Solving Constraint Satisfaction Problems Research Articles

Hazard Rate Scaling of the Abandonment Distribution for the GI/M/n + GI Queue in Heavy Traffic

We obtain a heavy traffic limit for the GI/M/n + GI queue, which includes the entire patience time distribution. Our main approach is to scale the hazard rate function of the patience time distribution in such a way that our resulting diffusion approximation contains the entire hazard rate function. We then show through numerical studies that for various performance measures, our approximations tend to outperform those commonly used in practice. The robustness of our results is also demonstrated by applying them to solving constraint satisfaction problems arising in the context of telephone call centers.

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The analysis of evolutionary techniques for constraint satisfaction problem solving is executed.Their advantages and disadvantages have been defined

Solving constraint satisfaction problems with SAT modulo theories

Due to significant advances in SAT technology in the last years, its use for solving constraint satisfaction problems has been gaining wide acceptance. Solvers for satisfiability modulo theories (SMT) generalize SAT solving by adding the ability to handle arithmetic and other theories. Although there are results pointing out the adequacy of SMT solvers for solving CSPs, there are no available tools to extensively explore such adequacy. For this reason, in this paper we introduce a tool for translating FLATZINC (MINIZINC intermediate code) instances of CSPs to the standard SMT-LIB language. We provide extensive performance comparisons between state-of-the-art SMT solvers and most of the available FLATZINC solvers on standard FLATZINC problems. The obtained results suggest that state-of-the-art SMT solvers can be effectively used to solve CSPs.

Self-control of the time complexity of a constraint satisfaction problem solver program

This paper presents the self-controlling software paradigm and reports on its use to control the branch and bound based constraint satisfaction problem solving algorithm. In this paradigm, an algorithm is first conceptualized as a dynamical system and then a feedback control loop is added to control its behavior. The loop includes a Quality of Service component that assesses the performance of the algorithm during its run time and a controller that adjusts the parameters of the algorithm in order to achieve the control goal. Although other approaches – generally termed as “self-*” – make use of control loops, this use is limited to the structure of the software system, rather than to its behavior and its dynamics. This paper advocates the analysis of dynamics of any program with control loops. The self-controlling software paradigm is evaluated on two different NP-hard constraint satisfaction and optimization problems. The results of the evaluation show an improvement in the performance due to the added control loop for both of the tested constraint satisfaction problems.

Local Consistency and SAT-Solvers

Local consistency techniques such as k-consistency are a key component of specialised solvers for constraint satisfaction problems. In this paper we show that the power of using k-consistency techniques on a constraint satisfaction problem is precisely captured by using a particular inference rule, which we call negative-hyper-resolution, on the standard direct encoding of the problem into Boolean clauses. We also show that current clause-learning SAT-solvers will discover in expected polynomial time any inconsistency that can be deduced from a given set of clauses using negative-hyper-resolvents of a fixed size. We combine these two results to show that, without being explicitly designed to do so, current clause-learning SAT-solvers efficiently simulate k-consistency techniques, for all fixed values of k. We then give some experimental results to show that this feature allows clause-learning SAT-solvers to efficiently solve certain families of constraint problems which are challenging for conventional constraint-programming solvers.

Generating Balanced Incomplete Block Designs by SAT Encoding

Propositional Satisfiability (SAT) is fundamental in solving many application problems in Artificial Intelligence and Computer Science. Remarkable improvements in the efficiency of SAT solvers have beenmade over the last decade. Such improvements encourage researchers to solve constraint satisfaction problems by encoding them into SAT (i.e. ``SAT encoding''). Balanced Incomplete Block Design (BIBD) is one of the most typical block designs. BIBDs have been applied in several fields such as design experiments, coding theory, and cryptography. In this paper, we consider the problem of generating BIBDs by SAT encoding. We present a new SAT encoding that is an enhancement of order encoding with the idea of binary tree. It is designed to reduce the number of clauses required for cardinality constraints, compared with order encoding. In our experiments, our encoding was able to give a greater number of solutions than order encoding and state-of-the-art constraint solvers Mistral and choco.

LSVF: a New Search Heuristic to Reduce the Backtracking Calls for Solving Constraint Satisfaction Problem

Many researchers in Artificial Intelligence seek for new algorithms to reduce the amount of memory/ time consumed for general searches in Constraint Satisfaction Problems. These improvements are accomplished by the use of heuristics which either prune useless tree search branches or even indicate the path to reach the (optimal) solution faster than the blind version of the search. Many heuristics were proposed in the literature, like the Least Constraining Value (LCV). In this paper we propose a new pre-processing search heuristic to reduce the amount of backtracking calls, namely the Least Suggested Value First: a solution whenever the LCV solely cannot measure how much a value is constrained. In this paper, we present a pedagogical example, as well as the preliminary results.

FirstCS—New Aspects on Combining Constraint Programming with Object-Orientation in Java

The aim of the presented constraint programming library firstCS is the integration of the constraint programming paradigm in the object-oriented programming language Java. This open-box library provides its users with the necessary concepts to model and solve constraint satisfaction problems and even constraint optimization problems over finite integer domains. The application focus of firstCS is constraint-based scheduling and resource allocations (e.g. Sandow in INFORMATIK 2011, LNI, vol. P-192, p. 248, 2011), however, it offers all primitives to realize new constraints and according propagation algorithms as well as problem-specific tree search heuristics to find good or even best solutions. Beyond related work and an overview over the general architecture of the system and the supported constraints, this presentation focuses on new aspects of the current version of firstCS, i.e. redundancy checking and the assembling of new search strategies from existing ones using the implementation language Java. The presentation is completed by code fragments showing interesting implementation details.

An Approach of Solving Constraint Satisfaction Problem Based on Cycle-Cut

Firstly a backtrack-free algorithm Tree_Search is given to solve the cycle-free CSPs. Secondly,by embedding the cycle-cut idea in the MAC3rm algorithm which is the most popular solver for binary CSPs in recent years,the new algorithm,called CCS,is presented.CCS separates the backtracking procedure into two steps,the former step searches the partial solution for the variables in the cycle-cut set and simplifies the problem into a cycle-free problem that is arc consistency,and the latter step solves the rest variables by Tree_Search algorithm.As a result, CCS has improved MAC3rm.It is proved that the partial solution which is found by MAC3rm can be extended to a global solution and MAC3rm can not find a partial solution on the cycle_cut set if the global solution does not exist.The experiments show that CCS is more efficient than MAC3rm.While solving the random CSPs which are at the phase transition,CCS can reach a maximum of 140 times more efficient than MAC3rm,and while solving some of the benchmarks, CCS can reach up to 100 times more efficient than MAC3rm.

Applying constraint satisfaction approach to solve product configuration problems with cardinality-based configuration rules

In this paper, the product configuration problems that are characterized by cardinality-based configuration rules are dealt with. Novel configuration rules including FI and EI rules are presented to clarify the semantics of inclusion rules when cardinalities and hierarchies of products are encountered. Then, a configuration graph is proposed to visualize structural rules and configuration rules in product configuration problem. An encoding approach is elaborated to transform the configuration graph as a CSP (Constraint Satisfaction Problem). As a consequence, existing CSP solver, i.e. JCL (Java Constraint Library), is employed to implement the configuration system for product configuration problem with cardinality-related configuration rules. A case study of a bus configuration is used throughout this paper to illustrate the effectiveness of the presented approach.

Case-based reasoning integrations

This article presents an overview and survey of current work in case-based reasoning (CBR) integrations. There has been a recent upsurge in the integration of CBR with other reasoning modalities and computing paradigms, especially rule-based reasoning (RBR) and constraint-satisfaction problem (CSP) solving. CBR integrations with model-based reasoning (MBR), genetic algorithms, and information retrieval are also discussed. This article characterizes the types of multimodal reasoning integrations where CBR can play a role, identifies the types of roles that CBR components can fulfill, and provides examples of integrated CBR systems. Past progress, current trends, and issues for future research are discussed.

Deriving Information from Sampling and Diving

We investigate the impact of information extracted from sampling and diving on the solution of Constraint Satisfaction Problems (CSP). A sample is a complete assignment of variables to values taken from their domain according to a given distribution. Diving consists in repeatedly performing depth first search attempts with random variable and value selection, constraint propagation enabled and backtracking disabled; each attempt is called a dive and, unless a feasible solution is found, it is a partial assignment of variables (whereas a sample is a -possibly infeasible- complete assignment). While the probability of finding a feasible solution via sampling or diving is negligible if the problem is difficult enough, samples and dives are very fast to generate and, intuitively, even when they are infeasible, they can provide some statistical information on search space structure. The aim of this paper is to understand to what extent it is possible to support the CSP solving process with information derived from sampling and diving. In particular, we are interested in extracting from samples and dives precise indications on the quality of individual variable-value assignments with respect to feasibility. We formally prove that even uniform sampling could provide precise evaluation of the quality of single variable-value assignments; as expected, this requires huge sample sizes and is therefore not useful in practice. On the contrary, diving is much better suited for assignment evaluation purposes. We undertake a thorough experimental analysis on a collection of Partial Latin Square and Car Sequencing instances to assess the quality of information provided by dives. Dive features are identified and their impact on search is evaluated. Results show that diving provides information that can be fruitfully exploited.

Solving kinematics problems by efficient interval partitioning

In this study, a generic solution methodology is presented for solving constraint satisfaction problems with smooth continuous constraint functions. We apply the proposed method in solving small scale kinematics problems with the goal of identifying all real solutions to a given problem. The developed approach assumes a collaborative methodology that integrates interval partitioning, a new interval inference method, and local search. The resulting methodology aims at reducing the search space and discarding infeasible sub-spaces effectively and reliably during the early stages of the search so that exact solutions can be identified faster by local methods.

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.

Interleaving solving and elicitation of constraint satisfaction problems based on expected cost

We consider Constraint Satisfaction Problems in which constraints can be initially incomplete, where it is unknown whether certain tuples satisfy the constraint or not. We assume that we can determine the satisfaction of such an unknown tuple, i.e., find out whether this tuple is in the constraint or not, but doing so incurs a known cost, which may vary between tuples. We also assume that we know the probability of an unknown tuple satisfying a constraint. We define algorithms for this problem, based on backtracking search. Specifically, we consider a simple iterative algorithm based on a cost limit on the unknowns that may be determined, and a more complex algorithm that delays determining an unknown in order to estimate better whether doing so is worthwhile. We show experimentally that the more sophisticated algorithms can greatly reduce the average cost.

A workflow framework for intelligent service composition

In practice, service composition and its evaluation are initiated by participant web services’ functional and non-functional attributes. It often consists of functional property-based service location, non-functional property-based quality evaluation, and then a finial executive plan. This scheduling process is often unfolded in a workflow framework. Generally, selecting qualified services and composing them manually are time-consuming and error-prone. In view of this challenge, a workflow framework is presented in this paper for intelligently navigating service composition. This workflow framework consists of two primary processing modules, i.e., Planning Module and CSP (Constraint Satisfaction Problems) Solving Module. Taking advantage of services’ functional attributes, Planning Module aims at producing referred composite plans that play as general patterns. CSP Solving Module focuses on selecting qualified services to implement the composite plans, based on their non-functional attributes’ evaluation. Finally, a case study is presented to demonstrate the validity of framework.

A graph-based immune-inspired constraint satisfaction search

We propose an artificial immune algorithm to solve constraint satisfaction problems (CSPs). Recently, bio-inspired algorithms have been proposed to solve CSPs. They have shown to be efficient in solving hard problem instances. Given that recent publications indicate that immune-inspired algorithms offer advantages to solve complex problems, our main goal is to propose an efficient immune algorithm which can solve CSPs. We have calibrated our algorithm using relevance estimation and value calibration (REVAC), which is a new technique recently introduced to find the parameter values for evolutionary algorithms. The tests were carried out using randomly generated binary constraint satisfaction problems and instances of the three-colouring problem with different constraint networks. The results suggest that the technique may be successfully applied to solve CSPs.

A SAT-based Method for Solving the Two-dimensional Strip Packing Problem

We propose a satisfiability testing (SAT) based exact approach for solving the two-dimensional strip packing problem (2SPP). In this problem, we are given a set of rectangles and one large rectangle called a strip. The goal of the problem is to pack all rectangles without overlapping, into the strip by minimizing the overall height of the packing. Although the 2SPP has been studied in Operations Research, some instances are still hard to solve. Our method solves the 2SPP by translating it into a SAT problem through a SAT encoding called order encoding. The translated SAT problems tend to be large; thus, we apply several techniques to reduce the search space by symmetry breaking and positional relations of rectangles. To solve a 2SPP, that is, to compute the minimum height of a 2SPP, we need to repeatedly solve similar SAT problems. We thus reuse learned clauses and assumptions from the previously solved SAT problems. To evaluate our approach, we obtained results for 38 instances from the literature and made comparisons with a constraint satisfaction solver and an ad-hoc 2SPP solver.

An Adaptive Ontology Mapping Approach with Neural Network Based Constraint Satisfaction

Ontology mapping seeks to find semantic correspondences between similar elements of different ontologies. It is a key challenge to achieve semantic interoperability in building the Semantic Web. This paper proposes a new generic and adaptive ontology mapping approach, called the PRIOR , based on propagation theory, information retrieval techniques and artificial intelligence. The approach consists of three major modules, i.e., the IRbased similarity generator, the adaptive similarity filter and weighted similarity aggregator, and the neural network based constraint satisfaction solver. The approach first measures both linguistic and structural similarity of ontologies in a vector space model, and then aggregates them using an adaptive method based on their harmonies, which is defined as an estimator of performance of similarity. Finally to improve mapping accuracy the interactive activation and competition neural network is activated, if necessary, to search for a solution that can satisfy ontology constraints. The experimental results show that harmony is a good estimator of fmeasure; the harmony based adaptive aggregation outperforms other aggregation methods; neural network approach significantly boosts the performance in most cases. Our approach is competitive with topranked systems on benchmark tests at OAEI campaign 2007, and performs the best on real cases in OAEI benchmark tests.

An adaptive ontology mapping approach with neural network based constraint satisfaction

Ontology mapping seeks to find semantic correspondences between similar elements of different ontologies. It is a key challenge to achieve semantic interoperability in building the Semantic Web. This paper proposes a new generic and adaptive ontology mapping approach, called the PRIOR+, based on propagation theory, information retrieval techniques and artificial intelligence. The approach consists of three major modules, i.e., the IR-based similarity generator, the adaptive similarity filter and weighted similarity aggregator, and the neural network based constraint satisfaction solver. The approach first measures both linguistic and structural similarity of ontologies in a vector space model, and then aggregates them using an adaptive method based on their harmonies, which is defined as an estimator of performance of similarity. Finally to improve mapping accuracy the interactive activation and competition neural network is activated, if necessary, to search for a solution that can satisfy ontology constraints. The experimental results show that harmony is a good estimator of f-measure; the harmony based adaptive aggregation outperforms other aggregation methods; neural network approach significantly boosts the performance in most cases. Our approach is competitive with top-ranked systems on benchmark tests at OAEI campaign 2007, and performs the best on real cases in OAEI benchmark tests.