Constraint Propagation Research Articles

Enhanced Multi-View Subspace Clustering via Twist Tensor Nuclear Norm and Constraint Propagation

Enhanced Multi-View Subspace Clustering via Twist Tensor Nuclear Norm and Constraint Propagation

A technique for improving petroleum products forecasts using grey convolution models and genetic algorithms

Forecasting energy consumption is a major concern for policymakers, oil industry companies, and many other associated businesses. Though there exist many forecasting tool, selecting the most appropriate one is critical. GM(1,1) has proven to be one of the most successful forecasting tool. GM(1,1) does not require any specific information and can be adapted to predict energy consumption using a minimum of four observations. Unfortunately, GM(1,1) on its own will generate too large forecast errors because it performs well only when data follow an exponential trend and should be implemented in a political-socio-economic free environment. To reduce these short-comings, this paper proposes a new GM(1,n) convolution model optimized by genetic algorithms integrating a sequential selection mechanism and arc consistency, abbreviated Sequential-GMC(1,n)-GA. The new model, like some recent hybrid versions, is robust and reliable, with MAPE of 1.44%, and RMSE of 0.833.•Modification, extension and optimization of grey multivariate model is done.•The model is very generic can be applied to a wide variety of energy sectors.•The new hybrid model is a valid forecasting tool that can be used to track the growth of households’ energy demand.

Parallel progressive-based inductive subspace and fuzzy-based firefly algorithm for high ensemble data clustering

Recently, the framework is proposed with techniques such as random subspace and constraint propagation for handling high dimensional data ensemble clustering. Huge dataset clustering is difficult for conventional sequential clustering methods since it requires higher computation time. Distributed parallel processing and methods are consequently useful towards attaining results and scalability constraints of clustering huge datasets. So, in this work, the parallel progressive-based inductive subspace ensemble clustering (PPISEC) algorithm is introduced with the concept of MapReduce (MR) to perform high dimensional data clustering. Depending on micro-clusters and correspondence relative, the clustering method is designed which is easily parallelised via MR and completed in moderately with a small number of MR rounds. However, in the PPISEC algorithm, the centroid values are selected with the help of an improved support vector machine (ISVM) classifier. Thus, the incremental ensemble member chosen (IEMC) progression is performed with fuzzy-based firefly algorithm (FFA), and the normalised cut algorithm is established to accomplish high dimensional data clustering. The outcome shows that, the proposed PPISEC framework, which performs well on three benchmark samples by utilising high dimensionality and enhanced the results than the conventional clustering ensemble approaches.

Hypergraph based semi-supervised symmetric nonnegative matrix factorization for image clustering

Semi-supervised symmetric nonnegative matrix factorization (SNMF) has been shown to be a significant method for both linear and nonlinear data clustering applications. Nevertheless, existing SNMF-based methods only adopt a simple graph to construct the similarity matrix, and cannot fully use the limited supervised information for the construction of the similarity matrix. To overcome the drawbacks of previous SNMF-based methods, a new semi-supervised SNMF-based method called hypergraph based semi-supervised SNMF (HSSNMF), is proposed in this paper for image clustering. Specifically, HSSNMF adopts a predefined hypergraph to build a similarity matrix for capturing the high-order relationships of samples. By exploiting a new hypergraph based pairwise constraints propagation (HPCP) algorithm, HSSNMF propagates the pairwise constraints of the limited data points to the entire data points, which can make full use of the limited supervised information and construct a more informative similarity matrix. Using the multiplicative updating algorithm, a discriminative assignment matrix can then be obtained by solving the optimization problem of HSSNMF. Moreover, analyses of the convergence, supervisory information, and computational complexity of HSSNMF are presented. Finally, extensive clustering experiments have been conducted on six real-world image datasets, and the experimental results have demonstrated the superiority of HSSNMF while compared with several state-of-the-art methods.

Disequilibrium propagation of quantity constraints: application to the COVID lockdowns

AbstractThis paper develops a network economy model to study the propagation of the COVID lockdown shock. Firms are related to each other through buyer–seller relations in the market for intermediate inputs. Firms choose production levels and input combinations using prices that emerge from local interactions. Nothing forbids trade at out-of-equilibrium prices. In such a setting, disequilibrium spills over from one market to another due to the interconnections between markets. These disequilibrium dynamics are capable of generating unemployment when workers released by contracting firms are not frictionlessly absorbed by expanding firms. We calibrate the model to the US economy using a data set with more than 200,000 buyer–seller relations between about 70,000 firms. Computational experiments on the calibrated economy suggest that the COVID lockdown generates a sizeable decline in GDP. The endogenously generated unemployment dynamics is a primary determinant of the cost of the lockdown.

Forecasting petroleum products consumption in Cameroon's household sector using a sequential GMC(1,n) model optimized by genetic algorithms

Forecasting energy consumption is a major concern for policymakers, oil industry companies, and many other associated businesses. Though there exist many forecasting methodologies, selecting the most appropriate one is critical. GM(1,1) has proven to be one of the most successful forecasting tool. GM(1,1) does not require any specific information and can be adapted to predict energy consumption using a minimum of four observations. Unfortunately, GM(1,1) on its own will generate too large forecast errors because it performs well only when data follow an exponential trend and should be implemented in a political-socio-economic free environment. To reduce these errors, this study proposes a new GM(1,n) convolution model optimized by genetic algorithms integrating a sequential selection mechanism and arc consistency, abbreviated Sequential-GMC(1,n)-GA. Practically, the proposed approach, on one hand, highlights the forecast for petroleum products consumption in Cameroon's household sector. On the other hand, it estimates the amount of CO2 that would be reduced if petroleum products in this sector were switched to clean energy. The new model, like some recent hybrid versions, is robust and reliable, according to the results. Households petroleum products needs by 2025 are estimated to be 150,318 kilo tons of oil equivalent with MAPE of 1.44%, and RMSE of 0.833. Therefore, households GHG emissions would be reduced by 733.85 kilo tons of CO2 equivalent if clean energy was used instead of petroleum products. As a result, the new hybrid model is a valid forecasting tool that can be used to track the growth of Cameroon's household energy demand.

An algorithm-independent measure of progress for linear constraint propagation

Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite convergence. However, these heuristic stopping criteria can pose difficulties for fairly comparing the efficiency of different implementations of iterative propagation algorithms in a real-world setting. Most significantly, the presence of unbounded variable domains in the problem formulation makes it difficult to quantify the relative size of reductions performed on them. In this work, we develop a method to measure—independently of the algorithmic design—the progress that a given iterative propagation procedure has made at a given point in time during its execution. Our measure makes it possible to study and better compare the behavior of bounds propagation algorithms for linear constraints. We apply the new measure to answer two questions of practical relevance: (i) We investigate to what extent heuristic stopping criteria can lead to premature termination on real-world MIP instances. (ii) We compare a GPU-parallel propagation algorithm against a sequential state-of-the-art implementation and show that the parallel version is even more competitive in a real-world setting than originally reported.

Tiered State Expansion in Optimization Crosswords

Crosswords puzzles continue to be a popular form of entertainment. In Artificial Intelligence (AI), crosswords can be represented as a constraint problem, and attacked with a combinatorial search algorithm. In combinatorial search, the branching factor can play a crucial role on the search space size and thus on the search effort. We introduce tiered state expansion, a completeness-preserving technique to reduce the branching factor. In problems where the successors of a state correspond to the values in the domain of a state variable selected for instantiation, the domain is partitioned into two subsets called tiers. The instantiation of the two tiers is performed at different times, with tier 1 first and tier 2 in a subsequent state. Before a tier-2 instantiation occurs, its set of applicable values can shrink substantially due to constraint propagation, with a corresponding reduction of the branching factor. We apply tiered state expansion to a constraint optimization problem modeled on the Romanian Crosswords Competition, empirically demonstrating a substantial improvement. Tiered state expansion allows finding a full solution, with an average CPU time of up to 1.2 minutes, to many puzzles that would otherwise time out after 4 hours.

Actions of the hyperoctahedral group to compute minimal contractors

The hyperoctahedral group Bn is the group of symmetries of the hypercube [−1,1]n of Rn. For instance permutations, or symmetries along each of the n canonical planes of Rn all belong to Bn. Now, many sets of equations contain symmetries in Bn. This is the case of the addition constraint: x1+x2=x3 or the multiplication x1⋅x2=x3. In robotics, many specific geometrical constraints such as for instance constraints involving distances or angles used for localization also have these symmetries. This paper shows the fundamental role of the hyperoctahedral group for interval-based methods. These methods use operators, called contractors, which contract axis-aligned boxes, without removing any point of the solution set defined by a conjunction of constraints (typically equations, or inequalities). More precisely, the paper presents an algorithm which allows us to build minimal contractors associated to constraints with symmetries in Bn. As an application, we will consider the geometrical constraint associated to the angle between vectors. The corresponding contractor will then be used in a constraint propagation framework in order to localize a robot using several radars.

LGLNN: Label Guided Graph Learning-Neural Network for few-shot learning

Graph Neural Networks (GNNs) have been employed for few-shot learning (FSL) tasks. The aim of GNN based FSL is to transform the few-shot learning problem into a graph node classification or edge labeling tasks, which can thus fully explore the relationships among samples in support and query sets. However, existing works generally consider the graph learned by node features which ignore the initial pairwise label constraints and thus are generally not guaranteed to be optimal for FSL tasks. Also, existing works generally learn graph edges independently based on node’s own features which lack of considering the consistent relationships among different edges. To address these issues, we propose a novel Label Guided Graph Learning-Neural network (LGLNN) model for FSL tasks. The aim of LGLNN is to incorporate the label information to learn an optimal metric graph for GNN by employing the pairwise constraint propagation. The main advantage of LGLNN is that it can learn the metrics (both similarity and dissimilarity) for each graph edge by aggregating the metric information from its neighboring edges and thus can conduct metric learning of all edges cooperatively and consistently. Experimental results demonstrate the effectiveness and better performance of the proposed LGLNN method.

Multi-agent path finding with mutex propagation

Mutex propagation is a form of efficient constraint propagation popularly used in AI planning to tightly approximate the reachable states from a given state. We utilize this idea in the context of Multi-Agent Path Finding (MAPF). When adapted to MAPF, mutex propagation provides stronger constraints for conflict resolution in CBS, a popular optimal search-based MAPF algorithm, as well as in MDD-SAT, an optimal satisfiability-based MAPF algorithm. Mutex propagation provides CBS with the ability to break symmetries in MAPF and provides MDD-SAT with the ability to make stronger inferences than unit propagation. While existing work identifies a limited form of symmetries and requires the manual design of symmetry-breaking constraints, mutex propagation is more general and allows for the automated design of symmetry-breaking constraints. Our experimental results show that CBS with mutex propagation is capable of outperforming CBSH-RCT, a state-of-the-art variant of CBS, with respect to the success rate. We also show that MDD-SAT with mutex propagation often performs better than MDD-SAT with respect to the success rate.

Verification of Sigmoidal Artificial Neural Networks using iSAT

This paper presents an approach for verifying the behaviour of nonlinear Artificial Neural Networks (ANNs) found in cyber-physical safety-critical systems. We implement a dedicated interval constraint propagator for the sigmoid function into the SMT solver iSAT and compare this approach with a compositional approach encoding the sigmoid function by basic arithmetic features available in iSAT and an approximating approach. Our experimental results show that the dedicated and the compositional approach clearly outperform the approximating approach. Throughout all our benchmarks, the dedicated approach showed an equal or better performance compared to the compositional approach.

GEQCA: Generic Qualitative Constraint Acquisition

Many planning, scheduling or multi-dimensional packing problems involve the design of subtle logical combinations of temporal or spatial constraints. On the one hand, the precise modelling of these constraints, which are formulated in various relation algebras, entails a number of possible logical combinations and requires expertise in constraint-based modelling. On the other hand, active constraint acquisition (CA) has been used successfully to support non-experienced users in learning conjunctive constraint networks through the generation of a sequence of queries. In this paper, we propose GEACQ, which stands for Generic Qualitative Constraint Acquisition, an active CA method that learns qualitative constraints via the concept of qualitative queries. GEACQ combines qualitative queries with time-bounded path consistency (PC) and background knowledge propagation to acquire the qualitative constraints of any scheduling or packing problem. We prove soundness, completeness and termination of GEACQ by exploiting the jointly exhaustive and pairwise disjoint property of qualitative calculus and we give an experimental evaluation that shows (i) the efficiency of our approach in learning temporal constraints and, (ii) the use of GEACQ on real scheduling instances.

Propositional Encodings of Acyclicity and Reachability by Using Vertex Elimination

We introduce novel methods for encoding acyclicity and s-t-reachability constraints for propositional formulas with underlying directed graphs, based on vertex elimination graphs, which makes them suitable for cases where the underlying graph has a low directed elimination width. In contrast to solvers with ad hoc constraint propagators for graph constraints such as GraphSAT, our methods encode these constraints as standard propositional clauses, making them directly applicable with any SAT solver. An empirical study demonstrates that our methods do often outperform both earlier encodings of these constraints as well as GraphSAT especially when underlying graphs have a low directed elimination width.

Encoding Multi-Valued Decision Diagram Constraints as Binary Constraint Trees

Ordered Multi-valued Decision Diagram (MDD) is a compact representation used to model various constraints, such as regular constraints and table constraints. It can be particularly useful for representing ad-hoc problem specific constraints. Many algorithms have been proposed to enforce Generalized Arc Consistency (GAC) on MDD constraints. In this paper, we introduce a new compact representation called Binary Constraint Tree (BCT). We propose tree binary encodings to transform any MDD constraint into a BCT constraint. We also present a specialized algorithm enforcing GAC on the BCT constraint resulting from a MDD constraint. Experimental results on a large set of benchmarks show that the BCT GAC algorithm can significantly outperform state-of-the-art MDD as well as table GAC algorithms.

New first-order formulation of the Einstein equations exploiting analogies with electrodynamics

The Einstein and Maxwell equations are both systems of hyperbolic equations which need to satisfy a set of elliptic constraints throughout evolution. However, while electrodynamics (EM) and magnetohydrodynamics (MHD) have benefited from a large number of evolution schemes that are able to enforce these constraints and are easily applicable to curvilinear coordinates, unstructured meshes, or N-body simulations, many of these techniques cannot be straightforwardly applied to existing formulations of the Einstein equations. We develop a 3+1 a formulation of the Einstein equations which shows a striking resemblance to the equations of relativistic MHD and to EM in material media. The fundamental variables of this formulation are the frame fields, their exterior derivatives, and the Nester-Witten and Sparling forms. These mirror the roles of the electromagnetic 4-potential, the electromagnetic field strengths, the field excitations and the electric current. The role of the lapse function and shift vector, corresponds exactly to that of the scalar electric potential. The formulation, that we name dGREM (for differential forms, General Relativity and Electro-Magnetism), is manifestly first order and flux-conservative, which makes it suitable for high-resolution shock capturing schemes and finite-element methods. Being derived as a system of equations in exterior derivatives, it is directly applicable to any coordinate system and to unstructured meshes, and leads to a natural discretization potentially suitable for the use of machine-precision constraint propagation techniques such as the Yee algorithm and constrained transport. Due to these properties, we expect this new formulation to be beneficial in simulations of many astrophysical systems, such as binary compact objects and core-collapse supernovae as well as cosmological simulations of the early universe.

Tracking Data Provenance of Archaeological Temporal Information in Presence of Uncertainty

The interpretation process is one of the main tasks performed by archaeologists who, starting from ground data about evidences and findings, incrementally derive knowledge about ancient objects or events. Very often more than one archaeologist contributes in different time instants to discover details about the same finding and thus, it is important to keep track of history and provenance of the overall knowledge discovery process. To this aim, we propose a model and a set of derivation rules for tracking and refining data provenance during the archaeological interpretation process. In particular, among all the possible interpretation activities, we concentrate on the one concerning the dating that archaeologists perform to assign one or more time intervals to a finding to define its lifespan on the temporal axis. In this context, we propose a framework to represent and derive updated provenance data about temporal information after the mentioned derivation process. Archaeological data, and in particular their temporal dimension, are typically vague, since many different interpretations can coexist, thus, we will use Fuzzy Logic to assign a degree of confidence to values and Fuzzy Temporal Constraint Networks to model relationships between dating of different findings represented as a graph-based dataset. The derivation rules used to infer more precise temporal intervals are enriched to manage also provenance information and their following updates after a derivation step. A MapReduce version of the path consistency algorithm is also proposed to improve the efficiency of the refining process on big graph-based datasets.

Weak Gravitation in the 4+1 Formalism

The 4+1 formalism in general relativity (GR) prescribes field equations for the spacetime metric γμνx,τ which is local in the spacetime coordinates x and evolves according to an external “worldtime” τ. This formalism extends to GR the Stueckelberg Horwitz Piron (SHP) framework, developed to address the various issues known as the problem of time as they appear in electrodynamics. SHP field theories exhibit a formal 5D symmetry on (x,τ) that is strategically broken to 4+1 representations of the Lorentz group, resulting in a manifestly covariant canonical formalism describing the τ-evolution of spacetime structures as an initial value problem. Einstein equations for γμνx,τ are found by constructing a 5D pseudo-manifold (combining 4D geometry and τ-dynamics) and performing the natural foliation under broken 5D symmetry. This paper discusses weak gravitation in the 4+1 formalism, demonstrating the natural decomposition of the field equations into first-order evolution equations for the unconstrained 4D metric, and the propagation of constraints associated with the Bianchi identity.

Correct approximation of IEEE 754 floating-point arithmetic for program verification

Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs is due to the peculiarities of floating-point arithmetic: rounding errors, infinities, non-numeric objects (NaNs), signed zeroes, denormal numbers, different rounding modes, etc. One possibility to reason about floating-point arithmetic is to model a program computation path by means of a set of ternary constraints of the form and use constraint propagation techniques to infer new information on the variables’ possible values. In this setting, we define and prove the correctness of algorithms to precisely bound the value of one of the variables x, y or z, starting from the bounds known for the other two. We do this for each of the operations and for each rounding mode defined by the IEEE 754 binary floating-point standard, even in the case the rounding mode in effect is only partially known. This is the first time that such so-called filtering algorithms are defined and their correctness is formally proved. This is an important slab for paving the way to formal verification of programs that use floating-point arithmetics.

Solving string constraints with Regex-dependent functions through transducers with priorities and variables

Regular expressions are a classical concept in formal language theory. Regular expressions in programming languages (RegEx) such as JavaScript, feature non-standard semantics of operators (e.g. greedy/lazy Kleene star), as well as additional features such as capturing groups and references. While symbolic execution of programs containing RegExes appeals to string solvers natively supporting important features of RegEx, such a string solver is hitherto missing. In this paper, we propose the first string theory and string solver that natively provides such support. The key idea of our string solver is to introduce a new automata model, called prioritized streaming string transducers (PSST), to formalize the semantics of RegEx-dependent string functions. PSSTs combine priorities, which have previously been introduced in prioritized finite-state automata to capture greedy/lazy semantics, with string variables as in streaming string transducers to model capturing groups. We validate the consistency of the formal semantics with the actual JavaScript semantics by extensive experiments. Furthermore, to solve the string constraints, we show that PSSTs enjoy nice closure and algorithmic properties, in particular, the regularity-preserving property (i.e., pre-images of regular constraints under PSSTs are regular), and introduce a sound sequent calculus that exploits these properties and performs propagation of regular constraints by means of taking post-images or pre-images. Although the satisfiability of the string constraint language is generally undecidable, we show that our approach is complete for the so-called straight-line fragment. We evaluate the performance of our string solver on over 195000 string constraints generated from an open-source RegEx library. The experimental results show the efficacy of our approach, drastically improving the existing methods (via symbolic execution) in both precision and efficiency.