Model Constraints Research Articles

A method of automatic field of view generation and path planning for automated x‐ray inspection

AbstractWith the increasing accuracy and stability requirements of SMT equipment, automatic x‐ray inspection (AXI) is used as a new popular type of testing technology. First, an imaging constraint model is proposed to ensure that the detected object is not truncated. Second, an improved iterative self‐organizing clustering algorithm was proposed to realize an automatic optimal generation of the field of view and form a Hamiltonian path. Finally, the solution of the shortest Hamiltonian path problem is given by the proposed VTSP heuristic algorithm and VTSP + transformer deep learning algorithm. Experimental results show that, compared with the binary state compression DP method and the local shortest path planning method, the proposed method can support large‐scale nodes, and the performance is improved by 16% on 75 nodes and 31% on 200 nodes. The proposed method achieves a balance between x‐ray imaging efficiency and performance.

Congestion management for coordinated electricity and gas grids in the presence of multi-energy hubs: A risk-based optimal scheduling

Due to the development of cost-effective and high-efficient infrastructures in electricity and natural gas carriers, the need for optimal operation of multi-carrier energy systems is essential. On the other side, with the increasing penetration of renewable energy resources (RERs), and power demand, the congestion management (CM) of power systems is turning out to be a significant challenge for system operators. Motivated by these, this paper focuses on the congestion management problem for a multi-energy hub (MEH) system incorporated by RERs, flexible energy resources (FERs), and different energy conversion technologies to supply electrical, heat, and cooling demands, aiming to minimize the total operating costs. In current practice, the steady-state Weymouth equation and AC-power flow method for natural gas and electricity networks are implemented to investigate the interdependency of power and gas networks. The renewable energy generation variations are mitigated by the scenario-based stochastic framework. Also, to manage the risk associated with random variables, the downside risk constraint (DRC) model is employed to analyze the changes in the expected cost per several values of the risk parameters. The numerical results demonstrate that the proposed model can significantly utilize the energy hub’s flexibility to alleviate gas and power congestion while decreasing the total operation cost.

Targeting endothelial VCAM-1 in atherosclerosis: drug discovery and development of VCAM-1-directed novel therapeutics.

Vascular cell adhesion molecule-1 (VCAM-1) has been well established as a critical contributor to atherosclerosis and consequently, as an attractive therapeutic target for anti-atherosclerotic drug candidates. Many publications have demonstrated that disrupting VCAM-1 function blocks monocyte infiltration into the subendothelial space, which effectively prevents macrophage maturation and foam cell transformation necessary for atherosclerotic lesion formation. Currently, most VCAM-1-inhibiting drug candidates in pre-clinical and clinical testing do not directly target VCAM-1 itself, but rather downregulate its expression by inhibiting upstream cytokines and transcriptional regulators. However, the pleiotropic nature of these regulators within innate immunity means that optimizing dosage to a level that suppresses pathological activity while preserving normal physiological function is extremely challenging and oftentimes infeasible. In recent years, highly specific pharmacological strategies that selectively inhibit VCAM-1 function have emerged, particularly peptide- and antibody-based novel therapeutics. Studies in such VCAM-1-directed therapies so far remain scarce and are limited by the constraints of current experimental atherosclerosis models in accurately representing the complex pathophysiology of the disease. This has prompted the need for a comprehensive review that recounts the evolution of VCAM-1-directed pharmaceuticals and addresses the current challenges in novel anti-atherosclerotic drug development.

State‐contingent production technology formulation: Identifying states of nature using reduced‐form econometric models of crop yield

AbstractConducting experiments can be time consuming and expensive, and may not always be reasonable. Therefore, empirical research often derives structural parameters based on observational data and reduced‐form econometric models. The state‐contingent approach presents a consistent conceptual framework for analyzing producer decisions under uncertainty. However, application of this structural modeling approach has been hampered by data constraints, particularly the lack of information for mapping producers' stochastic outputs onto a set of the states of nature representing different uncertain events. Consistent mapping of uncertainty is particularly critical in the context of multiple output production where weather shocks often have different effects across crops and in microeconometric analyses when unobserved farm heterogeneity may confound the effect of uncertainty. Our study demonstrates how the application of reduced‐form approaches can overcome constraints of structural econometric modeling associated with the lack of relevant data and presents an approach for identifying states of nature in the context of multiple output production using reduced‐form econometric models of crop yield. In an empirical application based on Hungarian farm accountancy data, we demonstrate that the proposed approach allows a consistent mapping of production uncertainty in crop farming, utilizes panel data structure, and controls for potential endogeneity due to unobserved farm heterogeneity. We anticipate the presented approach to be useful for developing further the state‐contingent approach and to stimulate further studies combining the strengths of structural approaches and reduced‐form models.

Information Gap Decision Theory-Based Stochastic Optimization for Smart Microgrids with Multiple Transformers

Multi-microgrid collaborative scheduling can promote the local consumption of renewable energy in the smart grid and reduce the operating costs of the power grid park. At the same time, the access of the distributed energy storage (ES) system provides an opportunity to further enhance the park’s peak shaving and valley filling capacity, thereby reducing costs. However, the uncertainty of photovoltaic (PV) power generation and load demand seriously affects the profit maximization of the microgrid in the park. To address this challenge, this paper proposes a stochastic optimal scheduling strategy for industrial park smart microgrids with multiple transformers based on the information gap decision theory (IGDT). We first introduce a revenue maximization model for industrial parks, incorporating a two-part tariff system and distributed ES. Subsequently, we employ an envelope constraint model to accurately represent the uncertainty associated with PV generation and load demand. By integrating these components, we establish the IGDT stochastic optimization scheduling model for industrial parks with multiple transformers. Finally, we simulate and analyze the performance of the proposed IGDT model under various cost deviation factors during typical spring and summer days. The simulation results demonstrate the effectiveness of the proposed control strategy in mitigating the impact of PV generation and load uncertainty on industrial parks. The IGDT-based scheduling approach provides an efficient solution for maximizing revenue and enhancing the operational stability of industrial park microgrids.

Identification of Reservoir Distribution Using Extended Elastic Impedance (EEI) Inversion in the "Z" Field of the Kutai Basin

This research was conducted using EEI inversion on seismic data in Z Field, Kutai Basin. The EEI inversion is effectively used to determine the reservoir distribution by eliminating the angle limit on the elastic impedance to the Chi angle so that it can be correlated with petrophysical parameters that are sensitive to lithology and fluids. The data used in this study are well data, checkshots, horizons, and partial-stack angle gather 3D seismic data. The data obtained is processed to obtain the target zone first based on log interpretation. Based on data processing, the target zone is obtained at 1513 m to 1531 m. Sensitivity analysis was conducted to determine the sensitive parameters, which can separate the lithology of the formation. In the sensitivity analysis, the most sensitive log to separate lithology is the Vp/VS log, which can separate sandstone, shale, and coal. Furthermore, the EEI inversion analysis was carried out to obtain the most suiTable model for the inversion, the Based Hard Constraint model was obtained with a correlation reaching 0.997 and an error value of 0.078. Based on the EEI inversion, the target zone in the Z-field at a depth of 1258 ms - 1269 ms with a sandstone reservoir in the EEI range of 6000 (m/s)(g/cc) - 7500 (m/s)(g/cc) which spreads from northeast to south. The distribution of the sandstone reservoir is surrounded by coal with a range of EEI 7500 (m/s)(g/cc) - 12000 (m/s)(g/cc), and also the distribution of shale in the EEI range of 7500(m/s)( g/cc) - 9200(m/s)(g/cc).

The evolution of the Milky Way’s thin disc radial metallicity gradient with K2 asteroseismic ages

ABSTRACT The radial metallicity distribution of the Milky Way’s disc is an important observational constraint for models of the formation and evolution of our Galaxy. It informs our understanding of the chemical enrichment of the Galactic disc and the dynamical processes therein, particularly radial migration. We investigate how the metallicity changes with guiding radius in the thin disc using a sample of red giant stars with robust astrometric, spectroscopic, and asteroseismic parameters. Our sample contains 668 stars with guiding radii 4 < Rg < 11 kpc and asteroseismic ages covering the whole history of the thin disc with precision ${\approx} 25 {{\, \rm per\ cent}}$. We use MCMC analysis to measure the gradient and its intrinsic spread in bins of age and construct a hierarchical Bayesian model to investigate the evolution of these parameters independently of the bins. We find a smooth evolution of the gradient from ≈−0.07 dex kpc−1 in the youngest stars to ≈−0.04 dex kpc−1 in stars older than 10 Gyr, with no break at intermediate ages. Our results are consistent with those based on asteroseismic ages from CoRoT, with that found in Cepheid variables for stars younger than 1 Gyr, and with open clusters for stars younger than 6 Gyr. For older stars we find a significantly lower metallicity in our sample than in the clusters, suggesting a survival bias favouring more metal-rich clusters. We also find that the chemical evolution model of Chiappini '09 is too metal poor in the early stages of disc formation. Our results provide strong new constraints for the growth and enrichment of the thin disc and radial migration, which will facilitate new tests of model conditions and physics.

Coupling a light use efficiency model with a machine learning-based water constraint for predicting grassland gross primary production

Light use efficiency (LUE) model was established to estimate gross primary production (GPP) for understanding the carbon-climate feedbacks of the terrestrial ecosystems. However, water constraints in LUE models can cause large uncertainties in GPP estimates, especially in semiarid grasslands where water is a key forcing factor for multiple ecosystem processes. Here, we proposed a novel LUE-Gradient Boosting Regression Trees (GBRT) model framework where water scalar is derived from five different water constraints for improving the estimates of grassland GPP over the conterminous United States (CONUS). The performance of LUE-GBRT and ten other GPP models [i.e., LUE-RF, LUE-ERT, GBRT, RF, ERT, LUE-fEF, LUE-fVPD, LUE-fLSWI, LUE-fSM, and LUE-fLST] was evaluated against data from eddy covariance (EC) observations at 25 measurement sites over the CONUS domain from 2000 to 2021. We found that LUE-GBRT improved grassland GPP estimates at all EC sites and yielded the highest Kling-Gupta efficiency (0.85) and the lowest root-mean-square error (1.4 g C m−2 d−1) when compared with the five individual GPP models. LUE-GBRT also showed a superior performance compared to LUE-RF and LUE-ERT. Compared with GBRT, the improvements were particularly from the responses to extreme surface conditions that were better characterized and estimated. An innovation of this method is that LUE-GBRT takes machine learning complementary to the physical-based LUE framework for an optimal junction between GPP physical process and model accuracy.

Markov decision processes with burstiness constraints

We consider a Markov Decision Process (MDP), over a finite or infinite horizon, augmented by so-called (σ,ρ)-burstiness constraints. Such constraints, which had been introduced within the framework of network calculus, are meant to limit some additive quantity to a given rate over any time interval, plus a term which allows for occasional and limited bursts. We introduce this class of constraints for MDP models, and formulate the corresponding constrained optimization problems. Due to the burstiness constraints, constrained optimal policies are generally history-dependent. We use a recursive form of the constraints to define an augmented-state model, for which sufficiency of Markov or stationary policies is recovered and the standard theory may be applied, albeit over a larger state space. The analysis is mainly devoted to a characterization of feasible policies, followed by application to the constrained MDP optimization problem. A simple queuing example serves to illustrate some of the concepts and calculations involved.

Wasserstein barycenter for link prediction in temporal networks

Abstract We propose a flexible link forecast methodology for weighted temporal networks. Our probabilistic model estimates the evolving link dynamics among a set of nodes through Wasserstein barycentric coordinates arising within the optimal transport theory. Optimal transport theory is employed to interpolate among network evolution sequences and to compute the probability distribution of forthcoming links. Besides generating point link forecasts for weighted networks, the methodology provides the probability that a link attains weights in a certain interval, namely a quantile of the weights distribution. We test our approach to forecast the link dynamics of the worldwide Foreign Direct Investments network and of the World Trade Network, comparing the performance of the proposed methodology against several alternative models. The performance is evaluated by applying non-parametric diagnostics derived from binary classifications and error measures for regression models. We find that the optimal transport framework outperforms all the competing models when considering quantile forecast. On the other hand, for point forecast, our methodology produces accurate results that are comparable with the best performing alternative model. Results also highlight the role played by model constraints in the determination of future links emphasising that weights are better predicted when accounting for geographical rather than economic distance.

A Computationally Efficient Benders Decomposition for Energy Systems Planning Problems with Detailed Operations and Time-Coupling Constraints

Energy systems planning models identify least-cost strategies for expansion and operation of energy systems and provide decision support for investment, planning, regulation, and policy. Most are formulated as linear programming (LP) or mixed integer linear programming (MILP) problems. Despite the relative efficiency and maturity of LP and MILP solvers, large scale problems are often intractable without abstractions that impact quality of results and generalizability of findings. We consider a macro-energy systems planning problem with detailed operations and policy constraints and formulate a computationally efficient Benders decomposition separating investments from operations and decoupling operational timesteps using budgeting variables in the master model. This novel approach enables parallelization of operational subproblems and permits modeling of relevant constraints coupling decisions across time periods (e.g., policy constraints) within a decomposed framework. Runtime scales linearly with temporal resolution; tests demonstrate substantial runtime improvement for all MILP formulations and for some LP formulations depending on problem size relative to analogous monolithic models solved with state-of-the-art commercial solvers. Our algorithm is applicable to planning problems in other domains (e.g., water, transportation networks, production processes) and can solve large-scale problems otherwise intractable. We show that the increased resolution enabled by this algorithm mitigates structural uncertainty, improving recommendation accuracy. Funding: Funding for this work was provided by the Princeton Carbon Mitigation Initiative (funded by a gift from BP) and the Princeton Zero-carbon Technology Consortium (funded by gifts from GE, Google, ClearPath, and Breakthrough Energy). Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoo.2023.0005 .

Multi-View Enhanced Tensor Nuclear Norm and Local Constraint Model for Cancer Clustering and Feature Gene Selection.

The analysis of cancer data from multi-omics can effectively promote cancer research. The main focus of this article is to cluster cancer samples and identify feature genes to reveal the correlation between cancers and genes, with the primary approach being the analysis of multi-view cancer omics data. Our proposed solution, the Multi-View Enhanced Tensor Nuclear Norm and Local Constraint (MVET-LC) model, aims to utilize the consistency and complementarity of omics data to support biological research. The model is designed to maximize the utilization of multi-view data and incorporates a nuclear norm and local constraint to achieve this goal. The first step involves introducing the concept of enhanced partial sum of tensor nuclear norm, which significantly enhances the flexibility of the tensor nuclear norm. After that, we incorporate total variation regularization into the MVET-LC model to further augment its performance. It enables MVET-LC to make use of the relationship between tensor data structures and sparse data while paying attention to the feature details of the tensor data. To tackle the iterative optimization problem of MVET-LC, the alternating direction method of multipliers is utilized. Through experimental validation, it is demonstrated that our proposed model outperforms other comparison models.

Quantifying the energetics of molecular superbubbles in PHANGS galaxies

Context. Star formation and stellar feedback are interlinked processes that redistribute energy, turbulence, and material throughout galaxies. Because young and massive stars form in spatially clustered environments, they create pockets of expanding gas termed superbubbles, which retain information about the physical processes that drive them. As these processes play a critical role in shaping galaxy discs and regulating the baryon cycle, measuring the properties of superbubbles provides important input for galaxy evolution models. Aims. With the wide coverage and high angular resolution (∼50–150 pc) of the PHANGS–ALMA 12CO (J = 2−1) survey, we can now resolve, identify and characterise a statistically representative number of superbubbles using molecular gas in nearby galaxies. Methods. We identify superbubbles by requiring spatial correspondence between shells in CO with stellar populations identified in PHANGS–HST. Then, by combining the properties of the stellar populations with the CO, we quantify the energetics of the stars and constrain feedback models. We visually find 325 cavities across 18 PHANGS–ALMA galaxies, 88 of which have clear superbubble signatures (unbroken shells, central clusters, kinematic signatures of expansion). We measure their radii and expansion velocities using CO (2–1) to dynamically derive their ages and the mechanical power driving the bubbles, which we use to compute the expected properties of the parent stellar populations driving the bubbles. Results. We find consistency between the predicted and derived stellar ages and masses of the stellar populations if we use a supernova (SN) model that injects energy with a coupling efficiency of ∼10%. Not only does this confirm that molecular gas accurately traces superbubble properties, but it also provides key observational constraints for superbubble models. We also find evidence that the bubbles are sweeping up gas as they expand, and speculate that these sites have the potential to host new generations of stars. Conclusions. This work demonstrates that molecular superbubbles provide novel quantitative constraints on SNe feedback efficiencies and gas clearing times, and represent a promising environment to search for the propagation of star formation, all of which are needed to understand what sets the observed star formation rates in galaxies.

Vehicle distribution strategy in urban traffic by using coverage control

In order to optimize the distribution of the urban emergency rescue vehicles and achieve the rapid response of the traffic accident, the distribution of multi-emergency rescue vehicles for the minimum rescue time is studied. According to the coverage control and the influence of traffic congestion for rescue time, the main research contents are as follows: analysis of the overall time consumption on the target area, establishment of the optimization model which considers the responsible area and the driving constraints of each vehicle for rescue time consumption. In details, for the division problem of responsible area of emergency rescue vehicle, the responsible area of each vehicle is calculated by using Voronoi region allocation principle and taking the driving time of vehicle to any point in urban road networks as evaluation index. Then, in consideration of the driving constraints in urban road networks, the constraints in the optimization model is clarified further on the premise of analyzing the vehicle kinematic characteristics. Finally, the optimal distribution position of multi-emergency rescue vehicles in the target area and the corresponding responsible area are calculated by gradient descent. The results show that the vehicle can converge to the optimal distribution position from any position in the target city, and the traffic accidents in responsible area can be timely response.

Planetary evolution with atmospheric photoevaporation

Context. Observations by the Kepler satellite have revealed a gap between larger sub-Neptunes and smaller super-Earths that atmospheric escape models had predicted as an evaporation valley prior to discovery. Aims. We seek to contrast results from a simple X-ray and extreme-ultraviolet (XUV)-driven energy-limited escape model against those from a direct hydrodynamic model. The latter calculates the thermospheric temperature structure self-consistently, including cooling effects such as thermal conduction. Besides XUV-driven escape, it also includes the boil-off escape regime where the escape is driven by the atmospheric thermal energy and low planetary gravity, catalysed by stellar continuum irradiation. We coupled these two escape models to an internal structure model and followed the planets’ temporal evolution. Methods. To examine the population-wide imprint of the two escape models and to compare it to observations, we first employed a rectangular grid, tracking the evolution of planets as a function of core mass and orbital period over gigayear timescales. We then studied the slope of the valley also for initial conditions derived from the observed Kepler planet population. Results. For the rectangular grid, we find that the power-law slope of the valley with respect to orbital period is −0.18 and −0.11 in the energy-limited and hydrodynamic model, respectively. For the initial conditions derived from the Kepler planets, the results are similar (−0.16 and −0.10). While the slope found with the energy-limited model is steeper than observed, the one of the hydrodynamic model is in excellent agreement with observations. The reason for the shallower slope is caused by the two regimes in which the energy-limited approximation fails. The first one are low-mass planets at low-to-intermediate stellar irradiation. For them, boil-off dominates mass loss. However, boil-off is absent in the energy-limited model, and thus it underestimates escape relative to the hydrodynamic model. The second one are massive compact planets at high XUV irradiation. For them, the energy-limited approximation overestimates escape relative to the hydrodynamic model because of cooling by thermal conduction, which is neglected in the energy-limited model. Conclusions. The two effects act together in concert to yield, in the hydrodynamic model, a shallower slope of the valley that agrees very well with observations. We conclude that a hydrodynamic escape model that includes boil-off and a more realistic treatment of cooling mechanisms can reproduce one of the most important constraints for escape models, the valley slope.

Investigating the Origin of the Absorption-line Variability in the Narrow-line Seyfert 1 Galaxy WPVS 007

Broad absorption line quasars are actively accreting supermassive black holes that have strong outflows characterized by broad absorption lines in their rest-UV spectra. Variability in these absorption lines occurs over months to years depending on the source. WPVS 007, a low-redshift, low-luminosity narrow-line Seyfert 1 (NLS1) shows strong variability over shorter timescales, providing a unique opportunity to study the driving mechanism behind this variability that may mimic longer-scale variability in much more massive quasars. We present the first variability study using the spectral synthesis code SimBAL, which provides velocity-resolved changes in physical conditions of the gas using constraints from multiple absorption lines. Overall, we find WPVS 007 to have a highly ionized outflow with a large mass-loss rate and kinetic luminosity. We determine the primary cause of the absorption-line variability in WPVS 007 to be a change in covering fraction of the continuum by the outflow. This study is the first SimBAL analysis where multiple epochs of observation were fit simultaneously, demonstrating the ability of SimBAL to use the time domain as an additional constraint in spectral models.

Semi-Supervised Medical Image Segmentation With Voxel Stability and Reliability Constraints.

Semi-supervised learning is becoming an effective solution in medical image segmentation because annotations are costly and tedious to acquire. Methods based on the teacher-student model use consistency regularization and uncertainty estimation and have shown good potential in dealing with limited annotated data. Nevertheless, the existing teacher-student model is seriously limited by the exponential moving average algorithm, which leads to the optimization trap. Moreover, the classic uncertainty estimation method calculates the global uncertainty for images but does not consider local region-level uncertainty, which is unsuitable for medical images with blurry regions. In this paper, the Voxel Stability and Reliability Constraint (VSRC) model is proposed to address these issues. Specifically, the Voxel Stability Constraint (VSC) strategy is introduced to optimize parameters and exchange effective knowledge between two independent initialized models, which can break through the performance bottleneck and avoid model collapse. Moreover, a new uncertainty estimation strategy, the Voxel Reliability Constraint (VRC), is proposed for use in our semi-supervised model to consider the uncertainty at the local region level. We further extend our model to auxiliary tasks and propose a task-level consistency regularization with uncertainty estimation. Extensive experiments on two 3D medical image datasets demonstrate that our method outperforms other state-of-the-art semi-supervised medical image segmentation methods under limited supervision. The source code and pre-trained models of this method are available at https://github.com/zyvcks/JBHI-VSRC.

Three Time-Scale Singular Perturbation Hybrid Control and Large-Signal Analysis Stability in AC-Microgrids

This work is devoted to propose a distributed control hybrid algorithm for the primary and secondary control loops of AC-bus microgrids in islanded mode and to provide a large-signal stability. A primary control loop based on Hybrid Dynamical System (HDS) theory manages the DC/AC inverters considering structural non-linearities in the model (affine terms and hybrid dynamics of their signals) and implementation constraints (dwell-time) and ensures the robustness of the output voltage with respect to any model variation. Moreover, the secondary control loop is designed based on the droop concept, which ensures that SOCs, reactive and active powers converge to their reference values, and on Multi-Agent System (MAS) theory to get a consensus among the reactive power and the State Of Charge (SOC) of the batteries in discharging mode. Moreover, it guarantees reliability and robustness with respect to any disconnection. The tuned system parameters are chosen in order to fit a three-time scale model (a time scale for each control objective: power converter control, droop control and consensus controls), which allows providing a large-signal stability analysis for the complete hybrid system based on HDS, MAS and singular perturbation theory.

A Hybrid Regressor and Classifier-Assisted Evolutionary Algorithm for Expensive Optimization With Incomplete Constraint Information

Surrogate-assisted evolutionary algorithms (SAEAs) have become a popular tool to solve expensive optimization problems and have been gradually used to deal with expensive constraints. To handle inequality expensive constraints, existing SAEAs need both the information of constraint violation and satisfaction to construct surrogate models for constraints. However, many problems only feedback whether the candidate solution is feasible or how much degree it violates constraints. There is no detailed information of how much degree the candidate satisfies constraints. The performance of most existing SAEAs decreases a lot in solving expensive constrained optimization problems (ECOPs) with such incomplete constraint information. To solve the problem, this article proposes a hybrid regressor and classifier-assisted evolutionary algorithm (HRCEA). HRCEA adopts a radial basis function regression model to approximate the degree of constraint violation. In order to make a more credible prediction, a logistic regression classifier (LRC) is constructed for the offspring rectification. The classifier works in cooperation with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula> -cut strategy, in which the high confidence level can significantly improve the prediction reliability. Besides, the LRC is built based on the boundary training data selection strategy, which is devised to select samples around feasible boundaries. This strategy is helpful for the LRC to fit the local feasibility structure. Extensive experiments on commonly used benchmark functions in CEC2006 and CEC 2010 demonstrate that HRCEA has satisfactory performance in found results and execution efficiency when solving ECOPs with incomplete constraint information. Furthermore, HRCEA is utilized to solve ceramic formula design optimization problem, which shows its promising application in real-world optimization problems.

Robustness Verification of Swish Neural Networks Embedded in Autonomous Driving Systems

With the applications of deep learning in safety-critical domains such as autonomous driving systems gaining ground, it demands rigorous verification to guarantee the safety and reliability of corresponding systems. As the intelligent component in such systems, neural networks (NNs) must be robust in that their outputs are not affected by minor perturbation to inputs. Many research studies have shown that formal methods are effective ways to the robustness verification of NNs. However, most of the existing approaches are focused on NNs that contain monotonic activation functions, such as ReLU, Tanh, and Sigmoid. In this work, we propose an approach to verify the robustness of NNs with the nonmonotonic activation function called Swish. Such networks have been proved to have a better performance on image classification than other NNs. In our approach, we turn the robustness verification problem into a constraint-solving problem using the linear approximation technique. We first model the affine function of an NN into a linear constraint model. Then, for nonlinear activation functions, we leverage an efficient approximation strategy to linearly approximate them. Finally, we utilize the constraint solver gurobi to solve the model, which reveals that the model satisfies the robustness property. We develop a prototype tool and evaluate it with open-sourced NNs. Experimental results showed the effectiveness and efficiency of our approach.