General Optimization Framework Research Articles

Inverse design of nonlinear metasurfaces for sum frequency generation

Abstract Sum frequency generation (SFG) has multiple applications, from optical sources to imaging, where efficient conversion requires either long interaction distances or large field concentrations in a quadratic nonlinear material. Metasurfaces provide an essential avenue to enhanced SFG due to resonance with extreme field enhancements with an integrated ultrathin platform. In this work, we formulate a general theoretical framework for multi-objective topology optimization of nanopatterned metasurfaces that facilitate high-efficiency SFG and simultaneously select the emitted direction and tailor the metasurface polarization response. Based on this framework, we present novel metasurface designs showcasing ultimate flexibility in transforming the outgoing nonlinearly generated light for applications spanning from imaging to polarimetry. For example, one of our metasurfaces produces highly polarized and directional SFG emission with an efficiency of over 0.2 cm2 GW−1 in a 10 nm signal operating bandwidth.

LPI Sequences Optimization Method against Summation Detector Based on FFT Filter Bank

Waveform design is a crucial factor in electronic surveillance (ES) systems. In this paper, we introduce an algorithm that designs a low probability of intercept (LPI) radar waveform. Our approach directly minimizes the detection probability of summation detectors based on FFT filter banks. The algorithm is derived from the general quadratic optimization framework, which inherits the monotonic properties of such methods. To expedite overall convergence, we have integrated acceleration schemes based on the squared iterative method (SQUAREM). Additionally, the proposed algorithm can be executed through fast Fourier transform (FFT) operations, enhancing computational efficiency. With some modifications, the algorithm can be adjusted to incorporate spectral constraints, increasing its flexibility. Numerical experiments indicate that our proposed algorithm outperforms existing ones in terms of both intercept properties and computational complexity.

Optimisation approaches for organising hospital infrastructure function

Given the premise that flexible infrastructure offers a way to increase hospital capacity, we present the first general optimisation framework and guide for systematically (re)organising the function of treatment areas and treatment spaces within a hospital to increase capacity. To motivate the need for our approach, we first demonstrate how sensitive the throughput of a hospital is to the function of infrastructure. This is achieved via the application of a novel multicriteria optimisation approach. In our illustrative example, a case mix landscape (i.e. a set of non-dominated case mix) was generated for various hospital configurations. A comparison of the case mix landscapes is insightful. It shows where differences in output occur and the exact nature of the outputs which can/cannot be realised. Motivated by these findings, we applied mixed integer programming techniques to optimise the function of treatment areas and treatment spaces subject to various technical constraints. Two novel strategic models are proposed for this purpose. In different ways, they revise access of specialties to different operating rooms, wards, and their associated ward beds. A case study of a large tertiary hospital demonstrates the efficacy of these models and the practical ramifications.

A general multi-objective Bayesian optimization framework for the design of hybrid schemes towards adaptive complex flow simulations

Achieving accuracy with underresolved simulation of complex compressible flows with multiscale flow structures is a challenge. Either the numerical dissipation or the resolution and thereby the numerical cost is impractically high. Also, in the design of numerical solvers, the application of a solver for specific flow classes is balanced by robustness allowing the study of a broad range of flows. In this study, we propose a hybrid fifth-order targeted essentially non-oscillatory (TENO5)-based scheme tailored to optimally simulate compressible flows with underresolved dilatational and vortical multiscale structures. For optimal design, three data-driven objectives are defined. A novel objective that derives from the numerical dissipation rate analysis is a key element to deal with underresolved complex flows in practical applications. The optimization process employs a multi-objective Bayesian optimization framework with an expected hypervolume improvement and three flow configurations representative for a broad range of two- and three-dimensional flows with genuine and non-genuine subgrid scales. The optimized hybrid scheme is validated by comparing with shock-capturing schemes of the weighted essentially non-oscillatory (WENO)- and TENO- families with flows of complex shock interactions, Kelvin-Helmholtz instabilities, shock-vortex interactions, vortical and turbulent flows

Unifying Graph Neural Networks with a Generalized Optimization Framework

Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism, which has been demonstrated effective, is the most fundamental part of GNNs. Although most of the GNNs basically follow a message passing manner, little effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with an optimization problem. We show that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solutions of a generalized optimization framework with a flexible feature fitting function and a generalized graph regularization term. Actually, the optimization framework can not only help understand the propagation mechanisms of GNNs, but also open up opportunities for flexibly designing new GNNs. Through analyzing the general solutions of the optimization framework, we provide a more convenient way for deriving corresponding propagation results of GNNs. We further discover that existing works usually utilize naïve graph convolutional kernels for feature fitting function, or just utilize one-hop structural information (original topology graph) for graph regularization term. Correspondingly, we develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities and one novel objective function considering high-order structural information during propagation respectively. Extensive experiments on benchmark datasets clearly show that the newly proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with the generalized unified optimization framework.

Similarity-based active learning methods

Active Learning has been a popular method to circumvent the labeling cost in machine learning methods. The majority of active learning approaches can be classified into two categories: representative-based and informative-based methods, with some hybrid methods that combine both. This work presents a naïve query strategy, namely Similarity-Based Active Learning (SBAL), which computes the sum of a row in the similarity matrix at each selection step, and a general optimization framework that can accommodate a broad range of active learning algorithms. The label complexity for different classification metrics is used as a primary criterion for comparing different algorithms. The proposed algorithm’s numerical performance is illustrated using simulated data scenarios and by applying it to the real-world COVID-19 image classification. The results demonstrate that, based on the classification metric, labeling cost and label complexity, SBAL outperforms other hybrid methods, such as Adaptive Active Learning (AAL) and Maximizing Variance for Active Learning (MVAL).

Attribute reduction with fuzzy kernel-induced relations

Fuzzy rough sets have strong ability in dealing with data uncertainty, which have been widely applied in attribute reduction problems. Fuzzy relations are the cornerstones of fuzzy rough sets, and kernel-induced relations can simultaneously reflect the similarities of objects in both original space and high-dimensional Hilbert space. However, existing distance-based fuzzy relations (even kernel-induced) cannot truly reflect the correlations of objects under complex data distributions. To obtain better expressing ability for data, we propose a general optimization framework to get the memberships of objects with respect to categories. Considering various complex data distributions, the concepts of intra-class aggregation degree based on membership and inter-class dispersion degree based on nonmembership are proposed, and a separability measure is constructed to evaluate the importance of attributes to decisions. Correspondingly, a new attribute reduction algorithm is proposed, with a forward evaluation L-step strategy to skip local fluctuations in classification accuracy. Finally, we conduct a series of experiments to verify the effectiveness of the proposed algorithm. From the experiments on UCI, ELVIRA and face recognition datasets, it can be seen that the attribute subset obtained by the proposed algorithm not only has high classification accuracy and computational efficiency, but also has fewer attributes.

Fast Multilabel Feature Selection via Global Relevance and Redundancy Optimization.

Information theoretical-based methods have attracted a great attention in recent years and gained promising results for multilabel feature selection (MLFS). Nevertheless, most of the existing methods consider a heuristic way to the grid search of important features, and they may also suffer from the issue of fully utilizing labeling information. Thus, they are probable to deliver a suboptimal result with heavy computational burden. In this article, we propose a general optimization framework global relevance and redundancy optimization (GRRO) to solve the learning problem. The main technical contribution in GRRO is a formulation for MLFS while feature relevance, label relevance (i.e., label correlation), and feature redundancy are taken into account, which can avoid repetitive entropy calculations to obtain a global optimal solution efficiently. To further improve the efficiency, we extend GRRO to filter out inessential labels and features, thus facilitating fast MLFS. We call the extension as GRROfast, in which the key insights are twofold: 1) promising labels and related relevant features are investigated to reduce ineffective calculations in terms of features, even labels and 2) the framework of GRRO is reconstructed to generate the optimal result with an ensemble. Moreover, our proposed algorithms have an excellent mechanism for exploiting the inherent properties of multilabel data; specifically, we provide a formulation to enhance the proposal with label-specific features. Extensive experiments clearly reveal the effectiveness and efficiency of our proposed algorithms.

Robust contact-constrained topology optimization considering uncertainty at the contact support

In this paper, the general framework for contact-constrained topology optimization of Strömberg and Klarbring (2010) is extended to robust topology optimization. In doing so, a linear elastic design domain is considered and the augmented Lagrangian approach is used to model the unilateral contact. For topology optimization, the design space is parametrized with the SIMP-approach and the Sigmund’s filter is applied. Additionally, the robust framework considers uncertainties at the contact support such as deviations of the geometry of the contact surface and the friction coefficient. Both uncertainties are described by the first-order second-moment method which leads to minimal additional costs. In fact, only two additional linear equations must be solved to obtain the robust objective and its gradient with respect to the design variables. Having both the objective and the gradient, the design update is computed with the method of moving asymptotes. The robust framework is applied to 2D and 3D examples to prove its scalability for real-world applications.

A General Matrix Variable Optimization Framework for MIMO Assisted Wireless Communications

A General Matrix Variable Optimization Framework for MIMO Assisted Wireless Communications

Worst-Case Discriminative Feature Learning via Max-Min Ratio Analysis.

We propose a novel discriminative feature learning method via Max-Min Ratio Analysis (MMRA) for exclusively dealing with the long-standing "worst-case class separation" problem. Existing technologies simply consider maximizing the minimal pairwise distance on all class pairs in the low-dimensional subspace, which is unable to separate overlapped classes entirely especially when the distribution of samples within same class is diverging. We propose a new criterion, i.e., Max-Min Ratio Analysis (MMRA) that focuses on maximizing the minimal ratio value of between-class and within-class scatter to extremely enlarge the separability on the overlapped pairwise classes. Furthermore, we develop two novel discriminative feature learning models for dimensionality reduction and metric learning based on our MMRA criterion. However, solving such a non-smooth non-convex max-min ratio problem is challenging. As an important theoretical contribution in this paper, we systematically derive an alternative iterative algorithm based on a general max-min ratio optimization framework to solve a general max-min ratio problem with rigorous proofs of convergence. More importantly, we also present another solver based on bisection search strategy to solve the SDP problem efficiently. To evaluate the effectiveness of proposed methods, we conduct extensive pattern classification and image retrieval experiments on several artificial datasets and real-world ScRNA-seq datasets, and experimental results demonstrate the effectiveness of proposed methods.

Causal inference of general treatment effects using neural networks with a diverging number of confounders

Semiparametric efficient estimation of various multi-valued causal effects, including quantile treatment effects, is important in economic, biomedical, and other social sciences. Under the unconfoundedness condition, adjustment for confounders requires estimating the nuisance functions relating outcome or treatment to confounders nonparametrically. This paper considers a generalized optimization framework for efficient estimation of general treatment effects using artificial neural networks (ANNs) to approximate the unknown nuisance function of growing-dimensional confounders. We establish a new approximation error bound for the ANNs to the nuisance function belonging to a mixed smoothness class without a known sparsity structure. We show that the ANNs can alleviate the “curse of dimensionality” under this circumstance. We establish the root-n consistency and asymptotic normality of the proposed general treatment effects estimators, and apply a weighted bootstrap procedure for conducting inference. The proposed methods are illustrated via simulation studies and a real data application.

A generic design optimization framework for semiconductor cleanroom air-conditioning systems integrating heat recovery and free cooling for enhanced energy performance

High-tech industrial buildings, such as semiconductor cleanrooms, generally require strict temperature, humidity, and cleanliness controls, resulting in very high energy consumption of their air-conditioning systems. However, there exist two important problems in these air-conditioning systems, i.e., large cold-heat offset and low cooling efficiency. These two serious issues are generally neglected during the design stage and further cause great energy waste during the operation stage. This study therefore proposes a generic air-conditioning system design optimization framework for semiconductor cleanrooms by integrating heat recovery and free cooling techniques at air-side and water-side, respectively. The proposed design framework can fully eliminate cold-heat offset, simultaneously reduce cooling/heating loads and enhance cooling efficiency under full-range semiconductor applications. By detailed modeling and simulations, the proposed design framework is validated and tested under various indoor cooling loads, ventilation rates, and surrounding weather and climate conditions. Results show that 2.3–33.1 % energy savings are achieved and up to 15.8GJ/m2 annual primary energy is saved, compared with the conventional design. It is also observed that cities in cold and mild climates have higher energy-saving potentials than those in hot climates. It is recommended to utilize the proposed design framework as a benchmarking air-conditioning system design in new semiconductor cleanrooms.

Location Privacy-Aware and Energy-Efficient Offloading for Distributed Edge Computing

Driven by the ever-increasing scale and intensity of the computing tasks arising from various mobile applications, distributed edge computing has fostered wide research interests. It can effectively reduce the task processing delay by partitioning the original large-scale task into several small subtasks and offloading them to multiple edge nodes (ENs) for parallel computing. In edge computing, as the mobile user usually tends to offload computing tasks to closer ENs to save transmit power, the attacker may stealthily infer user location by exploiting this feature. Although there have been some pioneering works on offloading related location privacy, they mainly focused on the scenario where each task can only be offloaded to a single EN, and may not be directly applicable to distributed edge computing. Besides, the privacy issues considered in existing works are mainly based on good heuristics, and there is still a lack of concrete examples of location privacy attacks in edge computing. To the best of our knowledge, the location privacy issue in distributed edge computing still remains largely unexplored in existing literature. With this consideration, a location inference attack based on matrix sequential probability ratio test (MSPRT) is identified in this work. Besides, a countermeasure based on dynamic multi-EN selection is proposed, together with a location privacy-aware and energy-efficient distributed offloading scheme based on the generic Lyapunov optimization framework. Both theoretic analysis and simulations based on real-world channel measurements are employed to validate the feasibility of the identified MPSRT attack and the effectiveness of the proposed defense scheme.

Crop acreage planning for economy- resource- efficiency coordination: Grey information entropy based uncertain model

Reasonable adjustment of crop acreage can improve the sustainability of agriculture in arid zones by promoting economic development, alleviating water scarcity, and improving resource utilization efficiency but meets the challenges of various decision-maker preferences and uncertainties. With the objectives of maximizing economic benefits, minimizing evapotranspiration, and maximizing water productivity and water production efficiency, this study developed a grey entropy based multi-objective fuzzy constraint interval programming model (GEMOFCIP) through incorporation of information entropy technology, fuzzy constraints and interval programming approaches within a general optimization framework. The model is capable of (1) generating the crop acreage management schemes through trading off the different development goals; (2) dealing with the structure and parameter uncertainties of the optimization model; (3) measuring the relative importance of multiple objectives by the introduction of information entropy with the insufficient decision-maker’s preference information. Taking the crop acreage planning problem in Liangzhou, northwest China as a case study, the model was solved under different water-saving and satisfaction degree scenarios. It turned out that, after optimization, the economic benefit, water productivity and water production efficiency have been significantly improved, while the total ET and the total irrigation water have been significantly compressed in the study area. The GEMOFCIP model is superior to the previous models in that it takes into account the randomness of the relative importance of system objective, the vagueness of system constraints and the fluctuations of system coefficients, which would make the model more reasonable, stable and objective. Optimal results can help manage crop pattern with the economy-resource-efficiency consideration and accelerate the healthy development of agriculture in arid zones.

General optimization framework for accurate and efficient reconstruction of symmetric complex networks from dynamical data.

The challenging problem of network reconstruction from dynamical data can in general be formulated as an optimization task of solving multiple linear equations. Existing approaches are of the two types: Point-by-point (PBP) and global methods. The local PBP method is computationally efficient, but the accuracies of its solutions are somehow low, while a global method has the opposite traits: High accuracy and high computational cost. Taking advantage of the network symmetry, we develop a novel framework integrating the advantages of both the PBP and global methods while avoiding their shortcomings: i.e., high reconstruction accuracy is guaranteed, but the computational cost is orders of magnitude lower than that of the global methods in the literature. The mathematical principle underlying our framework is block coordinate descent (BCD) for solving optimization problems, where the various blocks are determined by the network symmetry. The reconstruction framework is validated by numerical examples with a variety of network structures (i.e., sparse and dense networks) and dynamical processes. Our success is a demonstration that the general principle of exploiting symmetry can be extended to tackling the challenging inverse problem or reverse engineering of complex networks. Since solving a large number of linear equationsis key to a plethora of problems in science and engineering, our BCD-based network reconstruction framework will find broader applications.

Optimization of module structure considering mechanical and thermal safety of pouch cell lithium-ion batteries using a reliability-based design optimization approach

Design optimization is an important method for improving the performance of lithium-ion batteries. However, the majority of earlier studies on battery optimization have generally concentrated on enhancing the performance of a single battery cell or focusing on particular objectives of the module and pack structures. Therefore, this study mainly focuses on developing a generalized optimization framework to increase the energy density of the module while satisfying the mechanical and thermal safety requirements. To the best of our knowledge, this work is the first to attempt to enhance the module performance while considering both mechanical and thermal safety. Moreover, this study develops a reliability-based design optimization (RBDO) framework for module structures that considers system uncertainties to mitigate the possibility of safety failures and obtain a reliable design. The mechanical behavior of the module shows how swelling, breathing, material types, and properties affect the final module length and stress. The effects of the C-rate and design parameters on the maximum temperature and temperature deviation are also investigated. All designs satisfy the target probability of failure, verifying that the RBDO framework of the module structure has been successfully established. The proposed RBDO framework provides guidance for the design and operation of battery modules.

Molecular Modeling of Water-in-Salt Electrolytes: A Comprehensive Analysis of Polarization Effects and Force Field Parameters in Molecular Dynamics Simulations.

Accurate modeling of highly concentrated aqueous solutions, such as water-in-salt (WiS) electrolytes in battery applications, requires proper consideration of polarization contributions to atomic interactions. Within the force field molecular dynamics (MD) simulations, the atomic polarization can be accounted for at various levels. Nonpolarizable force fields implicitly account for polarization effects by incorporating them into their van der Waals interaction parameters. They can additionally mimic electron polarization within a mean-field approximation through ionic charge scaling. Alternatively, explicit polarization description methods, such as the Drude oscillator model, can be selectively applied to either a subset of polarizable atoms or all polarizable atoms to enhance simulation accuracy. The trade-off between simulation accuracy and computational efficiency highlights the importance of determining an optimal level of accounting for atomic polarization. In this study, we analyze different approaches to include polarization effects in MD simulations of WiS electrolytes, with an example of a Na-OTF solution. These approaches range from a nonpolarizable to a fully polarizable force field. After careful examination of computational costs, simulation stability, and feasibility of controlling the electrolyte properties, we identify an efficient combination of force fields: the Drude polarizable force field for salt ions and non-polarizable models for water. This cost-effective combination is sufficiently flexible to reproduce a broad range of electrolyte properties, while ensuring simulation stability over a relatively wide range of force field parameters. Furthermore, we conduct a thorough evaluation of the influence of various force field parameters on both the simulation results and technical requirements, with the aim of establishing a general framework for force field optimization and facilitating parametrization of similar systems.

Operationalizing resilience: A deductive fault-driven resilience index for enabling adaptation

The impact of climate change and the dynamic nature of environmental conditions underscore the critical need to enhance resilience of systems and process safety considerations. The efficacy of such efforts primarily depends on how resilience is measured. Among the myriad efforts to quantify resilience, composite indicators have emerged as promising tools. However, these indicators typically employ statistical methods to derive weights for aggregation and rely on statistical homogeneity among indicators which can limit their scope and fidelity. In this study, we propose an alternative novel resilience index derived from a system’s structure and the essential conditions for safe operation during and after disruptions. The proposed measure reflects the systems’ ability to resist and respond to failures by addressing possibilities of impact propagation to other infrastructure systems. Moreover, it eliminates the need for weights and allows for compensability among its leading indicators. Using a case study based on the on-site wastewater treatment and disposal systems (OSTDS) in South Florida that faces increasing risks due to rising sea levels, we investigate the validity of the proposed index and perform a comparative analysis with statistically-driven measures. Furthermore, we demonstrate the adaptation of the proposed index for decision making within a generalized optimization framework.

General Optimization Framework of Water Huff-n-Puff Based on Embedded Discrete Fracture Model Technology in Fractured Tight Oil Reservoir: A Case Study of Mazhong Reservoir in the Santanghu Basin in China

Summary Water injection huff-n-puff (WHnP) is currently an important technology to improve the recovery of tight reservoirs. On the one hand, this technology can replenish the formation energy, and on the other hand, it can effectively replace the oil in a tight reservoir. In this paper, the effect of WHnP on cumulative oil production and oil increase rate is simulated and analyzed by comparing depleted development and WHnP scenarios, using numerical simulation methods. A field-scale numerical simulation was modeled based on typical fluid, reservoir, and fracture characteristics of Mazhong tight oil, coupled with geomechanical effects, stress sensitivity, and embedded discrete fractures. The result of different WHnP cycles is studied, and the limiting WHnP cycle is determined to be four cycles. The WHnP efficiency is compared for different permeability scales from 0.005 to 1 md, and it is determined that WHnP at a permeability of 0.01 md resulted in the largest production enhancement. Subsequently, sensitivity studies are conducted using an orthogonal experimental design for six uncertain parameters, including the WHnP cycle, production pressure difference, permeability, natural fracture density, hydraulic fracture half-length, and conductivity. The results show that throughput period and permeability are important parameters affecting cumulative oil production, and permeability and natural fracture density are important parameters affecting oil increase rate. In addition, contour plots of permeability and WHnP cycle, hydraulic fracture half-length, and conductivity are generated. Based on these plots, the optimal conditions with better enhanced recovery results in different WHnP scenarios can be easily determined. This study can better solve the problems encountered in WHnP of tight reservoirs and provide a theoretical basis for stable and efficient development.