Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either dire...Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.展开更多
Message passing algorithms,whose iterative nature captures complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages,provide a powerf...Message passing algorithms,whose iterative nature captures complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages,provide a powerful toolkit in tackling hard computational tasks in optimization,inference,and learning problems.In the context of constraint satisfaction problems(CSPs),when a control parameter(such as constraint density)is tuned,multiple threshold phenomena emerge,signaling fundamental structural transitions in their solution space.Finding solutions around these transition points is exceedingly challenging for algorithm design,where message passing algorithms suffer from a large message fiuctuation far from convergence.Here we introduce a residual-based updating step into message passing algorithms,in which messages with large variation between consecutive steps are given high priority in the updating process.For the specific example of model RB(revised B),a typical prototype of random CSPs with growing domains,we show that our algorithm improves the convergence of message updating and increases the success probability in finding solutions around the satisfiability threshold with a low computational cost.Our approach to message passing algorithms should be of value for exploring their power in developing algorithms to find ground-state solutions and understand the detailed structure of solution space of hard optimization problems.展开更多
The past decade witnessed rapid development of constraint satisfaction technologies, where algorithms are now able to cope with larger and harder problems. However, owing to the fact that constraints are inherently de...The past decade witnessed rapid development of constraint satisfaction technologies, where algorithms are now able to cope with larger and harder problems. However, owing to the fact that constraints are inherently declarative, attention is quickly turning toward developing high-level programming languages within which such problems can be modeled and also solved. Along these lines, this paper presents DEPICT, the language. Its use is illustrated through modeling a number of benchmark examples. The paper continues with a description of a prototype system within which such models may be interpreted. The paper concludes with a description of a sample run of this interpreter showing how a problem modeled as such is typically solved.展开更多
This research develops a solution method for project scheduling represented by a max-plus-linear (MPL) form. Max-plus-linear representation is an approach to model and analyze a class of discrete-event systems, in whi...This research develops a solution method for project scheduling represented by a max-plus-linear (MPL) form. Max-plus-linear representation is an approach to model and analyze a class of discrete-event systems, in which the behavior of a target system is represented by linear equations in max-plus algebra. Several types of MPL equations can be reduced to a constraint satisfaction problem (CSP) for mixed integer programming. The resulting formulation is flexible and easy-to-use for project scheduling;for example, we can obtain the earliest output times, latest task-starting times, and latest input times using an MPL form. We also develop a key method for identifying critical tasks under the framework of CSP. The developed methods are validated through a numerical example.展开更多
基于角色的协同RBC(Role-Based Collaboration)是一套研究角色及它们之间复杂关系的方法、理论和技术。在RBC中,群组角色分配GRA(Group Role Assignment)既是一个关键问题,也是一个难题。已有许多研究探讨了基于Q(Qualification)矩阵来...基于角色的协同RBC(Role-Based Collaboration)是一套研究角色及它们之间复杂关系的方法、理论和技术。在RBC中,群组角色分配GRA(Group Role Assignment)既是一个关键问题,也是一个难题。已有许多研究探讨了基于Q(Qualification)矩阵来处理GRA问题,但仅利用Q矩阵难以描述问题中的复杂约束关系。因此,将约束集(Constraint)引进E-CARGO模型,提出了带约束的EC-CARGO模型,研究了RBC、GRA、SAT(SATisfaction)和CSP(Constraint Satisfaction Problem)之间的联系,建立了RBC-GRA-SAT-CSP问题求解转换关系;提出应用EC-CARGO模型求解经典CSP约束满足问题的方法,进而描述了应用GRA求解CSP约束满足问题的通用框架。最后以N皇后问题为例,验证了通过GRA的约束指派求解CSP问题的有效性。展开更多
基金funded by the National Key R&D Program of China(Grant No.2024YFE0102500)the National Natural Science Foundation of China(Grant No.12404568)+1 种基金the Guangzhou Municipal Science and Technology Project(Grant No.2023A03J00904)the Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area,China and the Undergraduate Research Project from HKUST(Guangzhou).
文摘Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.
基金supported by Guangdong Major Project of Basic and Applied Basic Research No.2020B0301030008Science and Technology Program of Guangzhou No.2019050001+2 种基金the Chinese Academy of Sciences Grant QYZDJ-SSWSYS018the National Natural Science Foundation of China(Grant No.12171479)supported by the National Natural Science Foundation of China(Grant Nos.11301339 and 11491240108)。
文摘Message passing algorithms,whose iterative nature captures complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages,provide a powerful toolkit in tackling hard computational tasks in optimization,inference,and learning problems.In the context of constraint satisfaction problems(CSPs),when a control parameter(such as constraint density)is tuned,multiple threshold phenomena emerge,signaling fundamental structural transitions in their solution space.Finding solutions around these transition points is exceedingly challenging for algorithm design,where message passing algorithms suffer from a large message fiuctuation far from convergence.Here we introduce a residual-based updating step into message passing algorithms,in which messages with large variation between consecutive steps are given high priority in the updating process.For the specific example of model RB(revised B),a typical prototype of random CSPs with growing domains,we show that our algorithm improves the convergence of message updating and increases the success probability in finding solutions around the satisfiability threshold with a low computational cost.Our approach to message passing algorithms should be of value for exploring their power in developing algorithms to find ground-state solutions and understand the detailed structure of solution space of hard optimization problems.
基金This work was supported by Lebanese National Council for Scientific Research.
文摘The past decade witnessed rapid development of constraint satisfaction technologies, where algorithms are now able to cope with larger and harder problems. However, owing to the fact that constraints are inherently declarative, attention is quickly turning toward developing high-level programming languages within which such problems can be modeled and also solved. Along these lines, this paper presents DEPICT, the language. Its use is illustrated through modeling a number of benchmark examples. The paper continues with a description of a prototype system within which such models may be interpreted. The paper concludes with a description of a sample run of this interpreter showing how a problem modeled as such is typically solved.
文摘This research develops a solution method for project scheduling represented by a max-plus-linear (MPL) form. Max-plus-linear representation is an approach to model and analyze a class of discrete-event systems, in which the behavior of a target system is represented by linear equations in max-plus algebra. Several types of MPL equations can be reduced to a constraint satisfaction problem (CSP) for mixed integer programming. The resulting formulation is flexible and easy-to-use for project scheduling;for example, we can obtain the earliest output times, latest task-starting times, and latest input times using an MPL form. We also develop a key method for identifying critical tasks under the framework of CSP. The developed methods are validated through a numerical example.
