Constrained Optimization Framework Research Articles

Constrained optimization framework for interface-aware sub-scale dynamics discrete closure model for multimaterial cells in Lagrangian cell-centered hydrodynamics

We present the new discrete optimization-based interface-aware sub-scale dynamics (IA-SSD) closure model for multimaterial cells for Lagrangian cell-centered hydrodynamics. For the multimaterial cell, the kinematic and thermodynamic properties (e.g., velocity, density, pressure and internal energy) will typically vary between the materials. The discrete closure model is responsible for an accurate update of the thermodynamic states of the individual material components in the multimaterial cell, and for determining the nodal forces that move the vertices of the cell. The IA-SSD closure model consists of two stages — a bulk stage followed by a sub-scale stage. During the bulk stage, the total change in the volume of the cell, total force applied to the cell, and total work done on the cell are distributed between the materials to update their volume, velocity and total energy. This distribution is performed using volume fractions of the materials. During the second stage, sub-scale interactions of the materials inside the multimaterial cell are taken into account. At this stage, information about the topology of the materials inside the multimaterial cell is used, allowing the orientations of internal interfaces to be included in the model. Each material interacts in a pair-wise fashion with the materials with which it has a common boundary. The interactions are based on the solution of the acoustic Riemann problem between each pair of materials and are limited using physically justified constraints: positivity of volume, positivity of internal energy, and controlled rate of pressure relaxation. To determine the values of the limiter coefficients, a constrained-optimization framework is employed using a quadratic objective function with linear constraints. It is a first-of-its kind application of constrained optimization to develop discrete closure models in a more rigorous fashion. The pair-wise interaction between materials is essentially one dimensional in the direction that is normal to interface. For this reason, we demonstrate in this paper the performance of our new model on one dimensional numerical examples.

Cooperative Differential Evolution Framework for Constrained Multiobjective Optimization.

This paper presents a cooperative differential evolution framework (CCMODE) for constrained multiobjective optimization, and two instantiations of the CCMODE framework are implemented. The proposed framework has (M+1) populations, including M subpopulations for constrained single-objective optimization and an archive population for constrained M -objective optimization. Each subpopulation performs its own constrained single-objective differential evolution to optimize the assigned constrained single-objective optimization problem. For the archive population, the constraint handling techniques (CHTs) are modified for constrained multiobjective optimization. The proposed framework takes the advantage of existing effective constrained single-objective optimization algorithms, and extends them to deal with constrained multiobjective optimization problems. In two instantiations, two CHTs are implemented in CCMODE framework, respectively. Experiment results on several sets of benchmark problems with two, three, and many objectives show that the proposed algorithm is better than existing state-of-the-art constrained multiobjective evolutionary algorithms. The effectiveness of the subpopulations is also discussed.

Constrained optimization framework for interface-aware sub-scale dynamics models for voids closure in Lagrangian hydrodynamics

In hydrocodes, voids are used to represent vacuum and model free boundaries between vacuum and real materials. We give a systematic description of a new treatment of void closure in the framework of the multimaterial arbitrary Lagrangian–Eulerian (ALE) methods. This includes a new formulation of the interface-aware sub-scale-dynamics (IA-SSD) closure model for multimaterial cells with voids, which is used in the Lagrangian stage of our indirect ALE scheme.The results of the comprehensive testing of the new model are presented for one- and two-dimensional multimaterial calculations in the presence of voids. We also present a sneak peek of a realistic shaped charge calculation in the presence of voids and solids.

Simultaneous Optimization of Geometry and Firing Angles for In-Wheel Switched Reluctance Motor Drive

Interests in using rare-earth free motors such as switched reluctance motors (SRMs) for electric and hybrid electric vehicles continue to gain popularity, owing to their low cost and robustness. Optimal design of an SRM, to meet specific characteristics for an application, should involve simultaneous optimization of the motor geometry and control in order to achieve the highest performance with the lowest cost. This paper presents a constrained multiobjective optimization framework for design and control of an SRM based on a nondominated sorting genetic algorithm II. The proposed methodology optimizes SRM operation for high volume traction applications by considering multiple criteria including efficiency, average torque, and torque ripple. Several constraints are defined by the considered application, such as the motor stack length, outer diameter, minimum operating power, minimum desired efficiency, rated speed, rated current, and supply voltage. The outcome of this optimization includes an optimal geometry, outlining variables such as air gap length, rotor inner diameter, stator pole arc angle, rotor pole arc angle, rotor back iron, stator pole height, and stator inner diameter as well as optimal turn-on and turn-off firing angles. Then the machine is manufactured according to the obtained optimal specifications. Comprehensive finite-element analysis and experimental results are provided to validate the theoretical findings.

Constrained Optimization for Image Reshaping With Soft Conditions

Conventional image resizing problems demand hard conditions on size and aspect ratio, which must be met with no tolerance. In this paper, a generalized optimization framework is presented, which can handle soft conditions as well as the hard ones. The soft condition can be given by an allowable range of the image parameter, which is incorporated as an inequality condition in the constrained optimization framework. Given the soft constraints, the proposed framework seeks to find the set of image parameters that minimize the cost function. A constrained optimization via a linear programming framework is employed to manage a diverse combination of soft and hard conditions for the target image. The optimization is based on the image line, which optimally selects a set of image lines (columns and rows) to be deleted for size reduction in accordance with the cost function and the constraints. As a case study, the line-based optimal image resizing method based on the linear programming framework is applied for the pre-processing of VGG-19 convolutional neural network (CNN). Although the target input size is a hard condition of $224\times 224$ for the VGG-19 CNN, the proposed optimization framework with a soft condition on the image size firstly finds an optimal near-square image with a tradeoff against the saliency level of image features. Then, the optimal near-square image is linearly scaled to the final image size to meet the hard condition.

Spectrum efficiency analysis for multicast services in cognitive radio based wireless networks

Cognitive radio is a prominent technology for improving radio spectrum efficiency. In this paper, we study an underlay cognitive radio network (CRN), consisting of a cognitive base station (CBS) and multiple multicast group of secondary users (SUs). A common primary user (PU) channel is used to support multicast services to a group of SUs. Our objective is to minimize the outage probability of the SU multicast groups. The problem is formulated using constrained optimization framework under the constraints of PUs’ outage probability and CBS’s average transmit power. An efficient transmit power allocation scheme, which determines the optimal power for each SU multicast group, is proposed. Simulation results are presented to validate the proposed power allocation scheme, thereby improving the spectrum efficiency of the CRN.

Cross layer optimization for outage minimizing routing in cognitive radio ad hoc networks with primary users’ outage protection

Path selection to minimize end-to-end (e2e) outage experience of cognitive users (CUs) in a given communication session is one of the key challenges in multi-hop cognitive radio ad hoc networks, where each CU node experiences a unique spatio-temporal variation of spectrum access opportunity. We study the problem under the constraint of probabilistic interference to primary receivers, in contrast to the popular trend of considering detection probability of primary user (PU) transmissions. This is formulated as a joint transmit power control, spectrum assignment and routing problem and a constrained optimization framework are presented for it. Further, using a standard technique for solving the convex optimization problem, a closed form expression for the transmission power of source as well as relay nodes is derived. Based on this, a centralized solution is proposed for optimal spectrum assignment and route selection. In addition, due to the prohibitive complexity of the optimal solution, a low complexity spectrum aware-outage minimizing opportunistic routing (SA-OMOR) solution is presented, along with its possible distributed implementation. Simulation results are used to validate our analytical results as well as the performance comparison between the proposed SA-OMOR scheme and the optimal one.

A Gauss–Newton full-waveform inversion in PML-truncated domains using scalar probing waves

This study considers the characterization of subsurface shear wave velocity profiles in semi-infinite media using scalar waves. Using surficial responses caused by probing waves, a reconstruction of the material profile is sought using a Gauss–Newton full-waveform inversion method in a two-dimensional domain truncated by perfectly matched layer (PML) wave-absorbing boundaries. The PML is introduced to limit the semi-infinite extent of the half-space and to prevent reflections from the truncated boundaries. A hybrid unsplit-field PML is formulated in the inversion framework to enable more efficient wave simulations than with a fully mixed PML. The full-waveform inversion method is based on a constrained optimization framework that is implemented using Karush–Kuhn–Tucker (KKT) optimality conditions to minimize the objective functional augmented by PML-endowed wave equations via Lagrange multipliers. The KKT conditions consist of state, adjoint, and control problems, and are solved iteratively to update the shear wave velocity profile of the PML-truncated domain. Numerical examples show that the developed Gauss–Newton inversion method is accurate enough and more efficient than another inversion method. The algorithm's performance is demonstrated by the numerical examples including the case of noisy measurement responses and the case of reduced number of sources and receivers.

Active subspaces for the optimal meanline design of unconventional turbomachinery

The preliminary fluid dynamic design of turbomachinery operating with non-standard working fluids and unusual operating conditions and specifications can be very challenging because of the lack of know-how and guidelines. Examples are the design of turbomachinery for small-capacity organic Rankine cycle and supercritical CO2 cycle power plants, whereby the efficiency of turbomachinery components has also a strong influence on the net conversion efficiency of the system. These machines operate with the fluid in thermodynamic states which, for part of the process, largely deviate from those obeying to the ideal gas law. This in turn implies the presence of so-called non-ideal compressible fluid dynamics effects.Active subspaces, a model reduction technique, is at the basis of the methodology presented here, which is aimed at the optimal meanline design of unconventional turbomachinery. The resulting surrogate model depends on a very small set of non-physical variables, called active variables. The procedure integrates into a single constrained optimization framework the selection of the working fluid, the thermodynamic cycle calculation and the preliminary sizing of the turbomachinery component.As a demonstration of the advantages of the proposed approach, the design of a 10kW mini organic Rankine cycle turbine with a turbine inlet temperature of 240°C is illustrated. In this case, approximately the same maximum efficiency is estimated for three dissimilar turbines operating with different working fluids and rather different thermodynamic cycles. The use of active subspaces allows the seamless evaluation of the sensitivity of results to input parameters, both those related to the machine and the working fluid. The novel design procedure is compared in terms of computational efficiency to a conventional approach based on the coupling of a genetic algorithm directly with a meanline code. Results show that the calculation based on the use of surrogate models is more than two orders of magnitude faster. The surrogate can be used to solve any design problem within the specified boundaries of the design envelope. Results are affected by uncertainty on the estimation of losses and of non-ideal compressible fluid dynamics effects, which, in turn, do not affect the applicability of the method, which will become quantitatively accurate once this information will be available. Work to this end is underway in various laboratories.

Optimizing Adjustments to Transboundary Water Sharing Plans: A Multi-Basin Approach

Afghanistan contributes water supplies to Iran, Pakistan, Tajikistan, Turkmenistan, and Uzbekistan. However, with the exception of the Helmand Basin, Afghanistan has negotiated transboundary water sharing agreements with no downstream country. This paper describes a constrained optimization framework to minimize economic costs within each of nine Afghan transboundary basins of adapting to potential water sharing agreements. Model results show impacts of water agreements on farm income and food security for each Afghan basin. Our results show that unrestricted trading reduces the economic costs of adapting to water sharing treaties by two to 6 % compared to the conventional water sharing system. A higher scale of reservoir storage capacity as well as market trading of water among regions moderates costs of water shortages, both with and without water agreements in place.

On the Optimal Timing of Futility Interim Analyses

ABSTRACTFutility analyses provide a mechanism to stop a trial early because of low likelihood to achieve its efficacy objective. They are usually motivated by ethical and economic purposes, so that stopping a trial with poor efficacy could save patients and resources for other promising trials. There are various methods to address futility analyses in the literature but most focus on equally spaced interim looks. We consider a constrained optimization framework where the timing and the futility boundary are decided jointly to balance the risks between stopping trials which should continue, and continuing trials which should stop. The average sample size is used as a key parameter, which is evaluated under different degrees of power loss. Alternative objective functions and constraints are compared to assess the operating characteristics of the optimal futility scheme. Numerical results for single and multiple futility looks are provided. Supplementary materials for this article are available online.

A Bayesian Multivariate Functional Dynamic Linear Model

ABSTRACT We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data—functional, time dependent, and multivariate components—we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-invariant functional basis for the functional observations, which is smooth and interpretable, and can be made common across multivariate observations for additional information sharing. The Bayesian framework permits joint estimation of the model parameters, provides exact inference (up to MCMC error) on specific parameters, and allows generalized dependence structures. Sampling from the posterior distribution is accomplished with an efficient Gibbs sampling algorithm. We illustrate the proposed framework with two applications: (1) multi-economy yield curve data from the recent global recession, and (2) local field potential brain signals in rats, for which we develop a multivariate functional time series approach for multivariate time–frequency analysis. Supplementary materials, including R code and the multi-economy yield curve data, are available online.

Power Quality Constrained Optimal Management of Unbalanced Smart Microgrids During Scheduled Multiple Transitions Between Grid-Connected and Islanded Modes

In this paper, a novel power quality (PQ) constrained optimization framework for smart microgrids with nonlinear loads is proposed for scheduled multiple transitions between grid-connected and islanded modes. Loads, generation, and energy storage are optimally scheduled to maximize the overall microgrid profit, from selling energy to grid, while satisfying network and PQ constraints. Cost of power interruption to loads, steady-state frequency deviation during islanding, and power sharing among generators are considered. PQ and network constraints of three-phase unbalanced distribution microgrid are given in convex forms. Comprehensive simulation results are given for validating the proposed algorithm and effect of limiting total harmonic distortion on microgrid economics is investigated.

Nonlinear feature transformation and deep fusion for Alzheimer's Disease staging analysis

In this study, we develop a novel nonlinear metric learning method to improve biomarker identification for Alzheimer's Disease (AD) and Mild Cognitive Impairment (MCI). Formulated under a constrained optimization framework, the proposed method learns a smooth nonlinear feature space transformation that makes the mapped data more linearly separable for SVMs. The thin-plate spline (TPS) is chosen as the geometric model due to its remarkable versatility and representation power in generating sophisticated yet smooth deformations. In addition, a deep network based feature fusion strategy through stacked denoising sparse auto-encoder (DSAE) is adopted to integrate cross-sectional and longitudinal features estimated from MR brain images. Using the ADNI dataset, we evaluate the effectiveness of the proposed feature transformation and feature fusion strategies and demonstrate the improvements over the state-of-the-art solutions within the same category.

Solution of wind integrated thermal generation system for environmental optimal power flow using hybrid algorithm

A new evolutionary hybrid algorithm (HA) has been proposed in this work for environmental optimal power flow (EOPF) problem. The EOPF problem has been formulated in a nonlinear constrained multi objective optimization framework. Considering the intermittency of available wind power a cost model of the wind and thermal generation system is developed. Suitably formed objective function considering the operational cost, cost of emission, real power loss and cost of installation of FACTS devices for maintaining a stable voltage in the system has been optimized with HA and compared with particle swarm optimization algorithm (PSOA) to prove its effectiveness. All the simulations are carried out in MATLAB/SIMULINK environment taking IEEE30 bus as the test system.

Performance Assessment of an Urbain Collective Cars System

A constrained optimization framework of an autonomous urban transport system, associated with reduced rates, is presented. A decentralized management is considered where prior seat reservation is not a prerequisite for the system functioning. Well-adapted vehicle itineraries based on the current demand and vehicle state are constructed. The event-driven system dynamics characterizing the non-deterministic features of the corresponding complex mathematical problem, encourage for a discrete event system approach. The implied stressing needs of a comprehensive study, will be achieved by intense simulations. Various strategies, related to real time controls and system dimensioning as well, are studied. A methodology appraising the system performance is introduced where the resulting system behaviour is evaluated in terms of client waiting time, detours, vehicle occupancy, travel times etc. Moreover, optimal parameter tuning is discussed underlying the importance of reasonable trade-offs for achieving the desired performance. Thus, involving optimisation, operational research methods and simulation techniques a significantly efficacious well-operating system can be achieved, providing the best suited configuration for any demand level and geometry. Utilising previously wasted vehicle capacity may reduce costs for both vehicles and clients while forms an ongoing attempt to control extended traffic congestion, air pollution, energy consumption etc.

Fuzzy rule base simplification using multidimensional scaling and constrained optimization

This paper proposes a novel approach for the development of highly accurate and interpretable fuzzy models with Gaussian fuzzy sets, under the framework of multidimensional scaling and non-linear constrained optimization. Upon the assumption that an accurate initial fuzzy model has already been designed, we introduce an effective methodology to approximate the similarity measure between fuzzy sets. The resulting similarity degrees guide the quantification of the dissimilarity degrees between rule antecedents. We, then, put the multidimensional scaling in place in order to transform the rule antecedents into points in a low dimensional Euclidean space. The elaboration on the distribution of these points is carried out by means of an objective-function based fuzzy clustering using a cluster validity index. Rules that correspond to points belonging to the same cluster are similar and therefore, are unified through a specialized merging process. With respect to each dimension, the aforementioned merging process acts to create a topology of fuzzy sets that enables us to elicit interpretability constraints, which are used to minimize the model's performance index in terms of non-linear constrained optimization. The established fuzzy model appears to possess a simple and transparent (i.e. interpretable) structure while maintaining a highly accurate behavior. The overall method is rigorously tested and evaluated through a number of simulation experiments that involve low and high dimensional data sets.

FALCON: A matrix factorization framework for recommender systems using constrained optimization

Methods from the field of optimization theory have played an important role in developing training algorithms for matrix factorization in recommender systems. Indeed, the realization that simple stochastic unconstrained gradient descent can be applied with success to the factorization of the user-i tem matrix is responsible, to a great extent, for the recent research interest in this area, and the introduction of a plethora of matrix factorization methods. In this paper, motivated by earlier approaches in training neural networks, we introduce a constrained optimization framework for incorporating additional knowledge into the matrix factorization formalism, which can overcome certain drawbacks of the unconstrained minimization approach. We examine two types of such additional knowledge, and consequently derive two algorithms, as a result of incorporating the different knowledge types in the context of the constrained optimization framework. Both algorithms are designed to improve convergence and accuracy in the broader class of matrix factorization methods in recommender systems.

Subject- and resource-specific monitoring and proactive management of parallel radiofrequency transmission.

Develop a practical comprehensive package for proactive management of parallel radiofrequency (RF) transmission. With a constrained optimization framework and predictive models from a prescan based multichannel calibration, we presented a method supporting design and optimization of parallel RF excitation pulses that accurately obey the forward/reflected peak and average power limits of the RF power amplifiers in parallel transmit imaging experiments and Bloch simulations. Moreover, local SAR limits were incorporated into the parallel RF excitation pulses using electromagnetic field simulations. Virtual transmit coils concept for minimization of reflected power (effecting subject-specific matching) was additionally demonstrated by leveraging experimentally calibrated power models. Incorporation of experimentally calibrated power prediction models resulted in accurate compliance with prescribed hardware and global specific absorption rate (SAR) limits. Incorporation of spatial average 10 g SAR models, facilitated by simplifying numerical approximations, provided assurance of patient safety. RF pulses designed with various constraints demonstrated excellent excitation fidelity-the normalized root-mean-square error of the simulated excitation profiles was 2.6% for the fully constrained pulses, comparable to that of the unconstrained pulses. An RF shimming example showed a reduction of the reflected-to-forward power ratio to 1.7% from a conventional approach's 8.1%. Using the presented RF pulse design method, effective proactive management of the multifaceted power and SAR limits was demonstrated in experimental and simulation studies. Magn Reson Med 76:20-31, 2016. © 2015 Wiley Periodicals, Inc.

Uplink Scheduling of Visual Sensors: When View Popularity Matters

Decentralized camera sensors capture a 3D scene of interest from multiple perspectives. The captured video signals need to be transmitted to a central station over a shared wireless channel. A collocated server streams the gathered data to a collection of clients interested in experiencing the scene interactively. We design a constrained optimization framework for sharing the transmission bandwidth of the wireless channel across the sensors such that the average video quality over the client population is maximized. We consider scheduling the uplink resources of the wireless channel at the view or packet level. In the first case, the central station partitions the channel capacity across a select subset of views that are transmitted entirely. In the second case, the station coordinates the packet transmissions of every sensor. We formulate exact and approximate algorithms to solve the optimization of interest. We examine their transmission efficiency via simulation experiments that demonstrate considerable gains over the state-of-the-art and study the impact of view popularity.