Relaxed Region Research Articles

On the strength of Lagrangian duality in multiobjective integer programming

AbstractThis paper investigates the potential of Lagrangian relaxations to generate quality bounds on non-dominated images of multiobjective integer programs (MOIPs). Under some conditions on the relaxed constraints, we show that a set of Lagrangian relaxations can provide bounds that coincide with every bound generated by the convex hull relaxation. We also provide a guarantee of the relative quality of the Lagrangian bound at unsupported solutions. These results imply that, if the relaxed feasible region is bounded, some Lagrangian bounds will be strictly better than some convex hull bounds. We demonstrate that there exist Lagrangian multipliers which are sparse, satisfy a complementary slackness property, and generate tight relaxations at supported solutions. However, if all constraints are dualized, a relaxation can never be tight at an unsupported solution. These results characterize the strength of the Lagrangian dual at efficient solutions of an MOIP.

Analyzing the computational performance of balance constraints in the medium-term unit commitment problem: Tightness, compactness, and arduousness

Since its beginning, the computational performance of numerical optimization techniques has depended on utilizing efficient mathematical formulations to deal with large-size problems successfully. This fact is manifested in the unit commitment literature. Several approaches have been proposed to handle the complexity of accurately modeling real power systems. However, most of these methodologies focus on strengthening the technical features’ representations by reducing the number of constraints and variables of the associated optimization problem or approximating its relaxed feasible region to the integer one to improve resolution processes. Hence, the state-of-art of these effective procedures is periodically studied under operational research and commercial solvers developments. Nevertheless, the formulation comparisons frequently obviate analyzing the impact of the balance equations on the computational burden of the unit commitment problem. This constraint links every single technical restriction along the time span and sometimes provides an ample optimization space, sometimes a narrow one, directly affecting resolution proceedings. It can impose an electricity generation equal to demand, allow production excesses, include non-served energy, or establish profit-based relationships. This paper presents a computational analysis of the most popular balance equations, detailing solver performances and determining these methodologies’ tightness, compactness, and arduousness. Therefore, 1010 case studies were run utilizing different input profiles and optimality-convergence criteria.

EEG based stress analysis using rhythm specific spectral feature for video game play

Background and objective:For the emerging significance of mental stress, various research directives have been established over time to understand better the causes of stress and how to deal with it. In recent years, the rise of video gameplay has been unprecedented, further triggered by the lockdown imposed due to the COVID-19 pandemic. Several researchers and organizations have contributed to the practical analysis of the impacts of such extended periods of gameplay, which lacks coordinated studies to underline the outcomes and reflect those in future game designing and public awareness about video gameplay. Investigations have mainly focused on the “gameplay stress” based on physical syndromes. Some studies have analyzed the effects of video gameplay with Electroencephalogram (EEG), Magnetic resonance imaging (MRI), etc., without concentrating on the relaxation procedure after video gameplay. Methods:This paper presents an end-to-end stress analysis for video gaming stimuli using EEG. The power spectral density (PSD) of the Alpha and Beta bands is computed to calculate the Beta-to-Alpha ratio (BAR). The Alpha and Beta band power is computed, and the Beta-to-Alpha band power ratio (BAR) has been determined. In this article, BAR is used to denote mental stress. Subjects are chosen based on various factors such as gender, gameplay experience, age, and Body mass index (BMI). EEG is recorded using Scan SynAmps2 Express equipment. There are three types of video gameplay: strategic, puzzle, and combinational. Relaxation is accomplished in this study by using music of various pitches. Two types of regression analysis are done to mathematically model stress and relaxation curve. Brain topography is rendered to indicate the stressed and relaxed region of the brain. Results:In the relaxed state, the subjects have BAR 0.701, which is considered the baseline value. Non-gamer subjects have an average BAR of 2.403 for 1 h of strategic video gameplay, whereas gamers have 2.218 BAR concurrently. After 12 minutes of listening to low-pitch music, gamers achieved 0.709 BAR, which is nearly the baseline value. In comparison to Quartic regression, the 4PL symmetrical sigmoid function performs regression analysis with fewer parameters and computational power. Conclusion:Non-gamers experience more stress than gamers, whereas strategic games stress the human brain more. During gameplay, the beta band in the frontal region is mostly activated. For relaxation, low pitch music is the most useful medium. Residual stress is evident in the frontal lobe when the subjects have listened to high pitch music. Quartic regression and 4PL symmetrical sigmoid function have been employed to find the model parameters of the relaxation curve. Among them, quartic regression performs better in terms of Akaike information criterion (AIC) and R2 measure.

Derivation and generation of path-based valid inequalities for transmission expansion planning

This paper seeks to solve the long-term transmission expansion planning problem in power systems more effectively by reducing the solution search space and the computational effort. The proposed methodology finds and adds cutting planes based on structural insights about bus angle differences along paths. Two lemmas and a theorem are proposed which formally establish the validity of these cutting planes onto the underlying mathematical formulations. These path-based bus angle difference constraints, which tighten the relaxed feasible region, are used in combination with branch-and-bound to find lower bounds on the optimal investment of the transmission expansion planning problem. This work also creates an algorithm that automates the process of finding and applying the most effective valid inequalities, resulting in significantly reduced testing and computational time. The algorithm is implemented in Python, using Gurobi to add constraints and solve the exact DCOPF-based transmission expansion problem. This paper uses two different-sized systems to illustrate the effectiveness of the proposed framework: the GOC 500-bus system and a modified Polish 2383-bus system.

Estimation of gradient size of interfacial strain and its optimization for effective magnetoelectric coupling in (CoFe2O4) – (0.93Na0.5Bi0.5TiO3 – 0.07BaTiO3), 2-2 nano-composites

Strain-mediated coupling between the magnetic and electrically ordered phases plays a significant role in magnetoelectric (ME) nano-composites. This study explores a method to analyse and quantify interfacial strain using a grazing angle scan (α) in a ME composite optimised for a specific microstructure. The details of strain around the interface CoFe2O4 (CFO) – 0.93Na0.5Bi0.5TiO3 – 0.07BaTiO3 (NBT-BT) was determined by performing ‘α’ scan, in order to gather information at various depths of the NBT-BT layer around maximum intensity (110) reflection. The strain around the interface was observed to dominate over a spatial region of ∼20–30 nm away from the interface. The Piezoresponse force microscopy (PFM) studies performed near the interface reveal that the strain constrain experienced by the ferroelectric layer operates such that polarisation rotation and domain wall motion are constrained compared to the strain relaxed region of the film. For effective strain transfer, heterostructures grown with optimised thicknesses (∼20–30 nm) exhibited a superior inverse piezomagnetic effect.

Identification of rejuvenation and relaxation regions in a Zr-based metallic glass induced by laser shock peening

In this paper, laser shock peening (LSP) treatment was performed on Zr35Ti30Cu10Ni5Be20 bulk metallic glass (BMG) and the effects of induced energy on the characteristics of glassy structure were evaluated. The high resolution atomic force microscopy (AFM) and nanoindentation tests were carried out to characterize the nanoscale heterogeneity and micromechanical properties in the depth of material. According to the results, the surface of material showed a high heterogeneous structure, which was the sign of structural rejuvenation. However, with the move into the depth of material, the nanoscale heterogeneity decreased and eventually a relaxed region with the minimum heterogeneity was found in the 1.5–2 mm depth of BMG sample. Passing the relaxed region, again the nanoscale heterogeneity similar to the as-cast sample was observed. The nanoindentation results also confirmed the AFM outcomes. It is suggested that the relaxed region at the neighbor of rejuvenated region is due to the satisfaction of elastic adaptability which is resulted by the nanoscale shear events and the induced stress.

Stabilizing a multicopter using an NMPC design with a relaxed terminal region

Abstract This paper highlights the benefits of a feedback linearization local controller and the associated terminal bound constraints (box-type inequalities) in an NMPC (Nonlinear Model Predictive Control) design for a multicopter system. We replace the standard invariant construction for the terminal region of the NMPC design with two sets: i) a δ-invariant set (with δ the sampling time) which constrains the trajectories to re-enter it periodically, at pre-defined moments of time; ii) a constraint admissible safe set in which the trajectories lie in the remaining time instants. We show that this alternative construction verifies the recursive feasibility and asymptotic stability. Moreover, the additional degrees of freedom and simpler construction show advantages over similar NMPC designs with standard ellipsoidal terminal region.

Phased-Array Transmission for Secure mmWave Wireless Communication via Polygon Construction

This paper presents two secure transmission algorithms for millimeter-wave wireless communication, which are computationally attractive and have analytical solutions. In the proposed algorithms, we consider phased-array transmission structure and focus on phase shift keying (PSK) modulation. It is found that the traditional constellation synthesis problem can be solved with the aid of polygon construction in the complex plane. A detailed analysis is then carried out and an analytical procedure is developed to obtain a qualified phase solution. For a given synthesis task, it is derived that there exist infinite weight vector solutions under a mild condition. Based on this result, we propose the first secure transmission algorithm by varying the transmitting weight vector at symbol rate, thus resulting exact phases at the intended receiver and producing randomnesses at the undesired eavesdroppers. To improve the security without significantly degrading the symbol detection reliability for target receiver, the second secure transmission algorithm is devised by allowing a relaxed symbol region for the intended receiver. Compared to the first algorithm, the second one incorporates an additional random phase rotation operation to the transmitting weight vector and brings extra disturbance for the undesired eavesdroppers. Different from the existing works that are only feasible for the case of single-path mmWave channels, our proposed algorithms are applicable to more general multi-path channels. Moreover, all the antennas are active in the proposed algorithms and the on-off switching circuit is not needed. Simulations are presented to demonstrate the effectivenesses of the proposed algorithms under various situations.

Feasibility reduction approach for hierarchical decision making with multiple objectives

Several decision making problems with multiple decision makers in a hierarchical decision making scenario can be best described using multilevel optimization problem. Different organizational structure adapt a hierarchical decision making system where each decision maker controls parts of the decision variables and is affected by the decision of other decision makers. Recently, inspired by natural adaptation, a metaheuristic based algorithm is proposed for these problems. The algorithm works by using an initial solution generated by solving the leader’s problem, where the leader is the decision maker in the upper level. That solution will go through each level by adjusting and evolving its components. Even though the approach is tested to be promising, the final solution can be very different from the initial one given by the leader. Furthermore, no cooperation mechanism between the decision makers is given. In addition, the decision makers may have multiple and conflicting objectives. In this paper a cooperation mechanism where fuzzy membership function is used to link the cooperation between the decision makers is used. That means once the solution received by the lower level decision makers, a cooperative feasible region will be determined which is a subset of the relaxed feasible region. To deal with the multiobjective optimization problem, preference free method called ideal point method will be used. Bi-level numerical examples are also given to demonstrate how the algorithm works.

Processor-Tracing Guided Region Formation in Dynamic Binary Translation

Region formation is an important step in dynamic binary translation to select hot code regions for translation and optimization. The quality of the formed regions determines the extent of optimizations and thus determines the final execution performance. Moreover, the overall performance is very sensitive to the formation overhead, because region formation can have a non-trivial cost. For addressing the dual issues of region quality and region formation overhead, this article presents a lightweight region formation method guided by processor tracing, e.g., Intel PT. We leverage the branch history information stored in the processor to reconstruct the program execution profile and effectively form high-quality regions with low cost. Furthermore, we present the designs of lightweight hardware performance monitoring sampling and the branch instruction decode cache to minimize region formation overhead. Using ARM64 to x86-64 translations, the experiment results show that our method achieves a performance speedup of up to 1.53× (1.16× on average) for SPEC CPU2006 benchmarks with reference inputs, compared to the well-known software-based trace formation method, Next Executing Tail (NET). The performance results of x86-64 to ARM64 translations also show a speedup of up to 1.25× over NET for CINT2006 benchmarks with reference inputs. The comparison with a relaxed NETPlus region formation method further demonstrates that our method achieves the best performance and lowest compilation overhead.

New theoretical model for predicting and modelling fractures in folded fractured reservoirs

In this study, an attempt has been made to develop a new theoretical model that can be used to predict the fracture spacing/density that develops in a single competent layer and in multilayers as a result of folding. The work is based on earlier analyses concerned with the fracturing of unfolded strata subjected only to layer-normal compression. Such a stress state exists in the upper crust in any tectonically relaxed region where the principal cause of stress is the overburden. Unlike previous studies on theoretical fracture-spacing modelling that are mainly designed for a layer-parallel horizontal-extension system, this study has introduced a new theoretical model for the predicting and modelling of fracture spacing/density in ‘folded’ reservoirs, which contain > 85% of the world's oil and gas traps. This theoretical model is an integrated model: that is, it takes into account both rock mechanical and geometrical properties of the reservoir. The big advantage of the theoretical model developed in this study is that it provides well- and reservoir-scale estimates of the fracture spacing, for both axial and cross-axial fractures (i.e. the dominant fracture sets in folded reservoirs), which can be used for predicting fracture density (the reciprocal of fracture spacing), fracture aperture, the Rock Fracture Potential Index (RFPI), fracture porosity, fracture permeability, the shape factor (sigma) and for optimizing the drilling (i.e. the Optimum Drilling Direction (ODD) and the Optimum Drilling Angle (ODA) to maximize the fracture intersection in the wells) in three dimensions in folded, single layer and multilayer fractured reservoirs. In addition, new approaches are described for quantifying the mechanical bed thickness (MBT) or mechanical unit thickness (MUT), estimating the fracture aperture ( w ), estimating the distance from the neutral surface ( a ) and determining the RFPI data that are essential for implementing the theoretical model presented in this paper related to subsurface, folded, fractured reservoirs. The expressions derived for fracture spacing/density, for both axial and cross-axial fracture sets, involve data that are always available for every field development (i.e. seismic, well and core data). An understanding of the distribution of the fracture spacing/density, fracture aperture and the RFPI at an early stage in the development of a fractured reservoir is crucial in selecting a proper field development strategy, managing well placement and for monitoring production from the reservoir. In summary, based on several case studies, one of which is presented in this paper, it can be confirmed that the theoretical model, expressed in equations given in this paper, predicts what has been observed in the folded clastic reservoirs of the study area. It is concluded that curvature alone cannot reveal the location of natural fractures in a reservoir and that the mechanical properties of the reservoir rock play a significant role in the development of a natural fracture system. Rock can accommodate strain by fracturing (i.e. if its RFPI is high) or (if its RFPI is low) use its internal strain storage capability (associated with its mechanical properties: e.g. porosity collapsing, grain sliding and the formation of intra-grain hairline fractures) to consume the stress without the need to accommodate strain by fracturing.

Energy-Efficient Symbol-Level Precoding in Multiuser MISO Based on Relaxed Detection Region

This paper addresses the problem of exploiting interference among simultaneous multiuser transmissions in the downlink of multiple-antenna systems. Using symbol-level precoding, a new approach towards addressing the multiuser interference is discussed through jointly utilizing the channel state information (CSI) and data information (DI). The interference among the data streams is transformed under certain conditions to a useful signal that can improve the signal-to-interference noise ratio (SINR) of the downlink transmissions and as a result the system's energy efficiency. In this context, new constructive interference precoding techniques that tackle the transmit power minimization (min power) with individual SINR constraints at each user's receiver have been proposed. In this paper, we generalize the CI precoding design under the assumption that the received MPSK symbol can reside in a relaxed region in order to be correctly detected. Moreover, a weighted maximization of the minimum SNR among all users is studied taking into account the relaxed detection region. Symbol error rate analysis (SER) for the proposed precoding is discussed to characterize the tradeoff between transmit power reduction and SER increase due to the relaxation. Based on this tradeoff, the energy efficiency performance of the proposed technique is analyzed. Finally, extensive numerical results show that the proposed schemes outperform other state-of-the-art techniques.

A relaxed nonmonotone adaptive trust region method for solving unconstrained optimization problems

In this paper, we present a new relaxed nonmonotone trust region method with adaptive radius for solving unconstrained optimization problems. The proposed method combines a relaxed nonmonotone technique with a modified version of the adaptive trust region strategy proposed by Shi and Guo (J Comput Appl Math 213:509---520, 2008). Under some suitable and standard assumptions, we establish the global convergence property as well as the superlinear convergence rate for the new method. Numerical results on some test problems show the efficiency and effectiveness of the new proposed method in practice.

Ambient tectonic stress as fragile geological feature

Strong seismic waves produce frictional failure within shallow pervasively cracked rocks. Distributed failure preferentially relaxes ambient tectonic stresses, providing a fragility measure of past strong shaking. Relaxation of the regional fault-normal compression appears to have occurred within granite from 768 m down to ∼1000–1600 m depth at the Pilot Hole near Parkfield, California. Subsequent movements on the main fault have imposed strike-slip stress within the relaxed region. Peak ground velocities of ∼2 m s−1 are inferred for infrequent (few 1000 yr recurrence) past earthquakes from stress relaxation within the granite and from the variation of S wave velocity with depth in the overlying sandstone. Conversely, frequent strong shaking in slowly deforming regions relaxes shallow ambient tectonic stress. This situation is expected beneath Whittier Narrows, where strong Love waves from numerous San Andreas events repeatedly produced nonlinear behavior.

Near-surface controls on the composition of growing crystals: Car–Parrinello molecular dynamics (CPMD) simulations of Ti energetics and diffusion in alpha quartz

Ab initio molecular dynamics simulations were used to explore changes in the vacancy-formation energy for Ti atoms and Ti–O bond characteristics in the outermost monolayers of the (100) and (010) prism faces of α quartz. Within 2 or 3 polyhedral layers of the crystal surface, the Ti vacancy-formation energy is substantially smaller than the bulk-lattice value of 11.8eV. This is true of both oxygen-terminated surfaces and the geologically more realistic case in which the outermost oxygens are bonded to hydrogen. A key additional finding is that the Ti vacancy-formation energy near the H-terminated (100) surface differs by 1–2eV from that near the H-terminated (010) surface. This difference means that the energy change accompanying Ti↔Si exchange between the bulk lattice and the near surface is also different for (100) and (010). Ultimately, therefore, the equilibrium concentrations of Ti near these two prism faces will not be the same. During crystal growth, this compositional difference may be “captured” by the quartz lattice and preserved as sectoral variation in Ti content—a feature commonly observed in both synthetic and natural α quartz. In this respect, the MD simulations provide direct support for the growth entrapment model (GEM; Watson, 2004) for non-equilibrium uptake of trace elements.To complement the vacancy-formation energy results, we used the first-principles metadynamics method to calculate diffusion pathways and free energy barriers for Ti diffusion in the bulk α quartz lattice and in the near-surface region. The computed estimate of the bulk-lattice activation energy compares favorably with the experimentally determined value of 2.8eV (Cherniak et al., 2007), lending credence to the method. Diffusion results for the near-surface reveal a steep decrease in the activation energy for Ti diffusion approaching the surface in the outermost 2–3 polyhedral layers of the crystal. This finding implies depth-dependent Ti diffusion in the near-surface (∼0.5nm), which is also a key aspect of the growth-entrapment model.Although our results are strictly applicable only to Ti in α quartz, the demonstration that impurity atom energetics and diffusion are functions of depth in the near-surface region may be broadly applicable, given the similarity in measured length scale of the near-surface relaxed region in a wide variety of minerals. Kinetic models of impurity uptake that do not consider these factors may be incomplete.

Spatially resolved investigation of strain and composition variations in (In,Ga)N/GaN epilayers

The strain state and composition of a 400 nm thick (In,Ga)N layer grown by metal-organic chemical vapor deposition on a GaN template are investigated by spatially integrated x-ray diffraction and cathodoluminescence (CL) spectroscopy as well as by spatially resolved CL and energy dispersive x-ray analysis. The CL investigations confirm a process of strain relaxation accompanied by an increasing indium content toward the surface of the (In,Ga)N layer, which is known as the compositional pulling effect. Moreover, we identify the strained bottom, unstrained top, and gradually relaxed intermediate region of the (In,Ga)N layer. In addition to an increase of the indium content along the growth direction, the strain relaxation leads to an enhancement of the lateral variations of the indium distribution toward the surface.

Toughening fragile matter: mechanical properties of particle solids assembled from polymer-grafted hybrid particles synthesized by ATRP

The effect of polymer-graft modification on the structure formation and mechanical characteristics of inorganic (silica) nanoparticle solids is evaluated as a function of the degree of polymerization of surface-grafted chains. A transition from ‘hard-sphere-like’ to ‘polymer-like’ mechanical characteristics of particle solids is observed for increasing degree of polymerization of grafted chains. The elastic modulus of particle solids increases by about 200% and levels off at intermediate molecular weights of surface-grafted chains, a trend that is rationalized as a consequence of the elastic modulus being determined by dispersion interactions between the polymeric grafts. A pronounced increase (of about one order of magnitude) of the fracture toughness of particle solids is observed as the degree of polymerization of grafted chains exceeds a threshold value that is similar for both polystyrene and poly(methyl methacrylate) grafts. The increased resistance to fracture is interpreted as a consequence of the existence of entanglements between surface-grafted chains that give rise to energy dissipation during fracture through microscopic plastic deformation and craze formation. Within the experimental uncertainty the transition to polymer-like deformation characteristics is captured by a mean field scaling model that interprets the structure of the polymer shell of polymer-grafted particles as effective ‘two-phase’ systems consisting of a stretched inner region and a relaxed outer region. The model is applied to predict the minimum degree of polymerization needed to induce polymer-like mechanical characteristics and thus to establish ‘design criteria’ for the synthesis of polymer-modified particles that are capable of forming mechanically robust and formable particle solid structures.

Formal Verification of Temporal Properties for Reduced Overhead in Grid Scientific Workflows

With quick development of grid techniques and growing complexity of grid applications, it is becoming critical for seasoning temporal properties of grid workflows to probe potential pitfalls and errors, in order to ensure reliability and trustworthiness at the initial design phase. A state Pi calculus is proposed and implemented in this work, which not only enables flexible abstraction and management of historical grid system events, but also facilitates modeling and temporal verification of grid workflows. Furthermore, a relaxed region analysis (RRA) approach is proposed to decompose large scale grid workflows into sequentially composed regions with relaxation of parallel workflow branches, and corresponding verification strategies are also decomposed following modular verification principles. Performance evaluation results show that the RRA approach can dramatically reduce CPU time and memory usage of formal verification

Orientational Relationships and Atomic Arrangements of GaN Nanorods Grown on Al<SUB>2</SUB>O<SUB>3</SUB> (0001) Substrates by Using Hydride Vapor Phase Epitaxy

Scanning electron microscopy (SEM) images and transmission electron microscopy (TEM) images showed that the one-dimensional GaN nanorods were formed on Al2O3 (0001) substrates by using hydride vapor phase epitaxy without a catalyst. Selected area electron diffraction (SAED) pattern and high-resolution TEM (HRTEM) results showed that GaN nanorods grown on Al2O3 (0001) substrates had crystalline wurzite structures and (0001) preferential orientation. The morphologies of GaN nanorods were affected by the flow rates of the source materials. The orientational relationships between the GaN nanorods and the Al2O3 substrates were (0001)GaN perpendicular (0001) Al2O3 and [0110]GaN perpendicular [1120] Al2O3. Cross-sectional and plan-view atomic arrangements of the fully relaxed interfacial region are described on the basis of the TEM, the SAED pattern, and the HRTEM results.

Local analysis of the edge dislocation core in BaTiO3 thin film by STEM‐EELS

The a <100> edge dislocation core formed in an epitaxial BaTiO(3) (BTO) thin film grown on a substrate was investigated by scanning transmission electron microscopy combined with electron energy-loss spectroscopy. Elemental analysis using core-loss spectrum indicates that the atomic ratios of O/Ti and Ba/Ti are decreased at the dislocation core. The near-edge fine structure of the oxygen K-edge recorded from the dislocation core differs slightly from that of relaxed BTO region, which suggests that Ba-O bonding is decreased at the dislocation core. The structure of the dislocation core is discussed using a high-angle annular dark-field image and the electron energy-loss spectroscopy results.