Bounding Technique Research Articles

Novel mathematical formulations for parallel-batching processing machine scheduling problems

We study mathematical formulations for batch-processing machine scheduling problems (BPMPs), which are the challenging issues in the machine scheduling literature where machines are capable of processing a batch of jobs simultaneously if jobs with non-identical sizes can be packed in a capacitated machine. In this paper, we tackle single- and parallel-machine BPMPs, and other interesting problem variants that aim at minimizing the makespan. We develop novel formulations along with valid inequalities and an algorithm framework that makes use of dual information and bounding techniques to achieve efficiency when instances are intractable. Extensive computational experiments on benchmark instances show that our approaches achieve state-of-the-art results and prove the optimality of intractable instances in the literature.

Improved a posteriori error bounds for reduced port-Hamiltonian systems

Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically known to be highly pessimistic in the sense of largely overestimating the true error. This work applies two improved error bounding techniques, namely (a) a hierarchical error bound and (b) an error bound based on an auxiliary linear problem, to the case of port-Hamiltonian systems. The approaches rely on a secondary approximation of (a) the dynamical system and (b) the error system. In this paper, these methods are adapted to port-Hamiltonian systems. The mathematical relationship between the two methods is discussed both theoretically and numerically. The effectiveness of the described methods is demonstrated using a challenging three-dimensional port-Hamiltonian model of a classical guitar with fluid–structure interaction.

A tight formulation for the dial-a-ride problem

Ridepooling services play an increasingly important role in modern transportation systems. With soaring demand and growing fleet sizes, the underlying route planning problems become increasingly challenging. In this context, we consider the dial-a-ride problem (DARP): Given a set of transportation requests with pick-up and delivery locations, passenger numbers, time windows, and maximum ride times, an optimal routing for a fleet of vehicles, including an optimized passenger assignment, needs to be determined. We present tight mixed-integer linear programming (MILP) formulations for the DARP by combining two state-of-the-art models into novel location-augmented-event-based formulations. Strong valid inequalities and lower and upper bounding techniques are derived to further improve the formulations. We then demonstrate the theoretical and computational superiority of the new models: First, the linear programming relaxations of the new formulations are stronger than existing location-based approaches. Second, extensive numerical experiments on benchmark instances show that computational times are on average reduced by 53.9% compared to state-of-the-art event-based approaches.

Land ownership and nutrition in Nepal

AbstractThis paper provides empirical evidence on the relationship between women's land ownership and nutritional outcomes in Nepal. Using three waves of the Nepal Demographic and Health Survey and employing a bounding technique by Oster, I estimate bounded treatment effects of land ownership. The results show that women's land ownership is associated with a reduction in the incidence of childhood underweight and stunting and an increase in women's body mass index. Additionally, I find the selection on unobservable characteristics has to be larger than the selection on observable characteristics to drive these estimates to zero, suggesting that land ownership credibly improves nutritional outcomes. Furthermore, heterogeneous results show that the negative association between land ownership and childhood nutritional status is more prominent in male children and children from the Brahmin caste. Similarly, the negative relationship between land ownership and underweight in women is more pronounced in women employed in agriculture and rural areas. While I argue that landownership improves nutrition, these estimates are sensitive to the assumptions made.

Assessment of false discovery rate control in tandem mass spectrometry analysis using entrapment.

A pressing statistical challenge in the field of mass spectrometry proteomics is how to assess whether a given software tool provides accurate error control. Each software tool for searching such data uses its own internally implemented methodology for reporting and controlling the error. Many of these software tools are closed source, with incompletely documented methodology, and the strategies for validating the error are inconsistent across tools. In this work, we identify three different methods for validating false discovery rate (FDR) control in use in the field, one of which is invalid, one of which can only provide a lower bound rather than an upper bound, and one of which is valid but under-powered. The result is that the field has a very poor understanding of how well we are doing with respect to FDR control, particularly for the analysis of data-independent acquisition (DIA) data. We therefore propose a new, more powerful method for evaluating FDR control in this setting, and we then employ that method, along with an existing lower bounding technique, to characterize a variety of popular search tools. We find that the search tools for analysis of data-dependent acquisition (DDA) data generally seem to control the FDR at the peptide level, whereas none of the DIA search tools consistently controls the FDR at the peptide level across all the datasets we investigated. Furthermore, this problem becomes much worse when the latter tools are evaluated at the protein level. These results may have significant implications for various downstream analyses, since proper FDR control has the potential to reduce noise in discovery lists and thereby boost statistical power.

Consolidation effects on pipe-soil interaction due to tunneling

Existing studies on soil-pipe interaction due to tunneling mainly focus on short-term responses. However, in areas with high water tables and low permeability soil, long-term ground movement and associated pipe responses may occur due to dissipation of excess pore pressure generated during tunnel construction. In this paper, a Winkler solution with time-varying subgrade modulus and the corresponding greenfield soil displacement formula are developed to investigate the tunneling effects on existing pipelines. The pipe is considered as an infinite Euler beam of finite width resting on a poroelastic half-space, and adhesion and drainage effects between the pipe and soil are considered using bounding techniques. The greenfield consolidation settlement is evaluated using a modified Gaussian curve. The findings indicate that the subgrade modulus decreases while greenfield soil displacement increases during the consolidation process. The time-dependent behavior of the subgrade modulus is governed by the drainage condition at the pipe-soil interface, whereas the greenfield soil displacement is primarily influenced by the drainage condition at the tunnel-soil interface. The study reveals that the bonded contact condition, hydraulic boundary condition, and displacement constraint conditions all influence the bending moment of the pipe.

A new branch and bound method for solving linear multiplicative programming problems

ABSTRACT This paper studies a class of linear multiplicative problems (LMP). To find a global optimal solution of problem (LMP), we first convert problem (LMP) into an equivalent problem (EP) via auxiliary variables, then problem (EP) is expressed as a two-layer problem (EP1). On the basis of problems (EP) and (EP1), a new bounding technique which integrates two linear relaxation processes is proposed to obtain a valid lower bound for the optimal value of (LMP). Combining the bounding technique with the bisection branching rule, a novel branch and bound algorithm is designed. Also, we establish the global convergence of the proposed algorithm and estimate its computational complexity. Preliminary numerical results verify the feasibility and effectiveness of the presented method.

Low-Order Automatic Domain Splitting Approach for Nonlinear Uncertainty Mapping

This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second-order Taylor expansions and polynomial bounding techniques is first introduced to estimate the Jacobian variation of a nonlinear transformation. This index is then embedded into a low-order automatic domain splitting algorithm that accurately describes the mapping of an initial uncertainty set through a generic nonlinear transformation by splitting the domain whenever nonlinearities grow above a predefined threshold. The algorithm is illustrated in the critical case of orbital uncertainty propagation, and it is coupled with a tailored merging process that limits the growth of the domains in time by recombining them when nonlinearities decrease. The low-order automatic domain splitting algorithm is then combined with Gaussian mixture models to accurately describe the propagation of a probability density function.

The effects of class attendance on academic performance: Evidence from synchronous courses during Covid-19 at a Chinese research university

Using 13,584 observations of 4772 undergraduate students enrolled in 523 online classes offered synchronously at a research university in China, and using online-learning platform data and administrative data, this paper examines the impacts of class attendance on academic performance. Based on student-level and course-level fixed effects models with a unique set of student-course level control variables, this paper finds class attendance to have a significantly positive impact on academic performance. This effect is larger for low-performing students and smaller for students in courses with larger class sizes. The above findings survive a number of robustness checks, including a bounding technique, restricting sample to compulsory courses and limiting variation in attendance caused by whole day absence.

A Decomposition of Economic Vulnerability Among Indigenous and Non‐Indigenous Adults in Canada

Using the 2004–2007 and 2008–2011 panels of the Canadian Survey of Labour and Income Dynamics, we examine earnings and employment disparities between Indigenous and non‐Indigenous adults. While an income gap exists and tends not to significantly change over time, taxes and transfers reduce it by almost 40 percent. Further, the gap is generally largest at the bottom of the income distribution. The explained component of the gap is primarily due to differences in education, particularly for young workers, and although the unexplained portion decreases over time, this is due to increased differences in observed labor market characteristics, implying that labor market discrimination may be on the rise. In addition, the probability of joblessness is higher for Indigenous adults and the male gap has increased. Results are robust to a bounding technique that adjusts for labor force participation differences and tend to be driven by First Nations (as opposed to Métis) adults.

Dimensioning Cuboid and Cylindrical Objects Using Only Noisy and Partially Observed Time-of-Flight Data.

One of the challenges of using Time-of-Flight (ToF) sensors for dimensioning objects is that the depth information suffers from issues such as low resolution, self-occlusions, noise, and multipath interference, which distort the shape and size of objects. In this work, we successfully apply a superquadric fitting framework for dimensioning cuboid and cylindrical objects from point cloud data generated using a ToF sensor. Our work demonstrates that an average error of less than 1 cm is possible for a box with the largest dimension of about 30 cm and a cylinder with the largest dimension of about 20 cm that are each placed 1.5 m from a ToF sensor. We also quantify the performance of dimensioning objects using various object orientations, ground plane surfaces, and model fitting methods. For cuboid objects, our results show that the proposed superquadric fitting framework is able to achieve absolute dimensioning errors between 4% and 9% using the bounding technique and between 8% and 15% using the mirroring technique across all tested surfaces. For cylindrical objects, our results show that the proposed superquadric fitting framework is able to achieve absolute dimensioning errors between 2.97% and 6.61% when the object is in a horizontal orientation and between 8.01% and 13.13% when the object is in a vertical orientation using the bounding technique across all tested surfaces.

Optimal Tuning of a Bounded e-Modified Adaptive Control Law using a Particle Swarm Optimization algorithm

This paper presents the gain tuning of an adaptive control law by means of Particle Swarm Optimization (PSO). The restrictions imposed on the particles in the PSO are obtained from the stability analysis of the adaptive control law. In this way, the PSO produces particles associated with optimal gains that simultaneously guarantee closed-loop stability and the minimization of the Fitness Function. The adaptive controller employs the velocity and acceleration of the desired trajectory signal for constructing the regressor vector used in the updated law. In addition, a new bounding technique is proposed for the estimated parameters allowing them to remain within certain prescribed limits. The performance of the adaptive law tuned using the PSO is evaluated by experiments on a low-cost servo system.

Novel stability criteria of generalized neural networks with time-varying delay based on the same augmented LKF and bounding technique

This paper researches the stability issue of generalized neural networks (GNN) with time-varying delay. For the delay, its derivative has an upper bound or is unknown. Firstly, the augmented Lyapunov-Krasovskii functional (LKF) is constructed based on the state vectors of the third order integral inequalities. Then, by introducing two sets of state vectors, the LKF derivative is presented as the quadratic and quintic polynomials of the delay, respectively. Next, the new quadratic and quintic polynomial negative definite conditions (NDCs) are proposed to set up the linear matrix inequalities (LMIs). In addition, based on the same LKF and third order integral inequalities, this paper proves that the introduction of extra state vectors increases the conservatism of the derived stability conditions. Eventually, the advantages of the provided conditions are illustrated by several numerical examples.

Upper Bounds on the Mismatched Reliability Function and Capacity Using a Genie Receiver

We develop a novel framework for proving converse theorems for channel coding, which is based on the analysis technique of multicast transmission with an additional auxiliary receiver, which serves as a genie to the original receiver. The genie provides the original receiver a certain narrowed list of codewords to choose from that includes the transmitted one. This technique is used to derive upper bounds on the mismatch capacity of discrete memoryless channels as well as the reliability function with a mismatched decoding metric. Unlike previous works, our bounding technique exploits also the inherent symmetric requirement from the codewords, leading to these new upper bounds. Since the computations of most of the known bounds on the mismatch capacity are rather complicated, we further present a method to obtain relaxed bounds that are easier to compute. As an example, we analyze the obtained bounds in the binary-input channels case. We conclude by presenting simpler bounds on the reliability function, and provide sufficient conditions for their tightness in certain ranges of rates.

Distributed global adaptive bipartite consensus of multi-agent systems with signed communication topology structure

This paper focuses on designing a fully distributed adaptive fuzzy bipartite consensus control protocol for unknown nonlinear multi-agent systems with a class of undirected signed graph. Utilizing the fuzzy logical system universal approximator as a compensator to describe the uncertain nonlinear dynamics, a fully distributed adaptive fuzzy control protocol is proposed by means of re-parameterized approach and bounding technique, the global bipartite consensus of leader-following multi-agent systems without using any dynamics of the leader is proven via constructing a new Lyapunov function. The proposed protocol overcomes the drawback of the semi-global consensus in existing literature. Furthermore, as an extension of the former result, a bipartite formation control problem is also solved. Finally, the proposed methods are validated by simulation examples.

H∞‐optimal observer design for systems with multiple delays in states, inputs and outputs: A PIE approach

AbstractThis article investigates the ‐optimal estimation problem of a class of linear system with delays in states, disturbance input, and outputs. The estimator uses an extended Luenberger estimator format which estimates both the present and history states. The estimator is designed using an equivalent Partial Integral Equation (PIE) representation of the coupled nominal system. The advantage of the resulting PIE representation is compact and delay free—obviating the need for commonly used bounding technique such as integral inequalities which typically introduces conservatism into the resulting optimization problem. The ‐optimal estimator synthesis problem is then reformulated as a Linear Partial Inequality (LPI)—a form of convex optimization using operator variables and inequlities. Such LPI‐based optimization problems can be solved using semidefinite programming via the PIETOOLS toolbox in Matlab. Compared with previous work, the proposed method simplifies the analysis and computation process and resulting in observers which are non‐conservtism to 4 decimal places when compared with Pad‐based ODE observer design methodologies. Numerical examples and simulation results are given to illustrate the effectiveness and scalability of the proposed approach.

Rate analysis of ZF receiver for uplink cell-free massive MIMO systems with D2D communications

This paper proposes a transmission structure of zero forcing (ZF) receiver for uplink cell-free massive multiple-input multiple-output (MIMO) systems with device-to-device (D2D) communications, followed by a rate analysis. We assumed that D2D users (DUEs) can utilize orthogonal radio resources to improve the efficiency of the scarce utilization or repurpose the time–frequency-spectrum resources currently used by the cell-free users (CFUEs). Assuming that the imperfect channel state information (CSI) is realizable, after that, the use-and-forget bounding technique is then used to respectively obtain the closed-form expressions of the CFUEs and DUEs, which provide the lower bounds on the ergodic approximate realizable rate of both communication links. First, we calculate the minimum-mean-square error (MMSE) estimation for all channels. Then, the derived results of the achievable uplink sum rate provide us with a tool that enables us to explain how some important parameters, such as the number of access points (APs)/CFUEs, each AP/CFUE/antenna, and the density of DUEs, affect system performance, highlighting the significance of cooperation between cell-free massive MIMO and D2D communication.

Nonlinearly Parametrized Modeling and Adaptive Control for a Generic Hypersonic Vehicle

This paper constructs a nonlinearly parametrized hypersonic cruise vehicle model on the basis of the existing on-orbit flight data using a curve-fitting technique. The hypersonic cruise vehicle system is separated into two interconnected subsystem: an attitude subsystem with rotational dynamics and a velocity subsystem with engine dynamics. The continuous adaptive controllers are designed for two subsystems using a novel function bounding technique and appropriate coordinate transformations, respectively, which ensure the global boundedness of all signals and achieve the non-zero equilibrium point regulation of nonlinearly parametrized hypersonic vehicle systems. One of the implications of this result is that growing nonlinearities in the uncertain model of the hypersonic vehicle system may be allowed for global stabilization. A simulation result verifies the effectiveness of the proposed adaptive control scheme.

Learned Upper Bounds for the Time-Dependent Travelling Salesman Problem

Given a graph whose arc traversal times vary over time, the Time-Dependent Travelling Salesman Problem consists in finding a Hamiltonian tour of least total duration covering the vertices of the graph. The main goal of this work is to define tight upper bounds for this problem by reusing the information gained when solving instances with similar features. This is customary in distribution management, where vehicle routes have to be generated over and over again with similar input data. To this aim, we devise an upper bounding technique based on the solution of a classical (and simpler) time-independent Asymmetric Travelling Salesman Problem, where the constant arc costs are suitably defined by the combined use of a Linear Program and a mix of unsupervised and supervised Machine Learning techniques. The effectiveness of this approach has been assessed through a computational campaign on the real travel time functions of two European cities: Paris and London. The overall average gap between our heuristic and the best-known solutions is about 0.001\%. For 31 instances, new best solutions have been obtained.

Modeling and adaptive control of air vehicles with partial nonlinear parametrization

This paper studies the control of a generic longitudinal air vehicle dynamic model during the cruise phase with nonlinearly parametrized uncertain aerodynamic functions. Verified by the improved coefficient precision of the aerodynamic forces and moments, using a curve fitting technique on available flight data, it is demonstrated that a nonlinearly parametrized model can more accurately capture the vehicle dynamics than a linearly parametrized model. For control design, the air vehicle model is decomposed into a flight-path angle subsystem with rotational dynamics and a speed subsystem with engine actuation dynamics. An adaptive control scheme is developed using the combination of a function bounding technique and a modified backstepping control method for two interconnected subsystems. The designed adaptive control laws ensure both global stabilization and adaptive non-zero equilibrium point regulation of the closed-loop control system. A thorough simulation study is presented to show the effectiveness of the developed adaptive control scheme for a nonlinearly parametrized air vehicle system model.