Separation Constraints Research Articles

The Normalized Direct Trigonometry Model for the Two-Dimensional Irregular Strip Packing Problem

Background: The Irregular Strip Packing Problem (ISPP) involves packing a set of irregularly shaped items within a strip while minimizing its length. Methods: This study introduces the Normalized Direct Trigonometry Model (NDTM), an innovative enhancement of the Direct Trigonometry Model (DTM). The NDTM incorporates a distance function that supports the integration of the separation constraint, which mandates a minimum separation distance between items. Additionally, the paper proposes a new set of constraints based on the bounding boxes of the pieces aimed at improving the non-overlapping condition. Results: Comparative computational experiments were performed using a comprehensive set of 90 instances. Results show that the NDTM finds more feasible and optimal solutions than the DTM. While the NDTM allows for the implementation of the separation constraint, the number of feasible and optimal solutions tends to decrease as more separation among the items is considered, despite not increasing the number of variables or constraints. Conclusions: The NDTM outperforms the DTM. Moreover, the results indicate that the new set of non-overlapping constraints facilitates the exploration of feasible solutions at the expense of optimality in some cases.

K-means and gaussian mixture modeling with a separation constraint

We consider the problem of clustering with K-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the K-means problem with a separation constraint on the centers, building on Wang and Song (2011). In the context of fitting a Gaussian mixture model, we then propose an EM algorithm that incorporates such a constraint. A separation constraint can help regularize the output of a clustering algorithm, and we provide both simulated and real data examples to illustrate this point.

A constrained control framework for unmanned aerial vehicles based on Explicit Reference Governor

This paper tackles the constrained control problem of unmanned aerial vehicles with planar multirotors. The proposed solution splits the constrained control problem into two separate tasks, i.e. stabilization and constraint enforcement. It is shown that the problems addressed by each individual layer is much simpler than the original combined problem. For the unconstrained control of UAVs we consider a control scheme based on a cascade structure. The Lyapunov function for the stabilized cascaded system is then derived. Using this Lyapunov function, we develop an Explicit Reference Governor for constraint enforcement. Numerical simulation shows the effectiveness of the proposed approach.

Chance-constrained UAM traffic flow optimization with fast disruption recovery under uncertain waypoint occupancy time

Trajectory-based operations offer a promising solution for effective urban air mobility (UAM) traffic management with conflict-free four-dimensional trajectories. However, these trajectories generated in strategic phases by existing methods could be significantly disrupted due to uncertainties such as flight delays and trajectory deviations. This paper develops a chance-constrained UAM traffic flow management (UTFM) optimization model with fast disruption recovery to solve observed disrupted trajectories and improve their resilience. Our model introduces a novel concept of waypoint occupancy time to cope with the probabilistic separation constraints induced by variables, notably urban wind field. We then convert the probabilistic constraint into a deterministic one, incorporating risk-bounded separation guarantees derived from flight experiment data. Furthermore, we develop a hierarchical stochastic search algorithm for solving the redefined deterministic optimization problem. Our comprehensive numerical studies demonstrate the model's effectiveness in restoring disrupted flights and resolving conflicts within seconds. Additionally, our reliability testing showcases the resilience of the model in managing disruptions, even at levels as high as 50%, and its adaptability in addressing varying levels of uncertainty risk. We further demonstrate the ability of the UTFM model to capture tail risks across Gaussian and non-Gaussian uncertainty distributions. Lastly, our scalability analysis highlights the potential capacity of the model to support up to 3,000 flights per hour in Singapore's urban airspace below 400 ft. This study introduces an adaptable framework to facilitate the modelling of robust traffic flow management and performance-based separation for a variety of eVTOL types under uncertainties.

Covid-19 and sociovirtualization: Exploring new ways to socialize

Following the Covid-19 pandemic, the globe has seen unheard-of modifications in many facets of daily life, including how we socialize. A term used to characterize the use of virtual platforms and technologies for social contact, sociovirtualization has become more prevalent due to the requirement for physical separation and gathering constraints. Research on the effects of Covid-19 on socialization and the emergence of novel digital modes of communication and interaction is crucial.
 This article examines socialization in the future, seeing sociovirtualization as the standard in our interpersonal interactions. In order to promote real human connections, it highlights the necessity of a well-rounded strategy that incorporates both virtual and in-person contacts. Through a thoughtful embrace of sociovirtualization, we can make sense of the situation now and get ready for a time when virtual and real-world interactions can coexist peacefully.

Solving Sparse Separable Bilinear Programs Using Lifted Bilinear Cover Inequalities

Recently a class of second-order cone representable convex inequalities called lifted bilinear cover inequalities were introduced, which are valid for a set described by a separable bilinear constraint together with bounds on variables. In this paper, we study the computational potential of these inequalities for separable bilinear optimization problems. We first prove that the semidefinite programming relaxation provides no benefit over the McCormick relaxation for such problems. We then design a simple randomized separation heuristic for lifted bilinear cover inequalities. In our computational experiments, we separate many rounds of these inequalities starting from McCormick’s relaxation of instances where each constraint is a separable bilinear constraint set. We demonstrate that there is a significant improvement in the performance of a state-of-the-art global solver in terms of gap closed, when these inequalities are added at the root node compared with when they are not. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: S. S. Dey gratefully acknowledges the support by the Office of Naval Research [Grant N000141912323].

Rational downstream development for adeno-associated virus full/empty capsid separation – A streamlined methodology based on high-throughput screening and mechanistic modeling

Recombinant adeno-associated virus (AAV) has emerged as one of the most promising systems for therapeutic gene delivery and has demonstrated clinical success in a wide range of genetic disorders. However, manufacturing of high-quality AAV in large amounts still remains a challenge. A significant difficulty for downstream processing is the need to remove empty capsids that are generated in all currently utilized expression systems and that represent product-related impurities that adversely affect safety and efficacy of AAV vectors. Empty and full capsids exhibit only subtle differences in surface charge and size, making chromatography-based separations highly challenging. Here, we present a rapid methodology for the systematic process development of the crucial AAV full/empty capsid separation on ion-exchange media based on high-throughput screening and mechanistic modeling. Two of the most commonly employed serotypes, AAV8 and AAV9, are used as case studies. First, high-throughput studies in filter-plate format are performed that allow the rapid and comprehensive study of binding and elution behavior of AAV on different resins, using different buffer systems, pH, salt conditions, and solution additives. Small amounts of separated empty and full AAV capsids are generated by iodixanol gradient centrifugation that allow studying the binding and elution behavior of the two vector species separately in miniaturized format. Process conditions that result in maximum differences in elution behavior between empty and full capsids are then transferred to benchtop chromatography systems that are used to generate calibration data for the estimation of steric mass-action isotherm and mass transport parameters for process simulation. The resulting column models are employed for in-silico process development that serves to enhance understanding of separation constraints and to identify optimized conditions for the removal of empty particles. Finally, optimized separation conditions are verified experimentally. The methodology presented in this work provides a systematic framework that affords mechanistic understanding of the crucial empty/full capsid separation and accelerates the development of a scalable AAV downstream process.

Remote Multi-Person Heart Rate Monitoring with Smart Speakers: Overcoming Separation Constraint.

Heart rate is a key vital sign that can be used to understand an individual's health condition. Recently, remote sensing techniques, especially acoustic-based sensing, have received increasing attention for their ability to non-invasively detect heart rate via commercial mobile devices such as smartphones and smart speakers. However, due to signal interference, existing methods have primarily focused on monitoring a single user and required a large separation between them when monitoring multiple people. These limitations hinder many common use cases such as couples sharing the same bed or two or more people located in close proximity. In this paper, we present an approach that can minimize interference and thereby enable simultaneous heart rate monitoring of multiple individuals in close proximity using a commonly available smart speaker prototype. Our user study, conducted under various real-life scenarios, demonstrates the system's accuracy in sensing two users' heart rates when they are seated next to each other with a median error of 0.66 beats per minute (bpm). Moreover, the system can successfully monitor up to four people in close proximity.

Comparison of 3 Different Therapeutic Particles in Radioembolization of Locally Advanced Intrahepatic Cholangiocarcinoma.

Our objective was to compare 3 different therapeutic particles used for radioembolization in locally advanced intrahepatic cholangiocarcinoma. Methods: 90Y-glass, 90Y-resin, and 166Ho-labeled poly(l-lactic acid) microsphere prescribed activity was calculated as per manufacturer recommendations. Posttreatment quantitative 90Y PET/CT and quantitative 166Ho SPECT/CT were used to determine tumor-absorbed dose, whole-normal-liver-absorbed dose, treated-normal-liver-absorbed dose, tumor-to-nontumor ratio, lung-absorbed dose, and lung shunt fraction. Response was assessed using RECIST 1.1 and the [18F]FDG PET-based change in total lesion glycolysis. Hepatotoxicity was assessed using the radioembolization-induced liver disease classification. Results: Six 90Y-glass, 8 90Y-resin, and 7 166Ho microsphere patients were included for analysis. The mean administered activity was 2.6 GBq for 90Y-glass, 1.5 GBq for 90Y-resin, and 7.0 GBq for 166Ho microspheres. Tumor-absorbed dose and treated-normal-liver-absorbed dose were significantly higher for 90Y-glass than for 90Y-resin and 166Ho microspheres (mean tumor-absorbed dose, 197 Gy for 90Y-glass vs. 73 Gy for 90Y-resin and 50 Gy for 166Ho; mean treated-normal-liver-absorbed dose, 79 Gy for 90Y-glass vs. 37 Gy for 90Y-resin and 31 Gy for 166Ho). The whole-normal-liver-absorbed dose and tumor-to-nontumor ratio did not significantly differ between the particles. All patients had a lung-absorbed dose under 30 Gy and a lung shunt fraction under 20%. The 3 groups showed similar toxicity and response according to RECIST 1.1 and [18F]FDG PET-based total lesion glycolysis changes. Conclusion: The therapeutic particles used for radioembolization differed from each other and showed significant differences in absorbed dose, whereas toxicity and response were similar for all groups. This finding emphasizes the need for separate dose constraints and dose targets for each particle.

Cleaving idioms with right-node-raising

Abstract This paper examines right-node-raising (RNR) with idiom chunks. RNR sentences allow idiomatic interpretation when they contain the whole idiom chunk within the pivot (i.e., the shared element) (e.g., Jessica believed, but Zac doubted, that Justin popped the question.), but those containing only a part of the idiom within the pivot do not (e.g., #John kicked, and Mary filled, the bucket.). Given this, Woo (2015) argues for a multidominance approach (cf. Wilder 1999) to RNR in that the multiply dominated pivot must not be partially shared for idiomatic interpretation. However, we report that even if the pivot contains the whole idiom part, the issue of missing idiomatic interpretation in RNR still lingers (e.g., #We played a party game, and they used an ice hammer, to break the ice.). In order to deal with this problem, multidominance, movement, or PF deletion analyses must resort to an extra interpretive parallelism according to which a pivot cannot be used in two different senses simultaneously. From this perspective, we argue that an LF copying approach can explain the idiomaticity in RNR without extra proviso since under this analysis, it is not necessary to postulate a separate LF constraint of interpretive symmetry. We extend our analysis to Korean (and Japanese) data pertaining to RNR with idiomatic or polysemous expressions. We thus conclude that lexical mismatches and interpretive mismatches in English and Korean RNR are solid evidence of interpretive identity in RNR.

A note on quadratic constraints with indicator variables: Convex hull description and perspective relaxation

In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization problems with uncertainty and in machine learning. We show that optimization over this set is NP-hard. Despite this negative result, we discover links between the convex hull of the set under study, and a family of polyhedral sets studied in the literature. Moreover, we show that although perspective relaxation in the literature for this set fails to match the structure of its convex hull, it is guaranteed to be a close approximation.

Robustness analysis of uncertain time‐varying systems with unknown initial conditions

SummaryThis paper focuses on the robustness analysis of discrete‐time, linear time‐varying (LTV) systems subject to various uncertainties, such as static and dynamic, time‐invariant and time‐varying, linear perturbations, and unknown initial conditions. The proposed approach is based on integral quadratic constraint theory and allows for a potentially more accurate characterization of the set in which the initial state resides by imposing separate constraints on the initial values of the state variables as opposed to simply requiring the initial state to lie in some ellipsoid. The adopted problem formulation facilitates the analysis of uncertain LTV systems subject to disturbance inputs that are bounded pointwise in time, and the developed results enable determining useful pointwise bounds on the performance outputs given such inputs. The main analysis result is given for eventually periodic nominal systems, which include linear time‐invariant, finite horizon, and periodic systems as special cases. The analysis conditions are expressed as linear matrix inequalities. Two additional results stemming from the main analysis theorem are provided that can be used to determine overapproximated ellipsoidal reachable sets. Finally, the utility of the proposed approach is demonstrated in an illustrative example.

An Efficient Trajectory Negotiation and Verification Method Based on Spatiotemporal Pattern Mining

In trajectory-based operations, trajectory negotiation and verification are conducive to using airspace resources fairly, reducing flight delay, and ensuring flight safety. However, most of the current methods are based on route negotiation, making it difficult to accommodate airspace user-initiated trajectory requests and dynamic flight environments. Therefore, this paper develops a framework for trajectory negotiation and verification and describes the trajectory prediction, negotiation, and verification processes based on a four-dimensional trajectory. Secondly, users predict flight trajectories based on aircraft performance and flight plans and submit them as requested flight trajectories to the air traffic management (ATM) system for negotiation in the airspace. Then, a spatiotemporal weighted pattern mining algorithm is proposed, which accurately identifies flight combinations that violate the minimum flight separation constraint from four-dimensional flight trajectories proposed by users, as well as flight combinations with close flight intervals and long flight delays in the airspace. Finally, the experimental results demonstrate that the algorithm efficiently verifies the user-proposed flight trajectory and promptly identifies flight conflicts during the trajectory negotiation and verification processes. The algorithm then analyzes the flight trajectories of aircrafts by applying various constraints based on the specific traffic environment; the flight combinations which satisfy constraints can be identified. Then, based on the results identified by the algorithm, the air traffic management system can negotiate with users to adjust the flight trajectory, so as to reduce flight delay and ensure flight safety.

Multi-Scale Concurrent Topology Optimization Based on BESO, Implemented in MATLAB

In multi-scale topology optimization methods, the analysis encompasses two distinct scales: the macro-scale and the micro-scale. The macro-scale refers to the overall size and dimensions of the structural domain being studied, while the micro-scale pertains to the periodic unit cell that constitutes the macro-scale. This unit cell represents the entire structure or component targeted for optimization. The primary objective of this research is to present a simplified MATLAB code that addresses the multi-scale concurrent topology optimization challenge. This involves simultaneously optimizing both the macro-scale and micro-scale aspects, taking into account their interactions and interdependencies. To achieve this goal, the proposed approach leverages the Bi-directional Evolutionary Structural Optimization (BESO) method. The formulation introduced in this study accommodates both cellular and composite materials, dealing with both separate volume constraints and the utilization of a single volume constraint. By offering this simplified formulation and harnessing the capabilities of the multi-scale approach, the research aims to provide valuable insights into the concurrent optimization of macro- and micro-scales. This advancement contributes to the field of topology optimization and enhances its applications across various engineering disciplines.

Semi-Continuous Descent Operation: A Fuel-Efficient Interval Management Algorithm

This paper presents a fuel-efficient interval management algorithm called semi-continuous descent operation (semi-CDO) to support air traffic controllers in issuing altitude and velocity instructions to arriving aircraft to ensure proper separation. The control logic of semi-CDO is stated as an optimization problem of minimizing the fuel consumption of the descending trajectory based on the prediction model under the separation constraints. Numerical experiments simulating the arrival traffic at Kansai International Airport in Japan were performed to verify the effectiveness of the proposed algorithm. The results showed that semi-CDO achieves the fuel-efficient descent for multiple arrival aircraft while maintaining proper separation between them.

Regional ionospheric TEC modeling during geomagnetic storm in August 2021- data fusion using multi-instrument observations

Regional ionospheric Total Electron Content (TEC) models are most significant to investigate the variability of ionosphere during all-weather conditions. Since the ground-based TEC measurements are not available in oceanic and polar regions, space-based observations are incorporated to increase the positional accuracy and reliability of Global Ionospheric TEC Maps (GIMs). Therefore, data fusion techniques are necessary to enhance the prediction capability of regional ionospheric models by considering multi-source data. In view of this, an attempt is made to investigate Equatorial Ionization Anomaly (EIA) structures in low-latitudinal Indian region using multi-instrument data. Data observations from background model CODEGIM, available International GNSS Service (IGS) stations in India, GNSS receivers at KLEF and Tripura stations, FORMOSAT/COSMIC radio occultation and SWARM during geomagnetic storm period August 26–28, 2021 are used for the study. Spherical Harmonics Function (SHF) of order 4 is employed along with Weighted Least Squares analysis (WLS), where separate weight constraint is computed for each data source. TEC maps of spatial resolution 5° x 5° and temporal resolution of 1 h are generated to illustrate the dynamic behavior of ionosphere. The standard deviation for 3 days is obtained as 0.42, 0.61 and 1.43 TECU respectively. TEC depletions and enhancements are observed on August 27 and 28, with mean values of 12.74 and 15.27 TECU respectively, demonstrating negative and positive storm effects.

The Role of Fidelity in Goal-Oriented Semantic Communication: A Rate Distortion Approach

We study a variant of a robust description source coding framework, which is a relevant model for goal-oriented semantic information transmission, via its corresponding characterization. Considering two individual single-letter separable distortion constraints and input and output data acting as the intrinsic and extrinsic message, respectively, we first derive a lower bound on the optimal rates of the problem, as well as necessary and sufficient conditions for this bound to be tight. Subsequently, we prove a general result that provides in parametric form the optimal solution of the characterization of this problem. Capitalizing on these results, we examine the structure of the solution for one case study of general binary alphabets under Hamming distortions and solve in closed form a special case. We also solve another general binary alphabet case where a Hamming and an erasure distortion coexist, as a means to highlight the importance of selecting the type of the distortion constraint in goal-oriented semantic communication. Furthermore, we develop a goal-oriented Blahut-Arimoto (BA) algorithm, which can be used for the computation of any finite alphabet intrinsic or extrinsic message under individual distortion criteria. Finally, we revisit the problem for multidimensional independent and identically distributed (i.i.d.) jointly Gaussian processes with individual mean-square error (MSE) distortion constraints, providing new insights that have previously been overlooked. This work reveals the cardinal role of context-dependent fidelity criteria in goal-oriented semantic communication.

Machine Learning Supporting Enhanced Optimized Spacing Delivery between Consecutive Departing Aircraft

The Optimised Spacing Delivery (further referred to as OSD) tool has the objective of calculating the necessary time spacing between two consecutive departing aircraft in order to fulfil all required spacing and separation constraints. OSD, developed in SESAR 2020 Wave 1 [1] is based on analytical models [2] to predict aircraft trajectory and speed profiles. The use of this tool by Air Traffic Controller supports the safe, consistent and efficient delivery of the required separation or spacing between consecutive departure pairs by providing the time required between departure aircraft pairs via an automated count-down timer to the tower runway controller. In order to improve OSD, this paper introduces the enhanced Optimised Spacing Delivery (further referred to as eOSD) tool which builds on the OSD tool using Machine Learning techniques to make more accurate predictions of aircraft behaviour (e.g. trajectory/climb profile, speed profile) and wind on the initial departure path, so further optimising spacing delivery between consecutive departures. Zurich airport data were used to develop and asses the performance of the eOSD tool compared to the OSD tool.

A game-theoretical constructive approach for the multi-objective frequency assignment problem

This study presents the game modeling of the multi-objective frequency assignment problem (FAP) in cellular networks considering two conflicting objectives: interference and separation costs, while respecting separation constraints, and thus improving the QoS for end users. Two types of cooperative games are suggested depending on the TRX and frequency selection strategies each using two players, one for each considered objective. A feasible solution consisting of a frequency assignment plan is built during the constructive process. At each step of the game, a player assigns a frequency to a TRX according to a given strategy. The proposed solution being part of both multi-objective optimization (MOO) and game theory (GT), we used the most important measures in these two fields: the hypervolume (HV) and the Nash value, to evaluate the performance of our solutions to able to compare our results with those of these two communities: MOO and GT. The proposed games achieve a good trade-off between the two considered objectives corroborated by tests on two real-world instances, Denver and Seattle, demonstrating the performance of the proposed approach in solving the problem. Furthermore, the proposed performance evaluation method is innovative and also generic, since it can be adapted to any algorithm based on both GT and MOO, taking into account these two aspects.

Passivity-Based Decentralized Criteria for Small-Signal Stability of Power Systems With Converter-Interfaced Generation

With the increasing penetration of converter-interfaced generation, it would be advantageous to specify local grid-connectivity criteria to ensure small-signal stability of the interconnected system, rather than carrying out centralized stability studies every time the connection of a new device is contemplated. Passivity of the device admittance, which is an example of a local criterion, has been used previously to avoid resonances between converter-interfaced systems and the lightly damped oscillatory modes of the network, but it is unsuitable in general due to the conservative nature of passivity. Therefore, a composite set of criteria are proposed in this paper, which include time-scale separation (slow-fast clustering) constraints on the transient behaviour, and distinct passivity constraints for the slow and fast clusters. The application of these criteria is demonstrated using a case study.