In this paper we present a new approach to modeling finite set domain constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We show that it is possible to construct an efficient set domain propagator which compactly represents many set domains and set constraints using ROBDDs. We demonstrate that the ROBDD-based approach provides unprecedented flexibility in modeling constraint satisfaction problems, leading to performance improvements. We also show that the ROBDD-based modeling approach can be extended to the modeling of integer and multiset constraint problems in a straightforward manner. Since domain propagation is not always practical, we also show how to incorporate less strict consistency notions into the ROBDD framework, such as set bounds, cardinality bounds and lexicographic bounds consistency. Finally, we present experimental results that demonstrate the ROBDD-based solver performs better than various more conventional constraint solvers on several standard set constraint problems.
University of Manouba（马努巴大学）；National School of Computer Science（国立计算机科学学院）；University of Strasbourg（斯特拉斯堡大学）；Taibah University（塔伊巴大学）；College of Computer Science and Engineering（计算机科学与工程学院）
Constraint satisfaction problem (CSP) has been actively used for modeling and solving a wide range of complex real-world problems. However, it has been proven that developing efficient methods for solving CSP, especially for large problems, is very difficult and challenging. Existing complete methods for problem-solving are in most cases unsuitable. Therefore, proposing hybrid CSP-based methods for problem-solving has been of increasing interest in the last decades. This paper aims at proposing a novel approach that combines incomplete and complete CSP methods for problem-solving. The proposed…
Aspartame: Solving Constraint Satisfaction Problems with Answer Set Programming
University of Kobe（神户大学）；University of Potsdam（波茨坦大学）；National Institute of Informatics（国立信息学研究所）；Simon Fraser University（西蒙弗雷泽大学）；Griffith University（格里菲斯大学）
International Institute of Information Technology Bhubaneswar（布巴内斯瓦尔国际信息技术学院）
Minesweeper is a popular spatial-based decision-making game that works with incomplete information. As an exemplary NP-complete problem, it is a major area of research employing various artificial intelligence paradigms. The present work models this game as Constraint Satisfaction Problem (CSP) and Markov Decision Process (MDP). We propose a new method named as dependents from the independent set using deterministic solution search (DSScsp) for the faster enumeration of all solutions of a CSP based Minesweeper game and improve the results by introducing heuristics. Using MDP, we implement mach…
FourierCSP: Differentiable Constraint Satisfaction Problem Solving by Walsh-Fourier Expansion
Department of Electrical and Computer Engineering, National University of Singapore, Singapore（新加坡国立大学电子与计算机工程系）；Department of Computer Science, Rice University, Houston, Texas, United States（美国得克萨斯州休斯敦市 Rice 大学计算机科学系）
Shandong University（山东大学）；Singapore Institute of Manufacturing Technology（新加坡制造技术研究院）；Nanyang Technological University（南洋理工大学）；Southwest Jiaotong University（西南交通大学）
Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP). The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are hand-crafted based on expert knowledge. In this paper, we propose a deep reinforcement learning based approach to automatically discover new variable ordering heuristics that are better adapted for a given class of CSP instances. We show that directly optimizing the search cost is hard for bootstrapping, and propose to optimize the expected cost of reaching a …
Institute of Computing, University of Campinas（坎皮纳斯大学计算研究所）
One-way car-sharing systems are transportation systems that allow customers to rent cars at stations scattered around the city, use them for a short journey, and return them at any station. The maximum customers' satisfaction problem concerns the task of assigning the cars, initially located at given stations, to maximize the number of satisfied customers. We consider the problem with two stations where each customer has exactly two demands in opposite directions between both stations, and a customer is satisfied only if both their demands are fulfilled. For solving this problem, we propose mi…
Stanford University（斯坦福大学）；Università di Roma La Sapienza（罗马第一大学）；Ecole Normale（巴黎高等师范学院）
Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is run after each step. Its outcome provides an heuristic to make choices at next step. This approach has been referred to as `decimation,' with reference to analogous procedures in statistical physics. The behavior of decimation procedures is poorly understood. Here we consider a simple randomized decimation algorithm based on belief propagation (BP), and analy…
The spreadsheet application is among the most widely used computing tools in modern society. It provides excellent usability and usefulness, and it easily enables a non-programmer to perform programming-like tasks in a visual tabular "pen and paper" approach. However, spreadsheets are mostly limited to bookkeeping-like applications due to their mono-directional data flow. This paper shows how the spreadsheet computing paradigm is extended to break this limitation for solving constraint satisfaction problems. We present an enhanced spreadsheet system where finite-domain constraint solving is we…
Constraint Satisfaction Problems (CSPs) typically have many solutions that satisfy all constraints. Often though, some solutions are preferred over others, that is, some solutions dominate other solutions. We present solution dominance as a formal framework to reason about such settings. We define Constraint Dominance Problems (CDPs) as CSPs with a dominance relation, that is, a preorder over the solutions of the CSP. This framework captures many well-known variants of constraint satisfaction, including optimization, multi-objective optimization, Max-CSP, minimal models, minimum correction sub…
Circumspect descent prevails in solving random constraint satisfaction problems
Helsinki University of Technology（赫尔辛基理工大学）；SICS Swedish Institute of Computer Science AB（瑞典计算机科学研究院）；AlbaNova University Centre（阿尔巴诺瓦大学中心）；KTH-Royal Institute of Technology（瑞典皇家理工学院）；University of Helsinki（赫尔辛基大学）；Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所）
CUNY Brooklyn College & Graduate Center（纽约市立大学布鲁克林学院及研究生中心）
Many constraint satisfaction problems involve synthesizing subgraphs that satisfy certain reachability constraints. This paper presents programs in Picat for four problems selected from the recent LP/CP programming competitions. The programs demonstrate the modeling capabilities of the Picat language and the solving efficiency of the cutting-edge SAT solvers empowered with effective encodings.
Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to va…
Purdue University（普渡大学）；ByteDance AI Lab（字节跳动人工智能实验室）
Generating natural language under complex constraints is a principled formulation towards controllable text generation. We present a framework to allow specification of combinatorial constraints for sentence generation. We propose TSMH, an efficient method to generate high likelihood sentences with respect to a pre-trained language model while satisfying the constraints. Our approach is highly flexible, requires no task-specific training, and leverages efficient constraint satisfaction solving techniques. To better handle the combinatorial constraints, a tree search algorithm is embedded into …
In this article we consider a certain sub class of Integer Equal Flow problem, which are known NP hard [8]. Currently there exist no direct solutions for the same. It is a common problem in various inventory management systems. Here we discuss a local minima solution which uses projection of the convex spaces to resolve the equal flows and turn the problem into a known linear integer programming or constraint satisfaction problem which have reasonable known solutions and can be effectively solved using simplex or other standard optimization strategies.
Domain reduction is an essential tool for solving the constraint satisfaction problem (CSP). In the binary CSP, neighbourhood substitution consists in eliminating a value if there exists another value which can be substituted for it in each constraint. We show that the notion of neighbourhood substitution can be strengthened in two distinct ways without increasing time complexity. We also show the theoretical result that, unlike neighbourhood substitution, finding an optimal sequence of these new operations is NP-hard.
University of Technology Sydney（悉尼科技大学）；Örebro University（厄勒布鲁大学）
Among the local consistency techniques used for solving constraint networks, path-consistency (PC) has received a great deal of attention. However, enforcing PC is computationally expensive and sometimes even unnecessary. Directional path-consistency (DPC) is a weaker notion of PC that considers a given variable ordering and can thus be enforced more efficiently than PC. This paper shows that DPC (the DPC enforcing algorithm of Dechter and Pearl) decides the constraint satisfaction problem (CSP) of a constraint language if it is complete and has the variable elimination property (VEP). However…
UC Berkeley（加州大学伯克利分校）；Meta AI Research（Meta人工智能研究院）；Princeton University（普林斯顿大学）；UT Austin（德克萨斯大学奥斯汀分校）
Object rearrangement is a challenge for embodied agents because solving these tasks requires generalizing across a combinatorially large set of configurations of entities and their locations. Worse, the representations of these entities are unknown and must be inferred from sensory percepts. We present a hierarchical abstraction approach to uncover these underlying entities and achieve combinatorial generalization from unstructured visual inputs. By constructing a factorized transition graph over clusters of entity representations inferred from pixels, we show how to learn a correspondence bet…
In this paper, we investigate the possibility of improvement of the widely-used filtering algorithm for the linear constraints in constraint satisfaction problems in the presence of the alldifferent constraints. In many cases, the fact that the variables in a linear constraint are also constrained by some alldifferent constraints may help us to calculate stronger bounds of the variables, leading to a stronger constraint propagation. We propose an improved filtering algorithm that targets such cases. We provide a detailed description of the proposed algorithm and prove its correctness. We evalu…
Constraint Satisfaction Problems (CSPs) play a central role in many applications in Artificial Intelligence and Operations Research. In general, solving CSPs is NP-complete. The structure of CSPs is best described by hypergraphs. Therefore, various forms of hypergraph decompositions have been proposed in the literature to identify tractable fragments of CSPs. However, also the computation of a concrete hypergraph decomposition is a challenging task in itself. In this paper, we report on recent progress in the study of hypergraph decompositions and we outline several directions for future resea…
The job-shop scheduling is one of the most studied optimization problems from the dawn of computer era to the present day. Its combinatorial nature makes it easily expressible as a constraint satisfaction problem. In this paper, we compare the performance of two constraint solvers on the job-shop scheduling problem. The solvers in question are: OR-Tools, an open-source solver developed by Google and winner of the last MiniZinc Challenge, and CP Optimizer, a proprietary IBM constraint solver targeted at industrial scheduling problems. The comparison is based on the goodness of the solutions fou…
In the past few years, the area of Machine Learning (ML) has witnessed tremendous advancements, becoming a pervasive technology in a wide range of applications. One area that can significantly benefit from the use of ML is Combinatorial Optimization. The three pillars of constraint satisfaction and optimization problem solving, i.e., modeling, search, and optimization, can exploit ML techniques to boost their accuracy, efficiency and effectiveness. In this survey we focus on the modeling component, whose effectiveness is crucial for solving the problem. The modeling activity has been tradition…
SemanticForge: Repository-Level Code Generation through Semantic Knowledge Graphs and Constraint Satisfaction
Department of Elec.&Comp. Science, University of Massachusetts Amherst（马萨诸塞大学阿姆赫斯特分校电子与计算机科学系）；Department of Computer Sys. Engineering, Northeastern University（东北大学计算机系统工程系）；Department of Computer Science, George Mason University（乔治·梅森大学计算机科学系）；Department of Info. Networking Institude, Carnegie Mellon University（卡内基梅隆大学信息网络研究所）；Department of Computer & Mathematical Sciences, Auckland University of Technology（奥克兰理工大学计算机与数学科学系）
Structural decomposition methods, such as generalized hypertree decompositions, have been successfully used for solving constraint satisfaction problems (CSPs). As decompositions can be reused to solve CSPs with the same constraint scopes, investing resources in computing good decompositions is beneficial, even though the computation itself is hard. Unfortunately, current methods need to compute a completely new decomposition even if the scopes change only slightly. In this paper, we make the first steps toward solving the problem of updating the decomposition of a CSP $P$ so that it becomes a…
University of Leeds（利兹大学）；Linköpings Universitet（林雪平大学）
The constraint satisfaction problem (CSP) has important applications in computer science and AI. In particular, infinite-domain CSPs have been intensively used in subareas of AI such as spatio-temporal reasoning. Since constraint satisfaction is a computationally hard problem, much work has been devoted to identifying restricted problems that are efficiently solvable. One way of doing this is to restrict the interactions of variables and constraints, and a highly successful approach is to bound the treewidth of the underlying primal graph. Bodirsky & Dalmau [J. Comput. System. Sci. 79(1), 2013…
Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；Johannes Kepler University Linz（林茨约翰内斯·开普勒大学）
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various forms, including, formulas in the propositional logic, linear inequalities over the reals or integers, Boolean combination of linear constraints. We describe some techniques and tools for solving the counting problems, as well as some applications (e.g., applications to automated reasoning, program analysis, formal verification and information security).
IIT Kanpur（印度理工学院坎普尔分校）；National University of Singapore（新加坡国立大学）
Symbolic execution is a powerful technique for bug finding and program testing. It is successful in finding bugs in real-world code. The core reasoning techniques use constraint solving, path exploration, and search, which are also the same techniques used in solving combinatorial problems, e.g., finite-domain constraint satisfaction problems (CSPs). We propose CSP instances as more challenging benchmarks to evaluate the effectiveness of the core techniques in symbolic execution. We transform CSP benchmarks into C programs suitable for testing the reasoning capabilities of symbolic execution t…
