Constructive Procedure Research Articles

A mathematical formulation and a tabu search heuristic for the joint vessel-UAV routing problem

Motivated by offshore inspection practices, we investigate a joint vessel-unmanned aerial vehicle (UAV) routing problem where vessels and UAVs work coordinately to perform inspection tasks. The problem is an extension of the mothership-drone routing problem by further considering multiple vessels and realistic constraints such as temporal-spatial coordination, service time, and inspection cycle. The goal is to minimize overall operational costs, including fixed vessel cost, and vessel and UAV routing costs. Decision-making involves task assignment, vessel route determination, and UAV take-off and landing locations. We formulate the problem as a mixed-integer second-order cone program. Addressing its NP-hard nature, we develop an enhanced tabu search algorithm (TS-RC), which incorporates two innovative mechanisms to reduce the computational burden. The first is to determine UAV take-off/landing points based on a new constructive procedure. The second is assessing neighborhood solutions using an approximate procedure. Results on a real-world case demonstrate a 10.29% reduction in operational costs compared to a classic vessel routing model. Moreover, numerical experiments on random instances with up to four vessels and 39 tasks demonstrate the performance of the proposed TS-RC method.

Inverse problems for discrete Sturm–Liouville operator having Bessel-type potential

In this paper, inverse problems are studied for Sturm–Liouville difference operators having p 2 − 1 / 4 m 2 type singularity. First, we define the Green's function and the corresponding Weyl function, some of their properties are investigated, and we give a method to find the potential function. Then we give the solution of the inverse nodal problem and present a constructive procedure for the solution of the inverse problem by using nodes.

Inverse spectral problem for differential pencils with a frozen argument

Abstract This paper deals with differential pencils possessing a term depending on the unknown function with a fixed argument. We deduce the so called main equation together with its fine structure for the spectral problem. Then, according to the boundary conditions and the position of argument, we describe two cases: degenerate and non-degenerate. For these two cases, the uniqueness of inverse spectral problem is studied and a constructive procedure for reconstructing the potentials along with necessary and sufficient conditions of the inverse problem solvability are obtained.

Convexification of Bilinear Terms over Network Polytopes

It is well-known that the McCormick relaxation for the bilinear constraint z = xy gives the convex hull over the box domains for x and y. In network applications where the domain of bilinear variables is described by a network polytope, the McCormick relaxation, also referred to as linearization, fails to provide the convex hull and often leads to poor dual bounds. We study the convex hull of the set containing bilinear constraints [Formula: see text] where xi represents the arc-flow variable in a network polytope, and yj is in a simplex. For the case where the simplex contains a single y variable, we introduce a systematic procedure to obtain the convex hull of the above set in the original space of variables, and show that all facet-defining inequalities of the convex hull can be obtained explicitly through identifying a special tree structure in the underlying network. For the generalization where the simplex contains multiple y variables, we design a constructive procedure to obtain an important class of facet-defining inequalities for the convex hull of the underlying bilinear set that is characterized by a special forest structure in the underlying network. Computational experiments conducted on different applications show the effectiveness of the proposed methods in improving the dual bounds obtained from alternative techniques. Funding: This work was supported by Air Force Office of Scientific Research [Grant FA9550-23-1-0183]; National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation [Grant 2338641]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2023.0001 .

A GRASP algorithm for the bus crew scheduling problem

This paper proposes a GRASP approach for solving the Bus Crew Scheduling Problem (BCSP) to find high-quality solutions within short computing times. The BCSP described the process related to the assignment of drivers and conductors to a bus company's regular daily operation of a mass transit system, seeking to minimize the cost of operation and, at the same time, the improvement of the working environment by considering the satisfaction of the drivers with the assigned shifts. The BCSP has drivers in charge of covering the demand for shifts, with an assignment that contains several constraints, such as minimum and maximum work blocks, minimum rest days, and shift sequences that must not be assigned. The former GRASP algorithm is proposed with a constructive procedure, a solution repair procedure, and two local search operators. Classical instances from the literature have been adapted for the shift assignment problem by adding a satisfaction variable. Besides, the proposed approach has been tested for a real company operating articulated and feeder vehicles. The results show that the satisfaction function adds value to the assignments, substantially improving the work environment and generating favorable results in terms of time and quality of the solution.

Realizations and invariants of Lie algebras

Lie algebras of first-order differential operators with smooth coefficients are considered and their construction methods are reviewed. Obstacles preventing contractions of such operators are emphasized and a constructive procedure for parameterizations is proposed. A number of illustrative examples are considered.

Perception-aware model predictive control for constrained control in unknown environments

The operation of autonomous systems is inherently constrained by their surrounding environment, which is often time-varying and unknown a priori, necessitating perception using sensors. Hence, control strategies for autonomous systems must take into account the uncertainty of the perceived environment in making decisions, while information acquired by sensors often depends on how the system is operated, e.g., where the sensors are pointed at, or what and how much sensor information is processed. We introduce a perception-aware chance-constrained model predictive control (PAC-MPC) strategy that accounts for the uncertainty of the perceived environment, as well as the dependence of the perception quality on the control actions. The system and the environment are coupled by chance constraints due to the uncertainty in the environment estimate, which depends on control actions. We establish the constraint satisfaction and stability properties of PAC-MPC through appropriate design of the cost function and terminal set, and propose a constructive design procedure for the case of linear dynamics.

An Inverse Sturm–Liouville-Type Problem with Constant Delay and Non-Zero Initial Function

We suggest a new statement of the inverse spectral problem for Sturm–Liouville-type operators with constant delay. This inverse problem consists of recovering the coefficient (often referred to as potential) of the delayed term in the corresponding equation from the spectra of two boundary value problems with one common boundary condition. The previous studies, however, focus mostly on the case of zero initial function, i.e., they exploit the assumption that the potential vanishes on the corresponding subinterval. In the present paper, we waive that assumption in favor of a continuously matching initial function, which leads to the appearance of an additional term with a frozen argument in the equation. For the resulting new inverse problem, we pay special attention to the situation when one of the spectra is given only partially. Sufficient conditions and necessary conditions on the corresponding subspectrum for the unique determination of the potential are obtained, and a constructive procedure for solving the inverse problem is given. Moreover, we obtain the characterization of the spectra for the zero initial function and the Neumann common boundary condition, which is found to include an additional restriction as compared with the case of the Dirichlet common condition.

On the existence of non-catastrophic p-encoders of (2,1) convolutional codes over ℤp2

In this work, we analyze the problem of catastrophicity of encoders of convolutional codes over the Laurent series with coefficients in [Formula: see text], [Formula: see text]. Kuijper and Pinto proved in [M. Kuijper and R. Pinto, On minimality of convolutional ring encoders, IEEE Trans. Autom. Control 55(11) (2009) 4890–4897] that, contrary to what happens for codes over [Formula: see text], where [Formula: see text] is a field, when dealing with [Formula: see text] there are convolutional codes that do not admit non-catastrophic encoders. Nevertheless it was conjectured that any catastrophic convolutional code admits another type of non-catastrophic encoder called [Formula: see text]-encoder. In this paper we solve this conjecture for a class of [Formula: see text] convolutional codes over [Formula: see text] and show that, in fact, these codes always admit a non-catastrophic p-encoder. We also describe a constructive procedure that allows us to obtain a non-catastrophic [Formula: see text]-encoder.

Total-Activity Conservation Analysis and Design of Boolean Networks.

The law of conservation of mass, represented in Boolean networks (BNs) as total-activity conservation, is one of the typical properties of biological networks. This article analyzes the total-activity conservation of BNs based on the algebraic state-space representation (ASSR) approach. First, the total-activity-conservative matrix is defined and a matrix-based criterion is proposed to verify the total-activity conservation of BNs. Meanwhile, when function perturbation is considered, robust total-activity conservation is investigated. Second, by means of the pseudo-Boolean function generated by total-activity conservation, a constructive design procedure of the Boolean dynamics is given to achieve the total-activity conservation. Third, the total-activity conservation of switched Boolean networks (SBNs) under arbitrary switching signal is studied, which together with network aggregation achieves the total-activity conservation of large-scale BNs.

Constructive Placement and Routing for Common-Centroid Capacitor Arrays in Binary-Weighted and Split DACs

Process variations and the effect of interconnect parasitics can cause significant perturbations in the performance metrics of capacitive digital-to-analog converters (DACs). This paper develops fast constructive procedures for common-centroid placement and routing for binary-weighted and split capacitor array topologies of charge-sharing DACs. Our approach particularly targets FinFET technologies with high wire and via parasitics: in these technology nodes, we show that the switching speed of the capacitor array, as measured by the 3dB frequency, can be severely degraded by these parasitics, and develop techniques to place and route the capacitor array, for both binary-weighted and split DACs, to optimize the switching speed. A balance between 3dB frequency and DAC INL/DNL is shown by trading off via counts with dispersion. The approach delivers high-quality results with low runtimes.

Advanced repeated structuring and learning procedure to detect acute myocardial ischemia in serial 12-lead ECGs

Objectives. Acute myocardial ischemia in the setting of acute coronary syndrome (ACS) may lead to myocardial infarction. Therefore, timely decisions, already in the pre-hospital phase, are crucial to preserving cardiac function as much as possible. Serial electrocardiography, a comparison of the acute electrocardiogram with a previously recorded (reference) ECG of the same patient, aids in identifying ischemia-induced electrocardiographic changes by correcting for interindividual ECG variability. Recently, the combination of deep learning and serial electrocardiography provided promising results in detecting emerging cardiac diseases; thus, the aim of our current study is the application of our novel Advanced Repeated Structuring and Learning Procedure (AdvRS&LP), specifically designed for acute myocardial ischemia detection in the pre-hospital phase by using serial ECG features. Approach. Data belong to the SUBTRACT study, which includes 1425 ECG pairs, 194 (14%) ACS patients, and 1035 (73%) controls. Each ECG pair was characterized by 28 serial features that, with sex and age, constituted the inputs of the AdvRS&LP, an automatic constructive procedure for creating supervised neural networks (NN). We created 100 NNs to compensate for statistical fluctuations due to random data divisions of a limited dataset. We compared the performance of the obtained NNs to a logistic regression (LR) procedure and the Glasgow program (Uni-G) in terms of area-under-the-curve (AUC) of the receiver-operating-characteristic curve, sensitivity (SE), and specificity (SP). Main Results. NNs (median AUC = 83%, median SE = 77%, and median SP = 89%) presented a statistically (P value lower than 0.05) higher testing performance than those presented by LR (median AUC = 80%, median SE = 67%, and median SP = 81%) and by the Uni-G algorithm (median SE = 72% and median SP = 82%). Significance. In conclusion, the positive results underscore the value of serial ECG comparison in ischemia detection, and NNs created by AdvRS&LP seem to be reliable tools in terms of generalization and clinical applicability.

Ideals and conjugacy classes in solvable Lie algebras

A constructive procedure is given to determine all ideals of a finite-dimensional solvable Lie algebra. This is used in determining all conjugacy classes of subalgebras of a given finite-dimensional solvable Lie algebra.

Inverse Nodal Problem for a Conformable Fractional Diffusion Operator With Parameter-Dependent Nonlocal Boundary Condition

In this paper, we consider the inverse nodal problem for the conformable fractional diffusion operator with parameter-dependent Bitsadze–Samarskii type nonlocal boundary condition. We obtain the asymptotics for the eigenvalues, the eigenfunctions, and the zeros of the eigenfunctions (called nodal points or nodes) of the considered operator, and provide a constructive procedure for solving the inverse nodal problem, i.e., we reconstruct the potential functions p(x) and q(x) by using a dense subset of the nodal points.

ANALYSIS OF WALLS AND PILLARS OF THE HYPOSTYLE HALL AT THE QH31 TOMB (ASWAN, EGYPT) BASED ON 3D MODELS

Abstract. This study describes the methodology developed and the results obtained about the geometric behaviour of walls and pillars of one of the most prominent rock-cut funerary structures of the Middle Kingdom period located in the Necropolis of Qubbet el-Hawa. More specifically, we selected the hypostyle hall of the QH31 hypogeum, one of the greatest in the Necropolis, to apply this methodology. The main objective is related to obtaining geometrical aspects of walls and pillars in order to understand the constructive procedure carried out almost four millennia ago. The methodology was based on photogrammetric and TLS surveys that allowed us to obtain a complete combined 3D model of the structure, geometrically contrasted and with real texture. From this product we obtained a high density point cloud, where some planes were fitted considering the walls and pillars that defined the structure. These planes were characterized by their normal vectors, which were used to analyse several geometric aspects such as inclinations, parallelism and perpendicularity. As results, we have obtained important information about the level of accuracy of the constructive procedure carried out by the ancient Egyptians. In this sense, the values obtained allow us to suggest and confirm several hypotheses about the construction of this hypogeum. The proposed methodology has demonstrated its feasibility for determining these geometric aspects of funerary structures through the analysis of the fitted planes obtained from the 3D model.

Constructive–destructive heuristics for the Safe Set Problem

The Weighted Safe Set Problem aims to determine in an undirected graph a subset of vertices such that the weights of the connected components they induce exceed the weights of the adjacent components induced by the complementary subset. We tackle the problem with various approaches based on randomised constructive and destructive procedures, comparing them with each other and with the only other existing heuristic approach, that is a randomised destructive heuristic. The experiments concern all the available benchmark instances (random graphs up to 60 vertices), but also new benchmark instances with larger size and different topologies, namely random, small-world, regular, planar, grid and real-world graphs up to 300 vertices. Dense random graphs, in fact, appear to become progressively easier to solve as their size grows. On the other instances, the best performance is obtained by combining a randomised constructive procedure, a deterministic destructive procedure, and delayed termination conditions that allow a deeper exploration of the feasible region.

On Recovering Sturm–Liouville-Type Operators with Global Delay on Graphs from Two Spectra

We suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, which is measured in the direction of a specific boundary vertex, called the root, propagates through the internal vertex to other edges. Now, we intend to recover the potentials from the spectra of two boundary value problems on the graph with a common set of boundary conditions at all boundary vertices except the root. For simplicity, we focus on star graphs with equal edges when the delay parameter is not less than their length. Under the assumption that the common boundary conditions are of the Robin type and they are known and pairwise linearly independent, the uniqueness theorem is proven and a constructive procedure for solving the proposed inverse problem is obtained.

Leopoldo Miguéz's Nocturnes Opp.10 and 20/1: Political Context and Stylistic Analysis in the "City of Pianos"

As in Europe, the piano reached the height of its popularity in the mid- to late nineteenth century in Brazil. Its presence in cultural life increased significantly, with performances in concert halls, theatres, and even cafés. Nocturnes— particularly Chopin's— were fre quently played at home and in public venues. Leopoldo Miguéz (1852–1902), considered at the time to be influenced by Wagner, Liszt, and the so-called Zukunftsmusik, was the first Brazilian composer to write a symphony, a violin sonata, and a symphonic poem. This ar ticle provides an overview of Miguéz's piano Nocturnes Opp.10 and 20/1 in the context of their relationship to contemporaneous Brazilian politics and his compositional practice. An in-depth analysis of the two nocturnes aims to map out his style, taking as parame ters his implementation of nineteenth-century constructive procedures previously established in analyses of his Violin Sonata Op.14 and his Allegro Appassionato Op.11 for piano. These include: the use of proto-themes, mediant regions, smooth voice-leading, complex tonal plans, motivic economy, and roving harmonies. These procedures are shown to be significant elements in Miguéz's palette of compositional traits and stylistic character istics; notably, they may have been common in Europe at the time but were unknown in Brazil. [...]

KANT AND THE CONSTRUCTION OF PURE REASON: AN ANALOGY WITH A CHEMICAL EXPERIMENT

This paper defends a constructive interpretation of the Critique of Pure Reason, which is built in analogy with an experimental construction that Kant believes to characteristic of chemistry. I also argue for a way to reconcile the methodological perspective of the constructivist method with that of transcendental reflection. I therefore provide a constructive explanation for what Kant describes as being pure reason and the argument of the transcendental deduction. I propose to frame the different perspectives in such a way that the experimental construction is the ratio cognoscendi of pure reason, while pure reason is the ratio essendi of the experimental construction. O’Neill (1989, 2015) is one of the most important scholars that have argued for a constructivist reading of the Critique of pure reason (CPR). In this paper I develop and explore new aspects of this line of interpretation. One of the main criticisms raised against constructivist readings of Kant’s philosophy is an alleged commitment to subjectivism or voluntarism (cf. Kleingeld & Willaschek 2019). This concern led some scholars to rename their position as constitutivist instead (Korsgaard 2009; Sensen 2013, 2017; Formosa 2011). Constitutivism, is intended to be a sort of constructivism capable of avoiding voluntarism. However, it becomes difficult, sometimes, to differentiate between the constitutivist and foundationalist positions, which are based on transcendental reflection and imply a sort of realist perspective on reason. The same preoccupation applies to the constructivist interpretation of the CPR. In order to deal with this issue, the following questions must be addressed: how can constructivism justify the necessity and universality of transcendental principles of pure reason without compromising the normative and procedural aspects of the construction? How to reconcile arguments based on the analysis of representations and faculties with a constructivist procedure? Or even, how may transcendental reflection, as a view of the possibility of a priori cognition, be rendered compatible with a constructive procedure? This paper is divided into three sections, followed by brief final remarks. The first section outlines the main characteristics of constructivism and relates them to Kant’s positions about the nature of philosophy and its method. The second part argues for a type of experimental constructivism that might serve as a guiding analogy to understand the method underlying the CPR. Thirdly, I will show how the transcendental subject and pure reason are derived from this experimental construction. The conclusion briefly points out some advantages of this position.

Observer-based Control Design for Systems with Potentially Metzler Dynamics

In this paper are solved problems concerning the state estimation in observer-based control of ostensible positive linear systems. The method is based on a composed form of the system matrix representation, where the constructive procedure is given to the observer synthesis. The method is flexible and allows to obtain the observer with the gain matrix being strictly positive. The design is computationally simple and reduces to feasibility of the LMI problem. Numerical simulation is presented to illustrate the validity of the proposed method.