Constraint Propagation Research Articles

A fix-propagate-repair heuristic for mixed integer programming

AbstractWe describe a diving heuristic framework based on constraint propagation for mixed integer linear programs. The proposed approach is an extension of the common fix-and-propagate scheme, with the addition of solution repairing after each step. The repair logic is loosely based on the WalkSAT strategy for boolean satisfiability. Different strategies for variable ranking and value selection, as well as other options, yield different diving heuristics. The overall method is relatively inexpensive, as it is basically LP-free: the full linear programming relaxation is solved only at the beginning (and only for the ranking strategies that make use of it), while additional, typically much smaller, LPs are only used to compute values for the continuous variables (if any), once at the bottom of a dive. While individual strategies are not very robust in finding feasible solutions on a heterogeneous testbed, a portfolio approach proved quite effective. In particular, it could consistently find feasible solutions in 189 out of 240 instances from the public MIPLIB 2017 benchmark testbed, in a matter of a few seconds of runtime. The framework has also been implemented inside the commercial MIP solver Xpress and shown to give a small performance improvement in time to optimality on a large internal heterogeneous testbed.

Symbolic testing of floating-point bugs and exceptions

Numerical software are susceptible to floating-point bugs and exceptions, which may lead to severe threats like denial of service attacks. Static analysis techniques such as symbolic execution are effective in detecting general bugs which often cause memory error or program crash. Unfortunately, these methods do not deal well with numerical code as they do not support floating-point constraints and math functions symbolically. In this paper, we propose a new analysis framework YUSE, which can detect floating-point bugs by constructing constraints and exploring paths which contain floating-point expressions. Specifically, we introduce interval computation and interval constraint propagation in non-relational numerical abstract domains, and symbolically model math functions, to accurately detect floating-point bugs and exceptions. Moreover, we leverage two-phase constraint solving to enhance YUSE’s performance. Experimental results show that YUSE outperforms two state-of-the-art tools, Frama-c and Fpse-study, in terms of effectiveness and efficiency, with 1.4× and 7.1× faster than Frama-c and Fpse-study, respectively. Moreover, YUSE found 20 new bugs in real-world software, 12 of which were assigned CVE IDs and 8 of which were confirmed by developers.

Semi-supervised pivotal-aware nonnegative matrix factorization with label and pairwise constraint propagation for data clustering

Semi-supervised nonnegative matrix factorization (NMF) methods have found extensive utility in data clustering applications. However, these existing methods encounter challenges in effectively leveraging the limited supervisory information to enhance the performance of clustering. In particular, the majority of these methods tend to solely utilize either the label information or the pairwise constraint information, neglecting the potential benefits of their joint utilization. To address this issue, a novel algorithm named semi-supervised pivotal-aware nonnegative matrix factorization (SPNMF) is proposed in this paper, which utilizes the label information and the pairwise constraint information simultaneously to enhance the performance in data clustering tasks. The proposed method has two main innovations: (1) adopting the dual constraint propagation (DCP) algorithm (i.e., label propagation and pairwise constraint propagation) to effectively utilize a meager amount of label information for learning a compact data representation; (2) incorporating the pivotal-aware technique to mitigate the negative impact of outliers. Notably, the DCP algorithm not only propagates limited label information to a multitude of unlabeled samples, but also disseminates the pairwise constraint supervisory information obtained from the labels to unconstrained samples, allowing for the acquisition of richer supervisory information in the form of pointwise and pairwise constraints. Furthermore, a comprehensive analysis of SPNMF is conducted. Extensive experimental results are executed on eight real-world image datasets. The results underscore the superior performance of SPNMF in comparison to several state-of-the-art methods.

On prime scenarios in qualitative spatial and temporal reasoning

The concept of prime implicant is a fundamental tool in Boolean algebra, which is used in Boolean circuit design and, recently, in explainable AI. This study investigates an analogous concept in qualitative spatial and temporal reasoning, called prime scenario. Specifically, we define a prime scenario of a qualitative constraint network (QCN) as a minimal set of decisions that can uniquely determine solutions of this QCN. We propose in this paper a collection of algorithms designed to address various problems related to prime scenarios, and also show how certain results can be useful for measuring the robustness of a QCN. In addition, we study the relationship between our notions in this paper and the notion of prime sub-QCN in the literature, and establish theoretical results in the process. Further, we devise a language based on the notion of prime scenario for knowledge compilation. Finally, an experimental evaluation is performed with instances of Allen's Interval Algebra and RCC8 to assess the efficiency of our algorithms and, hence, also the difficulty of the newly introduced problems here.

Solid Knitting

We introduce solid knitting, a new fabrication technique that combines the layer-by-layer volumetric approach of 3D printing with the topologically-entwined stitch structure of knitting to produce solid 3D objects. We define the basic building blocks of solid knitting and demonstrate a working prototype of a solid knitting machine controlled by a low-level instruction language, along with a volumetric design tool for creating machine-knittable patterns. Solid knitting uses a course-wale-layer structure, where every loop in a solid-knit object passes through both a loop from the previous layer and a loop from the previous course. Our machine uses two beds of latch needles to create stitches like a conventional V-bed knitting machine, but augments these needles with a pair of rotating hook arrays to provide storage locations for all of the loops in one layer of the object. It can autonomously produce solid-knit prisms of arbitrary length, although it requires manual intervention to cast on the first layer and bind off the final row. Our design tool allows users to create solid knitting patterns by connecting elementary stitches; objects designed in our interface can---after basic topological checks and constraint propagation---be exported as a sequence of instructions for fabrication on the solid knitting machine. We validate our solid knitting hardware and software on prism examples, detail the mechanical errors which we have encountered, and discuss potential extensions to the capability of our solid knitting machine.

A constraint programming framework for preliminary mission analysis: Applications for constellation-servicing active debris removal

Constraint Programming is a classical artificial intelligence paradigm characterised by its flexibility for the modelling of complex problems. In the field of space operations, this approach has been successfully used for mission planning and scheduling. This manuscript proposes a framework that leverages the strengths of Constraint Programming for the preliminary analysis of space missions, introducing some modifications to tailor it to the application at hand. Specifically, it uses constraint propagation and search techniques to thoroughly explore the configuration space of a mission in an efficient manner. Consequently, it is able to quantify the performance of precomputed mission choices with respect to the mission requirements, as well as generate new ones that optimise such performance. The proposed methodology has been particularised for two application cases involving active debris removal missions for large constellations in low Earth orbit, namely, a chaser case and a mothership case. The chaser case considers a servicing satellite that rendezvouses with the failed satellites of the constellation and directly transports them to a disposal orbit. The mothership case comprises a servicing satellite that installs deorbiting kits in each of the failed satellites, except for the one removed in the last place. This way, the servicing satellite will only transport this object, while the deorbiting kits will carry out the disposal of the rest of them. This methodology has been successfully used to evaluate a preliminary mission analysis of both application cases developed under ESA’s Sunrise project.

Efficient semi-supervised clustering with pairwise constraint propagation for multivariate time series

Semi-supervised clustering is an effective method, which improves the clustering performance based on pairwise constraints. However, state-of-the-art methods suffer from two issues: 1) due to the high dimensionality and multiple variables of multivariate time series (MTS) data, the competitive similarity approach DTW is time consuming on large-scale MTS data. 2) Traditional semi-supervised clustering methods could not make full use of pairwise constraints information, which affects clustering performance. To deal with these issues, we propose an efficient semi-supervised clustering with pairwise constraint propagation for MTS data. First, two approximate distance measure methods are designed based on dynamic time warping (DTW) from the perspectives of boundary and dimension reduction, which greatly improve the efficiency of clustering without sacrificing its accuracy. Then, a graph-based clustering method with pairwise constraints propagation (GCPCP) is advanced on multivariate time series data. In GCPCP, the pairwise constraint propagation matrix and the affinity matrix are jointly optimized to exploit the dependence between them, which finally improves the clustering performance. Experimental results on 12 multivariate time series datasets show the effectiveness and efficiency of our proposed method.

Using Constraint Propagation to Bound Linear Programs

We present an approach to compute bounds on the optimal value of linear programs based on constraint propagation. Given a feasible dual solution, we apply constraint propagation to the complementary slackness conditions and, if propagation succeeds to prove these conditions infeasible, the infeasibility certificate (in the sense of Farkas’ lemma) is reconstructed from the propagation history. This certificate is a dual-improving direction, which allows us to improve the bound. As constraint propagation need not always detect infeasibility of a linear inequality system, the method is not guaranteed to converge to a global solution of the linear program but only to an upper bound, whose tightness depends on the structure of the program and the used propagation method. The approach is suited for large sparse linear programs (such as LP relaxations of combinatorial optimization problems), for which the classical LP algorithms may be infeasible, if only for their super-linear space complexity. The approach can be seen as a generalization of the Virtual Arc Consistency (VAC) algorithm to bound the LP relaxation of the Weighted CSP (WCSP). We newly apply it to the LP relaxation of the Weighted Max-SAT problem, experimentally showing that the obtained bounds are often not far from optima of the relaxation and proving that they are exact for known tractable subclasses of Weighted Max-SAT.

Constraint propagation on GPU: a case study for the cumulative constraint

Constraint propagation on GPU: a case study for the cumulative constraint

Interval Split Covariance Intersection Filter: Theory and Its Application to Cooperative Localization in a Multi-Sensor Multi-Vehicle System.

The data incest problem causes inter-estimate correlation during data fusion processes, which yields inconsistent data fusion results. Especially in the multi-sensor multi-vehicle (MSMV) system, the data incest problem is serious due to multiple relative position estimations, which not only lead to pessimistic estimation but also cause additional computational overhead. In order to address the data incest problem, we propose a new data fusion method termed the interval split covariance intersection filter (ISCIF). The general consistency of the ISCIF is proven, serving as supplementary proof for the split covariance intersection filter (SCIF). Moreover, a decentralized MSMV localization system including absolute and relative positioning stages is designed. In the absolute positioning stage, each vehicle uses the ISCIF algorithm to update its own position based on absolute measurements. In the relative position stage, the interval constraint propagation (ICP) method is implemented to preprocess multiple relative position estimates and initially prepare input data for ISCIF. Then, the proposed ISCIF algorithm is employed to realize relative positioning. In addition, comparative simulations demonstrate that the proposed method can achieve both accurate and consistent results compared with the state-of-the-art methods.

DeepSaDe: Learning Neural Networks That Guarantee Domain Constraint Satisfaction

As machine learning models, specifically neural networks, are becoming increasingly popular, there are concerns regarding their trustworthiness, specially in safety-critical applications, e.g. actions of an autonomous vehicle must be safe. There are approaches that can train neural networks where such domain requirements are enforced as constraints, but they either cannot guarantee that the constraint will be satisfied by all possible predictions (even on unseen data) or they are limited in the type of constraints that can be enforced. In this paper, we present an approach to train neural networks which can enforce a wide variety of constraints and guarantee that the constraint is satisfied by all possible predictions. The approach builds on earlier work where learning linear models is formulated as a constraint satisfaction problem (CSP). To make this idea applicable to neural networks, two crucial new elements are added: constraint propagation over the network layers, and weight updates based on a mix of gradient descent and CSP solving. Evaluation on various machine learning tasks demonstrates that our approach is flexible enough to enforce a wide variety of domain constraints and is able to guarantee them in neural networks.

Semi-supervised nonnegative matrix factorization with label propagation and constraint propagation

Semi-supervised nonnegative matrix factorization (SNMF) improves the clustering effect of nonnegative matrix factorization (NMF) by integrating label information. However, as one of the most commonly used semi-supervised learning methods, label propagation algorithm (LP) has some limitations due to its heavy dependence on the predefined similarity matrix. To address this deficiency and effectively use limited supervisory information, a structural NMF algorithm with label propagation and constraint propagation (PNLP-SCNMF) is proposed in this paper, which simultaneously performs data representation and classification in a joint manner. Both positive label information and negative label information are introduced into the proposed method, and the factor matrix is constrained by label information to construct the tri-decomposition form. Constraint propagation algorithm (CPA) is used to correct the constructed similarity matrix, so that the low-dimensional subspace obtained by matrix decomposition can retain the geometric structure characteristics of the original sample space. In addition, an efficient iterative update optimization scheme is proposed to solve this objective function, and its convergence is proved theoretically. A large number of comparative experiments on nine real datasets show that the proposed method can consistently achieve higher clustering accuracy in image clustering tasks.

Efficient retrosynthetic planning with MCTS exploration enhanced A* search

Retrosynthetic planning, which aims to identify synthetic pathways for target molecules from starting materials, is a fundamental problem in synthetic chemistry. Computer-aided retrosynthesis has made significant progress, in which heuristic search algorithms, including Monte Carlo Tree Search (MCTS) and A* search, have played a crucial role. However, unreliable guiding heuristics often cause search failure due to insufficient exploration. Conversely, excessive exploration also prevents the search from reaching the optimal solution. In this paper, MCTS exploration enhanced A* (MEEA*) search is proposed to incorporate the exploratory behavior of MCTS into A* by providing a look-ahead search. Path consistency is adopted as a regularization to improve the generalization performance of heuristics. Extensive experimental results on 10 molecule datasets demonstrate the effectiveness of MEEA*. Especially, on the widely used United States Patent and Trademark Office (USPTO) benchmark, MEEA* achieves a 100.0% success rate. Moreover, for natural products, MEEA* successfully identifies bio-retrosynthetic pathways for 97.68% test compounds.

Рассуждения с темпоральными ограничениями

The work deals with the organization of temporal reasoning basing on constraint satisfaction methods. The definition of the constraint satisfaction problem and the notion of constraint consistency are given. The possibilities of epresentation of a planning problem as an interval constraint network are considered. As a mathematical apparatus for the formalization of temporal reasining, the Allen’s interval algebra is described, which main operations are composition and the intersection of temporal relations. A path consistency algorithm is given that implements one of the types of local consistency on interval constraint network and uses computations based on operations of interval algebra. An example of the application of this algorithm is presented. In the conclusion the prospects for the development of methods of temporal reasoning are considered.

Cooperative Vehicle Localization in Multi-Sensor Multi-Vehicle Systems Based on an Interval Split Covariance Intersection Filter with Fault Detection and Exclusion

In the cooperative multi-sensor multi-vehicle (MSMV) localization domain, the data incest problem yields inconsistent data fusion results, thereby reducing the accuracy of vehicle localization. In order to address this problem, we propose the interval split covariance intersection filter (ISCIF). At first, the proposed ISCIF method is applied to the absolute positioning step. Then, we combine the interval constraint propagation (ICP) method and the proposed ISCIF method to realize relative positioning. Additionally, in order to enhance the robustness of the MSMV localization system, a Kullback–Leibler divergence (KLD)-based fault detection and exclusion (FDE) method is implemented in our system. Three simulations were carried out: Simulation scenarios 1 and 2 aimed to assess the accuracy of the proposed ISCIF with various capabilities of absolute vehicle positioning, while simulation scenario 3 was designed to evaluate the localization performance when faults were present. The simulation results of scenarios 1 and 2 demonstrated that our proposed vehicle localization method reduced the root mean square error (RMSE) by 8.9% and 15.5%, respectively, compared to the conventional split covariance intersection filter (SCIF) method. The simulation results of scenario 3 indicated that the implemented FDE method could effectively reduce the RMSE of vehicles (by about 55%) when faults were present in the system.

De Novo Drug Design by Multi-Objective Path Consistency Learning with Beam A∗ Search.

Generating high-quality and drug-like molecules from scratch within the expansive chemical space presents a significant challenge in the field of drug discovery. In prior research, value-based reinforcement learning algorithms have been employed to generate molecules with multiple desired properties iteratively. The immediate reward was defined as the evaluation of intermediate-state molecules at each step, and the learning objective would be maximizing the expected cumulative evaluation scores for all molecules along the generative path. However, this definition of the reward was misleading, as in reality, the optimization target should be the evaluation score of only the final generated molecule. Furthermore, in previous works, randomness was introduced into the decision-making process, enabling the generation of diverse molecules but no longer pursuing the maximum future rewards. In this paper, immediate reward is defined as the improvement achieved through the modification of the molecule to maximize the evaluation score of the final generated molecule exclusively. Originating from the A ∗ search, path consistency (PC), i.e., f values on one optimal path should be identical, is employed as the objective function in the update of the f value estimator to train a multi-objective de novo drug designer. By incorporating the f value into the decision-making process of beam search, the DrugBA∗ algorithm is proposed to enable the large-scale generation of molecules that exhibit both high quality and diversity. Experimental results demonstrate a substantial enhancement over the state-of-theart algorithm QADD in multiple molecular properties of the generated molecules.

Two Improved Constraint-Solving Algorithms Based on lmaxRPC3rm

The Constraint Satisfaction Problem (CSP) is a significant research area in artificial intelligence, and includes a large number of symmetric or asymmetric structures. A backtracking search combined with constraint propagation is considered to be the best CSP-solving algorithm, and the consistency algorithm is the main algorithm used in the process of constraint propagation, which is the key factor in constraint-solving efficiency. Max-restricted path consistency (maxRPC) is a well-known and efficient consistency algorithm, whereas the lmaxRPC3rm algorithm is a classic lightweight algorithm for maxRPC. In this paper, we leverage the properties of symmetry to devise an improved pruning strategy aimed at efficiently diminishing the problem’s search space, thus enhancing the overall solving efficiency. Firstly, we propose the maxRPC3sim algorithm, which abandons the two complex data structures used by lmaxRPC3rm. We can render the algorithm to be more concise and competitive compared to the original algorithm while ensuring that it maintains the same average performance. Secondly, inspired by the RCP3 algorithm, we propose the maxRPC3simR algorithm, which uses the idea of residual support to cut down the redundant operation of the lmaxRPC3rm algorithm. Finally, combining the domain/weighted degree (dom/wdeg) heuristic with the activity-based search (ABS) heuristic, a new variable ordering heuristic, ADW, is proposed. Our heuristic prioritizes the selection of variables with symmetry for pruning, further enhancing the algorithm’s pruning capabilities. Experiments were conducted on both random and structural problems separately. The results indicate that our two algorithms generally outperform other algorithms in terms of performance on both problem classes. Moreover, the new heuristic algorithm demonstrates enhanced robustness across different problem types when compared to various existing algorithms.

An efficient circuit-based SAT solver and its application in logic equivalence checking

In this paper, we propose an integrated approach that combines a circuit-based SAT solver (CirSAT) with a technique based on XOR-Majority Graph (XMG) rewriting for logic equivalence checking. CirSAT harnesses circuit information to implement a variety of efficient SAT algorithms on the And-Inverter Graph (AIG). Specifically, we introduce the “AIG-J-frontier” algorithm to minimize unnecessary search space during SAT solving. This algorithm employs the fanout count of logic gates as a heuristic to guide conflict resolution decisions. Furthermore, we present a flexible and efficient two-pointer watching scheme for rapid Boolean constraint propagation. The XMG-based rewriting technique is used to simplify logic networks and accommodate a larger number of high fanout nodes. In experiments using ISCAS’85 and EPFL benchmark suites, our method outperforms CNF-based solvers such as Minisat and Lingeling with a 3.66 speedup. It also exhibits an 8.26 speedup compared to the circuit-based solver QuteSAT and a 5.99 speedup when compared to using the CirSAT solver independently.

Towards Systematization of Aurivillius Phases' Formula

Aurivillius structures are a family of layered perovskite that are of great importance due to the many properties they provide (ferroelectricity, dielectric ...) and the applications in which they can be used (thin films, micro-electromechanical devices, etc.); thus, the discovery of such materials can be very useful. Since their appearance, Aurivillius structures have been largely studied, but little work has focused on the systematization of the latter. The main idea of this paper is to systematize the formula of Aurivillius structures [Am-1 B­i2 Bm O3m+3], using combinatorial mathematical techniques to substitute elements in cations A and B, while taking into account the criteria of electronegativity (zero total charge) and structure (tolerance factor). Constraint propagation has been used as a key technique to significantly reduce the number of combinations and thus minimize the execution cost. The results of such a work can present a very large dataset which can be exploited into a research tool that brings a great help to researchers by providing a better visibility on chemical elements forming a potential Aurivillius structure, and thus, bringing a significant asset in the discovery of these materials.

Multiview Clustering via Hypergraph Induced Semi-Supervised Symmetric Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) based multiview technique has been commonly used in multiview data clustering tasks. However, previous NMF based multiview clustering approaches fail to take advantage of a small amount of supervisory information to effectively improve the clustering performance, and are easily affected by the additional post-processing method in clustering tasks. To cope with these issues, a novel framework named multiview clustering via hypergraph induced semi-supervised symmetric NMF (MVCHSS) is proposed in this paper for multiview data clustering applications. Specifically, the proposed method has the following features: 1) a new multiview based hypergraph pairwise constraints propagation (MHPCP) algorithm is developed in MVCHSS to construct a set of informative similarity matrices, revealing the high-order relationships effectively and fully utilizing the limited pairwise constraint supervisory information among samples of each view data; 2) the obtained similarity matrices with much supervisory information are not only enforced into the symmetric NMF (SNMF) model, but also incorporated into the graph regularization for each view data; 3) the optimization problem of MVCHSS is formulated for multiview data clustering tasks to acquire a more discriminative clustering indicator matrix (or called consensus assignment matrix) without additional post-processing method. Moreover, the proof of convergence and the computational complexity for MVCHSS are presented. Extensive experiments on five multiview datasets demonstrate that the proposed MVCHSS framework outperforms several state-of-the-art multiview clustering methods.