. A constrained objective function was used to optimize the refocusing flip angles. Phantom and/or in vivo data were used to assess relative contrast, T2 estimation, specific absorption rate (SAR), and focal liver lesion classification. STATISTICAL TESTS: t-Tests or Mann-Whitney Rank Sum tests were used. Phantom data did not show significant differences in mean relative contrast (P=0.10) and T2 accuracy (P=0.99) between RADTSE-VFA and RADTSE-CFA. Adding noise caused T2 overestimation predominantly for RADTSE-CFA and low T2 values. In vivo results did not show significant differences in mean spleen-to-liver (P=0.62) and kidney-to-liver (P=0.49) relative contrast between RADTSE-VFA and RADTSE-CFA. Mean T2 values were not significantly different between the two techniques for spleen (T2VFA =109.2 ± 12.3msec; T2CFA =110.7 ± 11.1msec; P=0.78) and kidney-medulla (T2VFA =113.0 ± 8.7msec; T2CFA =114.0 ± 8.6msec; P=0.79). Liver T2 was significantly higher for RADTSE-CFA (T2VFA =52.6 ± 6.6msec; T2CFA =60.4 ± 8.0msec) consistent with T2 overestimation in the phantom study. Focal liver lesion classification had comparable T2 distributions for RADTSE-VFA and RADTSE-CFA for malignancies (P=1.0) and benign lesions (P=0.39). RADTSE-VFA had significantly lower SAR than RADTSE-CFA increasing slice coverage by 1.5. RADTSE-VFA provided noise-robust T2 estimation compared to the constant flip angle counterpart while generating T2-weighted images with comparable contrast. The VFA scheme minimized SAR improving slice efficiency for breath-hold imaging. 2 TECHNICAL EFFICACY STAGE: 1.

Safe option-critic: learning safety in the option-critic architecture

AbstractDesigning hierarchical reinforcement learning algorithms that exhibit safe behaviour is not only vital for practical applications but also facilitates a better understanding of an agent’s decisions. We tackle this problem in the options framework (Sutton, Precup & Singh, 1999), a particular way to specify temporally abstract actions which allow an agent to use sub-policies with start and end conditions. We consider a behaviour assafethat avoids regions of state space with high uncertainty in the outcomes of actions. We propose an optimization objective that learnssafeoptions by encouraging the agent to visit states with higher behavioural consistency. The proposed objective results in a trade-off between maximizing the standard expected return and minimizing the effect of model uncertainty in the return. We propose a policy gradient algorithm to optimize the constrained objective function. We examine the quantitative and qualitative behaviours of the proposed approach in a tabular grid world, continuous-state puddle world, and three games from the Arcade Learning Environment: Ms. Pacman, Amidar, and Q*Bert. Our approach achieves a reduction in the variance of return, boosts performance in environments with intrinsic variability in the reward structure, and compares favourably both with primitive actions and with risk-neutral options.

New genetic algorithm for structural active control by considering the effect of time delay

This study focuses on a new active control method by improving specification of a well-known intelligent numerical search method, that is the genetic algorithm. The proposed scheme modifies the specifications of the common genetic algorithm by using two strategies. First, a new constrained objective function is proposed. Then, a procedure is designed for evaluating and reducing time delay in control process. These procedures lead to a new generation of the genetic algorithm, which is more reliable. For verifying the efficiency of the proposed method, vibrations of several structures are controlled, and results are compared with other well-known methods such as the common genetic algorithm, linear quadratic regulator, and equivalent critical damping. Numerical results clearly prove the accuracy and efficiency of the proposed control process in comparison with other methods.

Supervised deep semantics-preserving hashing for real-time pulmonary nodule image retrieval

Hashing-based medical image retrieval has drawn extensive attention recently, which aims at providing effective aided diagnosis for medical personnel. In the paper, a novel deep hashing framework is proposed in the medical image retrieval, where the processes of deep feature extraction, binary code learning, and deep hash function learning are jointly carried out in supervised fashion. Particularly, the discrete constrained objective function in the hash code learning is optimized iteratively, where the binary code can be directly solved with no need for relaxation. In the meantime, the semantic similarity is maintained by fully exploring supervision information during the discrete optimization, where the neighborhood structure of training data is preserved by applying a graph regularization term. Additionally, to gain the fine-grained ranking of the returned medical images sharing the same Hamming distance, a novel image re-ranking scheme is proposed to refine the similarity measurement by jointly considering Euclidean distance between the real-valued feature descriptors and their category information between those images. Extensive experiments on the pulmonary nodule image dataset demonstrate that the proposed method can achieve better retrieval performance over the state of the arts.

Optimal Power Flow in Uncertain Power System

Due to the increasing demand of electricity in ever-growing electricity market, it is necessary to observe the nature of load and map the effects of load uncertainties on the operation of power system. These uncertainties have also led to voltage instability which is sooner or later considered to be a fundamental cause of blackouts. The distributed generation sources can also be regarded as the source of uncertainties at the load ends of power systems. Along with the load uncertainties, wind turbine generation (WTG) and solar plants have also been used as a source of uncertainties in this paper. The load uncertainties have been incorporated in the system by designing a dynamic load flow program. Corresponding to all uncertain inputs critical case has been identified by the singularity property of load flow jacobian. For the optimal load flow a multi-objective optimization problem aiming to constrained objective function to enhance voltage stability, improve stability index value, reduce system losses and increase reactive reserve margins at generator buses has been formulated. Black hole algorithm has been used to achieve the optimal values of control variables and hence optimal load flow. The aforementioned problem has been tested on standard IEEE-14 bus system.

Bimodal Automated Carotid Ultrasound Segmentation Using Geometrically Constrained Deep Neural Networks

For asymptomatic patients suffering from carotid stenosis, the assessment of plaque morphology is an important clinical task which allows monitoring of the risk of plaque rupture and future incidents of stroke. Ultrasound Imaging provides a safe and non-invasive modality for this, and the segmentation of media-adventitia boundaries and lumen-intima boundaries of the Carotid artery form an essential part in this monitoring process. In this paper, we propose a novel Deep Neural Network as a fully automated segmentation tool, and its application in delineating both the media-adventitia boundary and the lumen-intima boundary. We develop a new geometrically constrained objective function as part of the Network's Stochastic Gradient Descent optimisation, thus tuning it to the problem at hand. Furthermore, we also apply a bimodal fusion of amplitude and phase congruency data proposed by us in previous work, as an input to the network, as the latter provides an intensity-invariant data source to the network. We finally report the segmentation performance of the network on transverse sections of the carotid. Tests are carried out on an augmented dataset of 81,000 images, and the results are compared to other studies by reporting the DICE coefficient of similarity, modified Hausdorff Distance, sensitivity and specificity. Our proposed modification is shown to yield improved results on the standard network over this larger dataset, with the advantage of it being fully automated. We conclude that Deep Neural Networks provide a reliable trained manner in which carotid ultrasound images may be automatically segmented, using amplitude data and intensity invariant phase congruency maps as a data source.

Modelling and Parameters Extraction of Flexible Amorphous Silicon Solar Cell a-Si:H

The precise of solar cell model parameters being the prerequisite for realizing accurate photovoltaic models. Hence, the parameters identification techniques have attracted immense interest over the years among the researchers. This paper proposes a modelling and prediction of electrical intrinsic parameter extraction method of flexible hydrogenated amorphous silicon a-Si:H solar cell, based on the meta-heuristic firefly algorithm (FA). The characteristics of solar cells are non-linear, multivariable and multi-modal and difficult to identifies the electrical intrinsic parameters by conventional and analytical methods with high accuracy. Recently, the firefly algorithm has attracted the attention to optimize the non-linear and complex systems, based on the flashing patterns and behaviour of firefly’s swarm. Besides, the proposed constrained objective function is derived from the current–voltage curve. It is the absolute errors between the experimental and calculated current and voltage values. Furthermore, the obtained results of the proposed algorithm are compared with the results obtained by quasi-Newton method (Q-N) and self-organizing migrating algorithm (SOMA). Indeed, to validate the performance of the algorithm, the statistical analyses are carried out to measure the accuracy of the estimated parameters. In the end, the theoretical results of the firefly algorithm show an excellent agreement with experimental data and more accurate compared to other compared techniques.

A collection of bivariate nonlinear optimisation test problems with graphical representations

Plotting objective functions, whenever possible, allows constraint activity, modality and convexity, as well as landscape features like basins, plateaus, valleys and saddle points, to be intuitively identified. Knowledge of these properties allow researchers to best select a set of functions for rating existing optimisation algorithms, when developing new search algorithms or for their control parameter tune-up. This paper offers a selection of 30 bivariate constrained objective functions accompanied by graphical representations. It is the first time a significant number of constrained-functions with their plots are gathered in one place. Also provided are the minima, maxima (global and local) and saddle point information of these functions, very useful in 'all optima' studies.

A collection of bivariate nonlinear optimisation test problems with graphical representations

Plotting objective functions, whenever possible, allows constraint activity, modality and convexity, as well as landscape features like basins, plateaus, valleys and saddle points, to be intuitively identified. Knowledge of these properties allow researchers to best select a set of functions for rating existing optimisation algorithms, when developing new search algorithms or for their control parameter tune-up. This paper offers a selection of 30 bivariate constrained objective functions accompanied by graphical representations. It is the first time a significant number of constrained-functions with their plots are gathered in one place. Also provided are the minima, maxima (global and local) and saddle point information of these functions, very useful in 'all optima' studies.