Algorithms For Constraint Satisfaction Problems Research Articles

A residual-based message passing algorithm for constraint satisfaction problems

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 fluctuation 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.

Optimization of long-term planning with a constraint satisfaction problem algorithm with a machine learning

The object of the long-term planning in shipyards is to assign the ordered vessels to the berths with the consideration of the workload balancing. However, there are limitations in establishing an optimized long-term plan because the workload balancing takes too much time due to the size and the complexity of the problem domain. Most shipyards currently overcome the limitations by dividing the long-term planning into two-phase of the berth planning and the capacity planning. The berth planning is being conducted with a heuristic method by considering some rules such as the berth priority and the closeness to delivery date. Then it is followed by the capacity planning, in which the workload data is considered for the workload balancing with the previously planned data. However, the heuristic method has a fundamental problems that the optimized solution is not guaranteed owing to the limits of the search range. Also, the previous production record cannot reflect the newly ordered vessel's workload precisely. In this study, a constraint satisfaction technique is used for the optimization of the berth planning. In addition, the workload prediction model is developed based on the supervised learning with a deep neural network. Finally, proposed methods are tested with the shipyard actual data, that shows the improved results.

Toward personalized XAI: A case study in intelligent tutoring systems

Our research is a step toward ascertaining the need for personalization in XAI, and we do so in the context of investigating the value of explanations of AI-driven hints and feedback in Intelligent Tutoring Systems (ITS). We added an explanation functionality to the Adaptive CSP (ACSP) applet, an interactive simulation that helps students learn an algorithm for constraint satisfaction problems by providing AI-driven hints adapted to their predicted level of learning. We present the design of the explanation functionality and the results of a controlled study to evaluate its impact on students' learning and perception of the ACPS hints. The study includes an analysis of how these outcomes are modulated by several user characteristics such as personality traits and cognitive abilities, to asses if explanations should be personalized to these characteristics. Our results indicate that providing explanations increase students' trust in the ACPS hints, perceived usefulness of the hints, and intention to use them again. In addition, we show that students' access of the ACSP explanation and learning gains are modulated by three user characteristics, Need for Cognition, Contentiousness and Reading Proficiency, providing insights on how to personalize the ACSP explanations to these traits, as well as initial evidence on the potential value of personalized Explainable AI (XAI) for ITS.

Partial (Neighbourhood) Singleton Arc Consistency for Constraint Satisfaction Problems

Algorithms based on singleton arc consistency (SAC) show considerable promise for improving backtrack search algorithms for constraint satisfaction problems (CSPs). The drawback is that even the most efficient of them is still comparatively expensive. Even when limited to preprocessing, they give overall improvement only when problems are quite difficult to solve with more typical procedures such as maintained arc consistency (MAC). The present work examines a form of partial SAC and neighbourhood SAC (NSAC) in which a subset of the variables in a CSP are chosen to be made SAC-consistent or neighbourhood-SAC-consistent. Such consistencies, despite their partial character, are still well-characterized in that algorithms have unique fixpoints. Heuristic strategies for choosing an effective subset of variables are described and tested, the best being choice by highest degree and a more complex strategy of choosing by constraint weight after random probing. Experimental results justify the claim that these methods can be nearly as effective as the corresponding full version of the algorithm in terms of values discarded or problems proven unsatisfiable, while significantly reducing the effort required to achieve this.

An Efficient Local Search algorithm for Over-Constrained CSPs

In industrial experiences of solving constraint satisfaction problems (CSPs), we may often meet an over-constraint situation, which means that we cannot find a solution that satisfies all the constraints. In such situations, the classical CSP is usually extended to take into account costs, preferences, etc. The new objective is usually to minimize the total constraint violation cost or other criterions. The new problems can be described as valued constraint satisfaction problems (VCSP). VCSP can hardly be resolved by the classical constraint satisfying techniques, and this paper provides an application of the Guided Local Search in solving VCSPs.

Robust Algorithms with Polynomial Loss for Near-Unanimity CSPs

An instance of the Constraint Satisfaction Problem (CSP) is given by a family of constraints on overlapping sets of variables, and the goal is to assign values from a xed domain to the variables so that all constraints are satised. In the optimization version, the goal is to maximize the number of satised constraints. An approximation algorithm for CSP is called robust if it outputs an assignment satisfying an (1????g())-fraction of constraints on any (1????)-satisable instance, where the loss function g is such that g() ! 0 as ! 0. We study how the robust approximability of CSPs depends on the set of constraint relations allowed in instances, the so-called constraint language. All constraint languages admitting a robust polynomial-time algorithm (with some g) have been characterised by Barto and Kozik, with the general bound on the loss g being doubly exponential, specically g() = O((log log(1=))= log(1=)). It is natural to ask when a better loss can be achieved: in particular, polynomial loss g() = O(1=k) for some constant k. In this paper, we consider CSPs with a constraint language having a nearunanimity polymorphism. This general condition almost matches a known necessary condition for having a robust algorithm with polynomial loss. We give two randomized robust algorithms with polynomial loss for such CSPs: one works for any near-unanimity polymorphism and the parameter k in the loss depends on the size of the domain and the arity of the relations in ????, while the other works for a special ternary near-unanimity operation called dual discriminator with k = 2 for any domain size. In the latter case, the CSP is a common generalisation of Unique Games with a xed domain and 2-Sat. In the former case, we use the algebraic approach to the CSP. Both cases use the standard semidenite programming relaxation for CSP.

Multi-robot grasp planning for sequential assembly operations

This paper addresses the problem of finding robot configurations to grasp assembly parts during a sequence of collaborative assembly operations. We formulate the search for such configurations as a constraint satisfaction problem (CSP). Collision constraints in an operation and transfer constraints between operations determine the sets of feasible robot configurations. We show that solving the connected constraint graph with off-the-shelf CSP algorithms can quickly become infeasible even for a few sequential assembly operations. We present an algorithm which, through the assumption of feasible regrasps, divides the CSP into independent smaller problems that can be solved exponentially faster. The algorithm then uses local search techniques to improve this solution by removing a gradually increasing number of regrasps from the plan. The algorithm enables the user to stop the planner anytime and use the current best plan if the cost of removing regrasps from the plan exceeds the cost of executing those regrasps. We present simulation experiments to compare our algorithm’s performance to a naive algorithm which directly solves the connected constraint graph. We also present a physical robot system which uses the output of our planner to grasp and bring parts together in assembly configurations.

Combining CSP and MPC for the operational control of water networks

This paper presents a control scheme which uses a combination of linear Model Predictive Control (MPC) and a Constraint Satisfaction Problem (CSP) to solve the non-linear operational optimal control of Drinking Water Networks (DWNs). The methodology has been divided into two functional layers: first, a CSP algorithm is used to transfer non-linear DWNs pressure equations into linear constraints on flows and tank volumes, which can enclose the feasible solution set of the hydraulic non-linear problem during the optimization process. Then, a linear MPC with tightened constraints produced in the CSP layer is solved to generate control strategies which optimize the control objectives. The proposed approach is simulated using Epanet to represent the real DWNs. Non-linear MPC is used for validation. To illustrate the performance of the proposed approach, a case study based on the Richmond water network is used and a realistic example, D-Town benchmark network, is added as a supplementary case study.

Robustness and Stability in Constraint Programming under Dynamism and Uncertainty

Many real life problems that can be solved by constraint programming, come from uncertain and dynamic environments. Because of the dynamism, the original problem may change over time, and thus the solution found for the original problem may become invalid. For this reason, dealing with such problems has become an important issue in the fields of constraint programming. In some cases, there exist extant knowledge about the uncertain and dynamic environment. In other cases, this information is fragmentary or unknown. In this paper, we extend the concept of robustness and stability for Constraint Satisfaction Problems (CSPs) with ordered domains, where only limited assumptions need to be made as to possible changes. We present a search algorithm that searches for both robust and stable solutions for CSPs of this nature. It is well-known that meeting both criteria simultaneously is a desirable objective for constraint solving in uncertain and dynamic environments. We also present compelling evidence that our search algorithm outperforms other general-purpose algorithms for dynamic CSPs using random instances and benchmarks derived from real life problems.

Combining CSP and MPC for the Operational Control of Water Networks Application to the Richmond Case Study

This paper presents the combination of linear Model Predictive Control (MPC) with Constraint Satisfaction Problem (CSP) for the operational control of drinking water networks. The methodology has been divided into two functional layers: First, a CSP algorithm is used to transfer non-linear pressure equations of drinking water networks (DWNs) into linear constraints, which can enclose feasible solution of the hydraulic non-linear problem during the optimizing process. Then, a linear MPC with added linear constraints is solved to generate control strategies which consider control objectives. Finally, the proposed approach is simulated using Epanet to represent the real DWNs. PLIO, which is a generic operational tool for controlling water networks that uses non-linear MPC, is used for validation. The Richmond water system is used as a case study.

Selecting the Appropriate Consistency Algorithm for CSPs Using Machine Learning Classifiers

Computing the minimal network of a Constraint Satisfaction Problem (CSP) is a useful and difficult task. Two algorithms, PerTuple and AllSol, were proposed to this end. The performances of these algorithms vary with the problem instance. We use Machine Learning techniques to build a classifier that predicts which of the two algorithms is likely to be more effective.

Feature selection with test cost constraint

Feature selection is an important preprocessing step in machine learning and data mining. In real-world applications, costs, including money, time and other resources, are required to acquire the features. In some cases, there is a test cost constraint due to limited resources. We shall deliberately select an informative and cheap feature subset for classification. This paper proposes the feature selection with test cost constraint problem for this issue. The new problem has a simple form while described as a constraint satisfaction problem (CSP). Backtracking is a general algorithm for CSP, and it is efficient in solving the new problem on medium-sized data. As the backtracking algorithm is not scalable to large datasets, a heuristic algorithm is also developed. Experimental results show that the heuristic algorithm can find the optimal solution in most cases. We also redefine some existing feature selection problems in rough sets, especially in decision-theoretic rough sets, from the viewpoint of CSP. These new definitions provide insight to some new research directions.

A REVIEW OF TREE CONVEX SETS TEST

A collection of sets may have some interesting properties which help identify efficient algorithms for constraint satisfaction problems and combinatorial auction problems. One of the properties is tree convexity. A collection S of sets is tree convex if we can find a tree T whose nodes are the union of the sets of S and each set of S is the nodes of a subtree of T. This concept extends that of row convex sets each of which is an interval over a total ordering of the elements of the union of these sets. An interesting problem is to find efficient algorithms to test whether a collection of sets is tree convex. It is not known before if there exists a linear time algorithm for this test. In this paper, we review the materials that are the key to a linear algorithm: hypergraphs, a characterization of tree convex sets and the acyclic hypergraph test algorithm. Some typos in the original paper of the acyclicity test are corrected here. Some experiments show that the linear algorithm is significantly faster than a well‐known existing algorithm.

CSP Model and Algorithm on Task Allocation for Earth Observation DSS

任务分配是对地观测分布式卫星系统(Distributed Satellites System, DSS)自主协作运行过程中的一个重要环节. 针对任务分配中的约束满足问题(Constraint Satisfaction Problem, CSP), 以DSS完成任务总耗能最少为原则, 构建了任务分配问题的CSP模型, 并引入MAS理论中的合同网协议, 给出模型的求解算法, 通过仿真算例对模型和算法进行了验证.

A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems

A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems Constraint programming is a powerful software technology for solving numerous real-life problems. Many of these problems can be modeled as Constraint Satisfaction Problems (CSPs) and solved using constraint programming techniques. However, solving a CSP is NP-complete so filtering techniques to reduce the search space are still necessary. Arc-consistency algorithms are widely used to prune the search space. The concept of arc-consistency is bidirectional, i.e., it must be ensured in both directions of the constraint (direct and inverse constraints). Two of the most well-known and frequently used arc-consistency algorithms for filtering CSPs are AC3 and AC4. These algorithms repeatedly carry out revisions and require support checks for identifying and deleting all unsupported values from the domains. Nevertheless, many revisions are ineffective, i.e., they cannot delete any value and consume a lot of checks and time. In this paper, we present AC4-OP, an optimized version of AC4 that manages the binary and non-normalized constraints in only one direction, storing the inverse founded supports for their later evaluation. Thus, it reduces the propagation phase avoiding unnecessary or ineffective checking. The use of AC4-OP reduces the number of constraint checks by 50% while pruning the same search space as AC4. The evaluation section shows the improvement of AC4-OP over AC4, AC6 and AC7 in random and non-normalized instances.

An interval partitioning algorithm for constraint satisfaction problems

We propose an efficient interval partitioning algorithm to solve the continuous constraint satisfaction problem (CSP). The method comprises a new dynamic tree search management system that also invokes local search in selected subintervals. This approach is compared with two classical tree search techniques and three other interval methods. We study some challenging kinematics problems for testing the algorithm. The goal in solving kinematics problems is to identify all real solutions of the system of equations defining the problem. In other words, it is desired to find all object positions and orientations that satisfy a coupled non-linear system of equations. The kinematics benchmarks used here arise in industrial applications.

Correctness of Specialization-Based Parallel Processing Algorithm for Constraint Satisfaction Problem

The purpose of this paper is to discuss the correctness of a method for constructing parallel processing programs from a problem description. The framework we adopt for this purpose is Equivalent Transformation Framework (ETF), which regards computation as transformation of definite clauses. In the framework, a problem's domain knowledge and a query are described in definite clauses, and its meaning is defined by a model of the set of definite clauses. Then meaning-preserving transformation rules for the query are generated. We propose a parallel processing method based on “specialization”, a part of operation in the transformations, and discuss new parallel processing method based on the specialization that maintains correctness of the computation. The specialization is generalized notion of substitution in logic programming, and it allows more rich representation. We examine the correctness of our approach based the specialization.

Learning cluster-based structure to solve constraint satisfaction problems

The hybrid search algorithm for constraint satisfaction problems described here first uses local search to detect crucial substructures and then applies that knowledge to solve the problem. This paper shows the difficulties encountered by traditional and state-of-the-art learning heuristics when these substructures are overlooked. It introduces a new algorithm, Foretell, to detect dense and tight substructures called clusters with local search. It also develops two ways to use clusters during global search: one supports variable-ordering heuristics and the other makes inferences adapted to them. Together they improve performance on both benchmark and real-world problems.

Efficient algorithms for spatial configuration information retrieval

The problem of spatial configuration information retrieval is a constraint satisfaction problem (CSP), which can be solved using traditional CSP algorithms. But the spatial data can be reorganized using index techniques like R-tree and the spatial data are approximated by their minimum bounding rectangles (MBRs), so the spatial configuration information retrieval is actually based on the MBRs and some special techniques can be studied. This paper studies the mapping relationships among the spatial relations for real spatial objects, the corresponding spatial relations for their MBRs and the corresponding spatial relations between the intermediate nodes and the MBRs in R-tree. Three algorithms are designed and studied, and their performances are compared.

A multiagent evolutionary algorithm for constraint satisfaction problems

With the intrinsic properties of constraint satisfaction problems (CSPs) in mind, we divide CSPs into two types, namely, permutation CSPs and nonpermutation CSPs. According to their characteristics, several behaviors are designed for agents by making use of the ability of agents to sense and act on the environment. These behaviors are controlled by means of evolution, so that the multiagent evolutionary algorithm for constraint satisfaction problems (MAEA-CSPs) results. To overcome the disadvantages of the general encoding methods, the minimum conflict encoding is also proposed. Theoretical analyzes show that MAEA-CSPs has a linear space complexity and converges to the global optimum. The first part of the experiments uses 250 benchmark binary CSPs and 79 graph coloring problems from the DIMACS challenge to test the performance of MAEA-CSPs for nonpermutation CSPs. MAEA-CSPs is compared with six well-defined algorithms and the effect of the parameters is analyzed systematically. The second part of the experiments uses a classical CSP, n-queen problems, and a more practical case, job-shop scheduling problems (JSPs), to test the performance of MAEA-CSPs for permutation CSPs. The scalability of MAEA-CSPs along n for n-queen problems is studied with great care. The results show that MAEA-CSPs achieves good performance when n increases from 10(4) to 10(7), and has a linear time complexity. Even for 10(7)-queen problems, MAEA-CSPs finds the solutions by only 150 seconds. For JSPs, 59 benchmark problems are used, and good performance is also obtained.