Constraint Matrices Research Articles

A simple multi-constraint fusion based semi-supervised non-negative matrix decomposition for image clustering

Semi-supervised non-negative matrix decomposition (SNMF) is a highly interpretable image clustering algorithm. We typically incorporate graph learning to enhance the model’s representation ability, while adding positive and negative labeling information and pairwise constraints to prevent overfitting and improve the discriminative performance. However, embedding positive and negative labels and pairwise constraints simultaneously in the SNMF model is challenging due to their dimension mismatch. Thus We propose a method named multi-constraint fusion based semi-supervised non-negative matrix decomposition (MCFSNMF), which effectively solves the above problem by constructing symmetric labeling matrices embedded with positive and negative labeling information and fusing them with pairwise constraint matrices. In addition, SNMF is essentially a feature extraction method, which cannot obtain clustering results directly. Therefore, we combine the label propagation algorithm to achieve feature learning and label assignment interaction, which not only avoids the impact of clustering post-processing operations but also enhances the representation of labeled data relative to unlabeled data. We compare multiple SNMF algorithms on six image datasets and show that the proposed algorithm can effectively enhance the clustering performance and validate the algorithm’s convergence.

Inverse optimization in semi-definite programs to impute unknown constraint matrices

In a typical (forward) optimization problem, a decision-maker uses given values of model parameters to compute the values of decision variables. The goal in inverse optimization (IO) is instead to infer parameters that render given values of decision variables optimal. Most papers on IO utilize duality to impute objective function parameters. A corresponding literature for imputing constraint parameters is essentially non-existent, even for linear programs. The difficulty is that these IO problems include nonconvex bilinear constraints and/or objectives. We study inverse semi-definite programs (SDPs) where matrices on the left-hand-sides of constraints are unknown. These unknown matrices must satisfy some side constraints. We consider two types of such problems, depending on which SDP decision variable values are given: primal or dual. In each situation, we study three sub-cases based on whether both the right-hand-side coefficients and the objective function matrix are known or only one of these two is known. This creates six variants of the inverse problem. For each variant, we first look for sufficient conditions, either on the side constraints or on problem structure, under which the nonconvex bilinear inverse problem can be simplified substantially. In particular, it either has a trivial solution or can be reformulated as a (set of) convex program(s). When such conditions are not evident, we propose three tailored heuristics called the Convex–Concave Procedure, Sequential Semi-definite Programming, and Alternate Convex Search. We perform computational experiments to gain insights into the performance of these three methods.

Generation of Construction Scheduling through Machine Learning and BIM: A Blueprint

Recent advancements in machine learning (ML) applications have set the stage for the development of autonomous construction project scheduling systems. This study presents a blueprint to demonstrate how construction project schedules can be generated automatically by employing machine learning (ML) and building information modeling (BIM). The proposed solution should utilize building information modeling (BIM) international foundation class (IFC) 3D files of previous projects to train the ML model. The training schedules (the dependent variable) are intended to be prepared by an experienced scheduler, and the 3D BIM files should be used as the source of the scheduled activities. Using the ML model can enhance the generalization of model application to different construction projects. Furthermore, the cost and required resources for each activity could be generated. Accordingly, unlike other solutions, the proposed solution could sequence activities based on an ML model instead of manually developed constraint matrices. The proposed solution is intended to generate the duration, cost, and required resources for each activity.

Solving constrained matrix games with fuzzy random linear constraints

In real-world games, players may face an uncertain environment where fuzziness and randomness coexist. The main difficulty in dealing with games involving fuzziness and randomness arises when comparing the payoffs. The purpose of this paper is to introduce a new approach to deal with constrained matrix games where the entries of the constraint matrices are LR-fuzzy random variables. Our methodology is based on constructing a new matrix game using the chance constraint method adapted to the probability-possibility measures. First, a specific type of saddle point is defined as an equilibrium solution. Then, conditions for the existence of the proposed solution are established. Further, a technique based on second-order programming for computing the saddle point is presented. Finally, a numerical illustration of the approach is provided.

Total Unimodularity and Strongly Polynomial Solvability of Constrained Minimum Input Selections for Structural Controllability: An LP-Based Method

This paper investigates several cost-sparsity induced optimal input selection problems for structured systems. Given an autonomous system and a prescribed set of input links, where each input link has a non-negative cost, the problems include selecting the minimum cost of input links and selecting the input links with the smallest possible cost while bounding their cardinality to achieve system structural controllability. Current studies show that in the dedicated input case (i.e., each input can actuate only one state variable), the former problem is polynomially solvable by some graph-theoretic algorithms, while the general nontrivial constrained case is largely unexplored. We show that these problems can be formulated as equivalent integer linear programming (ILP) problems. Subject to the 'source strongly-connected component grouped input constraint', which contains the dedicated input one as a special case, we demonstrate that the constraint matrices of these ILPs are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">totally unimodular</i> . This property allows us to solve these ILPs efficiently via their linear programming (LP) relaxations, leading to a unifying algebraic method for these problems with polynomial time complexity. We further show that these problems can be solved in strongly polynomial time, independent of the size of the costs and cardinality bounds. Finally, we provide an example to illustrate the power of the proposed method.

Parallel Dual-DQAM for Multi-Scenario Stochastic Economic Dispatch Model by Temporal and Scenario Decompositions

Large-scale multi-scenario stochastic economic dispatch (SED) is hard to directly solve due to the huge number of variables and constraints. To reduce the computational burden, a nested dual-DQAM (Diagonal Quadratic Approximation Method) is proposed in this paper to decouple the SED problem in both scenarios and time periods, where each subproblem only contains one time period and one scenario. Moreover, these subproblems can be handled in parallel, such that the computational performance can be significantly improved. Besides, we have investigated the optimal policy to select the best parallel structure of the proposed dual-DQAM, and the theorical convergence performance is proved. Numerical results on several test systems show the effectiveness of the proposed dual-DQAM. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Nowadays, the safe operation and economic dispatch in power system are greatly challenged by the high penetration of renewable energy. Although the uncertainty of renewable energy can be well modeled by stochastic programming, the solution complexity will seriously increase due to the large number of typical scenarios. For this problem, the parallel solution using decomposition methods is the state-of-the-art strategy. In this paper, we propose an efficient solution to the multi-scenario SED problem by temporal and scenario decompositions. It realizes an important innovation in both reducing the computational burden and improving the solving efficiency, which greatly promotes the application of SED in large-scale systems. To better use this method, the following two properties should be highlighted: i) the proposed method has a convergence guarantee and works especially well on SED due to the sparsity property of linking constraint matrices. ii) the computational efficiency of the proposed method becomes more significant as the number of time periods and scenarios grows and can be further improved under a fast ramp rate.

On polynomially solvable constrained input selections for fixed and switched linear structured systems

This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured (or structural) systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the inputs of the smallest possible cost with a bound on their cardinality, all to ensure system structural controllability. Those problems have attracted much attention recently; unfortunately, they are NP-hard in general. In this paper, it is found that, if the input structure satisfies certain ’regularizations’, which are characterized by the proposed restricted total unimodularity notion, those problems can be solvable in polynomial time via linear programming (LP) relaxations. Particularly, the obtained characterizations depend only on the incidence matrix relating the inputs and the source strongly connected components (SCC) of the system structure, irrespective of how the inputs actuate states within the same SCC. They cover all the currently known polynomially solvable cases (such as the dedicated input case), and contain many new cases unexplored in the past, among which the source-SCC separated input (SSSI) constraint is highlighted. Further, these results are extended to switched systems, and a polynomially solvable condition, namely the joint SSSI constraint, is obtained that does not require each of the subsystems to satisfy the SSSI constraint. We achieve these by first formulating those problems as equivalent integer linear programmings (ILPs), and then proving the total unimodularity of the corresponding constraint matrices. We also study solutions obtained via LP-relaxation and LP-rounding in the general case, resulting in some lower and upper bounds. Several examples are given to illustrate the obtained theoretical results.

Congruency-Constrained TU Problems Beyond the Bimodular Case

A long-standing open question in integer programming is whether integer programs with constraint matrices with bounded subdeterminants are efficiently solvable. An important special case thereof are congruency-constrained integer programs [Formula: see text] with a totally unimodular constraint matrix T. Such problems are shown to be polynomial-time solvable for m = 2, which led to an efficient algorithm for integer programs with bimodular constraint matrices, that is, full-rank matrices whose n × n subdeterminants are bounded by two in absolute value. Whereas these advances heavily rely on existing results on well-known combinatorial problems with parity constraints, new approaches are needed beyond the bimodular case, that is, for m &gt; 2. We make first progress in this direction through several new techniques. In particular, we show how to efficiently decide feasibility of congruency-constrained integer programs with a totally unimodular constraint matrix for m = 3 using a randomized algorithm. Furthermore, for general m, our techniques also allow for identifying flat directions of infeasible problems and deducing bounds on the proximity between solutions of the problem and its relaxation. Funding: This project received funding from the Swiss National Science Foundation [Grants 200021_184622 and P500PT_206742], the European Research Council under the European Union’s Horizon 2020 research and innovation program [Grant 817750], and the Deutsche Forschungsgemeinschaft (German Research Foundation) under Germany’s Excellence Strategy–GZ 2047/1 [Grant 390685813].

Study on the Influence of the Internal Elastic Constraint Stiffness on the Vib-Acoustic Performance of a Coupled Plate-Cylindrical Shell System

Regarding the vib-acoustic performance of internal coupled structures, basically all relevant studies have been confined to the classic form of connections. In this investigation, the boundary and internal elastic constraint matrices of the coupled structure are established, the vibration and sound calculation model of the coupled structure is then established, and numerical analysis is performed to show the effect of constraint stiffness on the vibration and acoustical performance of a coupled plate-cylindrical shell system. The results show that impedance matching between the structures is improved with the increase of the elastic connection stiffness, which is conducive to the vibration energy propagation. Moreover, the supporting coupling stiffness between elastic coupled structures plays an important role in vibration energy transfers.

Visible light fingerprint database recovery algorithm based on CP decomposition.

Visible light communication(VLC) is a new method of indoor communication. It can provide an effective solution for indoor positioning. Fingerprint-based visible light positioning(VLP) has been widely studied for its feasibility and high accuracy. The acquisition of 'fingerprint database' is crucial for accurate VLP. However, sparse sensors such as photodiode(PD) can only be arranged because of the space-limited scenario and high costs. Correspondingly, it results in the loss of the fingerprint database. Therefore, it is indispensable to solve the problem of how to effectively and accurately recover the fingerprint database from measurements of sparsely arranged sensors. In this paper, we propose a spatio-temporal constraint tensor completion (SCTC) algorithm based on CANDECOMP/PARAFAC (CP) decomposition to recover the fingerprint database from measurements of sparsely arranged sensors. Specifically, we model the measurements from the spatial and temporal dimensions as a tensor, and formulate the optimization problem based on the low-rank feature of the tensor. To improve the recovery accuracy, spatial and temporal constraint matrices are introduced to effectively constrain the optimization direction when completing the tensor. Spatial constraint matrices are constructed by utilizing the mode-n expansion matrix of the tensor based on the undirected graph theory. Accordingly, the Toeplitz matrix is used as the temporal constraint matrix to excavate the temporal correlation of the tensor. Since the optimization problem is non-convex and difficult to solve, we introduce CP decomposition to decompose the tensor into several factor matrices. By solving the factor matrices, the original tensor is reconstructed. The performance of the proposed SCTC algorithm is confirmed via experimental measured data.

Quantum Many-Body Theory from a Solution of the N-Representability Problem.

Here we present a many-body theory based on a solution of the N-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an equation that re-expresses physical constraints on higher-order RDMs to generate direct constraints on the 2-RDM, which are required for its derivation from an N-particle density matrix, known as N-representability conditions. The approach produces a complete hierarchy of 2-RDM constraints that do not depend explicitly upon the higher RDMs or the wave function. By using the two-particle part of a unitary decomposition of higher-order constraint matrices, we can solve the energy minimization by semidefinite programming in a form where the low-rank structure of these matrices can be potentially exploited. We illustrate by computing the ground-state electronic energy and properties of the H_{8} ring.

Selective disassembly sequence optimization based on the improved immune algorithm

PurposeThe purpose of this paper is to improve the automation of selective disassembly sequence planning (SDSP) and generate the optimal or near-optimal disassembly sequences.Design/methodology/approachThe disassembly constraints is automatically extracted from the computer-aided design (CAD) model of products and represented as disassembly constraint matrices for DSP. A new disassembly planning model is built for computing the optimal disassembly sequences. The immune algorithm (IA) is improved for finding the optimal or near-optimal disassembly sequences.FindingsThe workload for recognizing disassembly constraints is avoided for DSP. The disassembly constraints are useful for generating feasible and optimal solutions. The improved IA has the better performance than the genetic algorithm, IA and particle swarm optimization for DSP.Research limitations/implicationsAll parts must have rigid bodies, flexible and soft parts are not considered. After the global coordinate system is given, every part is disassembled along one of the six disassembly directions –X, +X, –Y, +Y, –Z and +Z. All connections between the parts can be removed, and all parts can be disassembled.Originality/valueThe disassembly constraints are extracted from CAD model of products, which improves the automation of DSP. The disassembly model is useful for reducing the computation of generating the feasible and optimal disassembly sequences. The improved IA converges to the optimal disassembly sequence quickly.

Fully distributed event‐triggered asymptotic attitude coordination of multiple spacecraft systems with disturbances

AbstractThis article studies the leader‐following attitude coordination problem of a group of rigid spacecraft subject to communication constraint, disturbances and uncertain control coefficient matrices. A fully distributed adaptive anti‐disturbance attitude coordinated control scheme with event‐triggering mechanism is developed. First, the event‐triggered adaptive distributed observer is designed for each follower to estimate the leader's information without continuous communication requirement. Based on the estimated information, the adaptive anti‐disturbance attitude tracking controller is designed such that asymptotic coordinated tracking can be achieved under additive disturbances and actuators' partial loss of efficiency. The proposed control scheme ensures that all the closed‐loop signals are bounded and the positive lower bound of inter‐event times exists in each subsystem. Simulation results illustrate the effectiveness and flexibility of the proposed control scheme.

Multi-View Point Clouds Registration Method Based on Overlap-Area Features and Local Distance Constraints for the Optical Measurement of Blade Profiles

The accurate and efficient measurement of blade profiles plays an important role in blade processing and quality monitoring. Currently, increasing attention is being paid to the optical measurement method for blade profiles due to its easy accessibility, high efficiency, and flexibility. However, as a key issue of blade profile measurement, the registration of multiview measured data still relies on the geometric accuracy and motion stability of the measurement system. Besides, multiple factors, including the various density and insufficient overlaps of multiview point cloud data, make the registration a challenging problem. To overcome these problems and realize accurate measurement of blade profiles, a fine registration algorithm is proposed in this article, which mainly comprises two novel constraint mechanisms: overlap-area features and local distance constraints. Two constraint matrices based on the features and distance information are constructed and integrated based on the Hadamard Product of matrices. In this way, the underlying corresponding mapping between multiview point clouds can be effectively recovered and the registration accuracy can be improved. The results of measurement experiment on three typical blades demonstrate the accuracy and feasibility of the proposed method.

A Phase-Domain Model of Dual Three-Phase Segmented Powered Linear PMSM for Hardware-Assisted Real-Time Simulation

In this article, a hardware-assisted real-time simulation phase-domain (PD) model of a dual three-phase segmented powered linear permanent magnet synchronous machine (SP-LPMSM) used in electromagnetic drive is established. The model is able to consider the end-effect, saturation effect, coupling effect, and open-phase fault conditions, which are specially occurs in the segmented structure in SP-LPMSM. The unbalanced inductances and saturation effect caused by the segmented structure are investigated and a simplified look-up table for inductances is introduced. Additionally, to accurately evaluate the coupling effect, the permanent magnet (PM) flux linkage is decoupled into the product of unit PM flux linkage and coupling coefficient. In order to avoid the numerical impulse caused by the derivative in the progress of calculating back-EMF, sigmoid function is adopted to express the coupling coefficient. Meanwhile, to make the PD-model compatible with the open-circuit fault conditions, incidence matrices and current constraint matrices are introduced to unify the PD-models with different winding connection types and open circuit faults into one general form. The PD-model realized in field-programmable gate arrays (FPGA) based hardware is validated in comparison with finite-element analysis results.

A novel disassembly sequence planning method based on spatial constraint matrices

A novel disassembly sequence planning method based on spatial constraint matrices

A novel switching adaptive control for randomly switching systems with an application to suspension systems

This paper presents a new control algorithm for controlling randomly switching systems under random disturbance. The proposed controller is designed based on a dual prescribed sliding mode control and a dual modified Riccati-like equation. The sliding surface of the proposed controller includes two parts: a classical type and a prescribed performance. The combined sliding surface provides strong disturbance rejection capability for the system. The dual Riccati equation provides two functionalities: (i) a classical type associated with the system parameters, and (ii) a disturbance-type with parameters associated with the boundaries of disturbance. A fuzzy model, which functions as a filter, is applied in the proposed control system for approximating uncertainty. Its fuzzified values are also used in the adaptation laws to improve the system performance. One of the innovative features of the proposed approach is expressed by its adaptation laws, which are formed by the constraint matrices, which are related to both the nominal system and disturbance. In these laws, the parameters of the PID component are updated based on the main matrices of Riccati equations. The composite controller, which combines a sliding mode control, Riccati equations, PID control, and fuzzy model, helps to improve the performance of the classical controls when the system works under severe disturbance conditions. The proposed controller is employed for a suspension system of bus driver and compared with an existing controller under two randomly disturbance conditions. The results of a computer simulation show that the proposed controller obtains good performance in terms of vibration compression.

Enumerating Integer Points in Polytopes with Bounded Subdeterminants

We show that one can enumerate the vertices of the convex hull of integer points in polytopes whose constraint matrices have bounded and nonzero subdeterminants, in time polynomial in the dimension and encoding size of the polytope. This extends a previous result by Artmann et al. who showed that integer linear optimization in such polytopes can be done in polynomial time.

Faster Maximum Feasible Subsystem solutions for dense constraint matrices

Finding a largest cardinality feasible subset of an infeasible set of linear constraints is the Maximum Feasible Subsystem problem (MAX FS). Solving this problem is crucial in a wide range of applications such as machine learning and compressive sensing. Although MAX FS is NP-hard, useful heuristic algorithms exist, but these can be slow for large problems. We extend the existing heuristics for the case of dense constraint matrices to greatly increase their speed while preserving or improving solution quality. We test the extended algorithms on two applications that have dense constraint matrices: binary classification, and sparse recovery in compressive sensing. In both cases, speed is greatly increased with no loss of accuracy.

Notes on {a,b,c}-Modular Matrices

Let A in mathbb {Z}^{m times n} be an integral matrix and a, b, c in mathbb {Z} satisfy a ≥ b ≥ c ≥ 0. The question is to recognize whether A is {a,b,c}-modular, i.e., whether the set of n × n subdeterminants of A in absolute value is {a,b,c}. We will succeed in solving this problem in polynomial time unless A possesses a duplicative relation, that is, A has nonzero n × n subdeterminants k1 and k2 satisfying 2 ⋅|k1| = |k2|. This is an extension of the well-known recognition algorithm for totally unimodular matrices. As a consequence of our analysis, we present a polynomial time algorithm to solve integer programs in standard form over {a,b,c}-modular constraint matrices for any constants a, b and c.