Knowledgesheet: A Graphical Spreadsheet Interface for Interactively Developing a Class of Constraint Programs

It has been shown that evolutionary algorithms are able to construct suitable search strategies for classes of Constraint Satisfaction Problems (CSPs) in Constraint Programming. This paper is an explanation of the use of multi-objective optimisation in contrast to simple additive weighting techniques with a view to develop search strategies to classes of CSPs. A hierarchical scheme is employed to select a candidate strategy from the Pareto frontier for final evaluation. The results demonstrate that multi-objective optimisation significantly outperforms the single objective scheme in the same number of objective evaluations. In situations where strategies developed for a class of problems fail to extend to unseen problem instances of the same class, it is found that the structure of the underlying CSPs do not resemble those employed in the training process.

In this paper we consider constraint satisfaction problems where the set of constraint relations is fixed. Feder and Vardi (1998) identified three families of constraint satisfaction problems containing all known polynomially solvable problems. We introduce a new class of problems called para-primal problems, incomparable with the families identified by Feder and Vardi (1998) and we prove that any constraint problem in this class is decidable in polynomial time. As an application of this result we prove a complete classification for the complexity of constraint satisfaction problems under the assumption that the basis contains all the permutation relations. In the proofs, we make an intensive use of algebraic results from clone theory about the structure of para-primal and homogeneous algebras.

Constraint Satisfaction with a Multi-Dimensional Domain

Practical implementation of random binning is one of the key challenges in achieving the largest available rate regions for many multiuser channels. This paper explores the use of low-density parity-check (LDPC) like codes for a particular kind of deterministic broadcast channel called the Blackwell channel and illustrates that random linear codes can be used to construct practical binning schemes at rates close to the capacity region of the Blackwell channel. The key ingredient is an encoding algorithm known as which is a generalization of the well-known belief propagation algorithm for LDPC codes. Survey propagation has been previously devised for a class of constraint satisfaction problems called K-SAT. This paper shows that the encoding problem for the Blackwell channel contains the same features as the constraint satisfaction problem and that the survey propagation algorithm, when concatenated with an outer error correcting code, works well at rates close to the Blackwell channel capacity region

The expressiveness of First Order Logic (FOL) languages is severely counterbalanced by the complexity of matching formulas on a universe. Matching is an instance of the class of Constraint Satisfaction Problems (CSP), which have shown to undergo a phase transition with respect to two order parameters: constraint density and constraint tightness. This paper analyzes the problem of satisfying FOL Horn clauses in the light of these recent results. By means of an extensive experimental analysis, we show how Horn clause verification exhibits a typical phase transition with respect to the number of binary (or greater arity) predicates, and with respect to the ratio between the number of constants in the universe and the cardinality of the basic predicates extension.

: The primary objective of this project has been the development of systems that reason in dynamic and open-ended environment and that use networks as their primary representation language. The focus of our research has been temporal reasoning, neural networks, truth maintenance, and default reasoning. This investigation has led to several basic results: the expressiveness of constraint networks was analyzed, tractable classes of constraint satisfaction problems were identified and effective processing techniques were developed.

Constraint programming offers a declarative approach to solving problems modeled as constraint satisfaction problems (CSPs). However, the precise specification of a set of constraints is sometimes not available, but may have to be learned, for instance, from a set of examples of its solutions and non-solutions. In general, one may wish to learn generalized CSPs involving classical, fuzzy, weighted or probabilistic constraints, for example. This paper introduces a unifying framework for CSP learning. The framework is generic in that it can be instantiated to obtain specific formulations for learning classical, fuzzy, weighted or probabilistic CSPs. In particular, a new formulation for classical CSP learning, which minimizes the number of examples violated by candidate CSPs, is obtained by instantiating the framework. This formulation is equivalent to a simple pseudo-boolean optimization problem, thus being efficiently solvable using many optimization tools.

A note on some collapse results of valued constraints

In the frame of classical constraint satisfaction problems (CSPs), the backtrack tree search, combined with learning methods, presents a double advantage: for static solving, it improves the search speed by avoiding redundant explorations; for dynamic solving (after a slight change of the problem) it reuses the previous searches to build a new solution quickly. Backtrack reasoning concludes the rejection of certain combinatorial choices. Nogood Recording memorizes these choices in order to not reproduce. We aim to use Nogood Recording in the wider scope of the CSP framework (VCSP) to enhance the branch and bound algorithm. Therefore, nogoods are used to increase the lower bound used by the branch and bound to prune the search. This issue leads to the definition of the Valued Nogoods and their use. This study focuses particularly on penalty and dynamic VCSPs which require special developments. However our results give an extension of the Nogood Recording to the general VCSP framework.

The N-Queen problem is a classical combinatorial optimization and constraint satisfaction problem that involves placing N queens on an N × N chessboard such that no two queens threaten each other. Due to its exponential search space and increasing computational complexity with larger board sizes, the problem serves as an important benchmark for evaluating the efficiency of heuristic and metaheuristic optimization techniques. This study presents a comprehensive performance analysis of the Simulated Annealing (SA) optimization approach for solving the N-Queen problem across varying board dimensions. The proposed methodology models the N-Queen problem as an optimization task by defining an objective function that minimizes the number of conflicting queen pairs. Simulated Annealing is employed to iteratively explore the solution space, allowing probabilistic acceptance of suboptimal solutions to escape local minima. Key parameters, including initial temperature, cooling schedule, and termination criteria, are systematically tuned to evaluate their impact on convergence speed and solution quality. Experimental results demonstrate that the SA-based approach effectively finds valid solutions for large values of N with high success rates and reduced computational effort compared to exhaustive and deterministic methods. Performance metrics such as solution accuracy, convergence time, number of iterations, and conflict reduction rate are analyzed and discussed. The results indicate that Simulated Annealing offers a robust and scalable solution for the N-Queen problem, particularly for higher-dimensional instances where traditional methods become impractical. Overall, this study highlights the suitability of Simulated Annealing as an efficient metaheuristic for solving complex combinatorial optimization problems and provides insights into its performance characteristics when applied to the N-Queen problem.

The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered in this paper have the characteristic that only a subset of the binary variables have non-zero objective function coefficients if modeled as an MILP. This class of problems is formulated as a hybrid MILP/CP model that involves some of the MILP constraints, a reduced set of the CP constraints, and equivalence relations between the MILP and the CP variables. An MILP/CP based decomposition method and an LP/CP-based branch-and-bound algorithm are proposed to solve these hybrid models. Both these algorithms rely on the same relaxed MILP and feasibility CP problems. An application example is considered in which the least-cost schedule has to be derived for processing a set of orders with release and due dates using a set of dissimilar parallel machines. It is shown that this problem can be modeled as an MILP, a CP, a combined MILP-CP OPL model (Van Hentenryck 1999), and a hybrid MILP/CP model. The computational performance of these models for several sets shows that the hybrid MILP/CP model can achieve two to three orders of magnitude reduction in CPU time.

During the last few decades, significant progress has been made in solving large-scale finite-dimensional and semi-infinite linear programming problems. In contrast, little progress has been made in solving linear programs in infinite-dimensional spaces despite their importance as models in manufacturing and communication systems. Inspired by the research on separated continuous linear programs, we propose a new class of continuous linear programming problems that has a variety of important applications in communications, manufacturing, and urban traffic control. This class of continuous linear programs contains the separated continuous linear programs as a subclass. Using ideas from quadratic programming, we propose an efficient algorithm for solving large-scale problems in this new class under mild assumptions on the form of the problem data. We prove algorithmically the absence of a duality gap for this class of problems without any boundedness assumptions on the solution set. We show this class of problems admits piecewise constant optimal control when the optimal solution exists. We give conditions for the existence of an optimal solution. We also report computational results which illustrate that the new algorithm is effective in solving large-scale realistic problems (with several hundred continuous variables) arising in manufacturing systems.

In object-oriented representation, inheritance determines the attributes of a given object, given its type. Conversely, recognition determines the type of an object, given its attributes. The author addresses the more general problem of recognition from constraints; arguing that it can be seen as a special case of the classical abduction process and that it can be implemented as an abduction operation on constraints. Abductive reasoning is common in most fields of artificial intelligence. Constraint logic programming (CLP) generalizes logic programming by replacing unification with constraint solving. He first explores the relationship between abduction and CLP and shows that CLP is a special case of abduction. A class of problems is then identified for which the usual unrestricted forms of abduction are unsuitable. Within the CLP framework a restricted form of abduction is formulated which is applicable to the whole class of problems, in which object-oriented recognition can be considered as a special case. >

The author (1992, 1993) earlier studied the equivalence of a class of 0–1 quadratic programs and their relaxed problems. Thus, a class of combinatorial optimization problems can be solved by solving a class of nonconvex quadratic programs. In this paper, a necessary and sufficient condition for local minima of this class of nonconvex quadratic programs is given; this will be the foundation for study of algorithms.

The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over the last 20 years. A new version of the CSP, the promise CSP (PCSP) has recently been proposed, motivated by open questions about the approximability of variants of satisfiability and graph colouring. The PCSP significantly extends the standard decision CSP. The complexity of CSPs with a fixed constraint language on a finite domain has recently been fully classified, greatly guided by the algebraic approach, which uses polymorphisms — high-dimensional symmetries of solution spaces — to analyse the complexity of problems. The corresponding classification for PCSPs is wide open and includes some long-standing open questions, such as the complexity of approximate graph colouring, as special cases. The basic algebraic approach to PCSP was initiated by Brakensiek and Guruswami, and in this paper we significantly extend it and lift it from concrete properties of polymorphisms to their abstract properties. We introduce a new class of problems that can be viewed as algebraic versions of the (Gap) Label Cover problem, and show that every PCSP with a fixed constraint language is equivalent to a problem of this form. This allows us to identify a ”measure of symmetry” that is well suited for comparing and relating the complexity of different PCSPs via the algebraic approach. We demonstrate how our theory can be applied by improving the state-of-the-art in approximate graph colouring: we show that, for any k≥ 3, it is NP-hard to find a (2k−1)-colouring of a given k-colourable graph.