Manual modeling in Constraint Programming is a substantial bottleneck, which Constraint Acquisition (CA) aims to automate. However, passive CA methods are prone to over-fitting, often learning models that include spurious global constraints when trained on limited data, while purely active methods can be query-intensive. We introduce a hybrid CA framework specifically designed to address the challenge of over-fitting in CA. Our approach integrates passive learning for initial candidate generation, a query-driven interactive refinement phase that utilizes probabilistic confidence scores (initialized by machine learning priors) to systematically identify over-fitted constraints, and a specialized subset exploration mechanism to recover valid substructures from rejected candidates. A final active learning phase ensures model completeness. Extensive experiments on diverse benchmarks demonstrate that our interactive refinement phase is crucial for achieving high target model coverage and overall model accuracy from limited examples, doing so with manageable query complexity. This framework represents a substantial advancement towards robust and practical constraint acquisition in data-limited scenarios.

Combinatorial problems stated as Constraint Satisfaction Problems (CSP) are examined. It is shown by example that any algorithm designed for the original CSP, and involving the AllDifferent constraint, has at least the same level of efficacy when simultaneously applied to both the original and its complementary problem. The 1-to-1 mapping employed to transform a CSP to its complementary problem, which is also a CSP, is introduced. This "Dual CSP" method and its application are outlined. The analysis of several random problem instances demonstrate the benefits of this method for variable domain reduction compared to the standard approach to CSP. Extensions to additional constraints other than AllDifferent, as well as the use of hybrid algorithms, are proposed as candidates for this Dual CSP method.

Icosoku is a challenging and interesting puzzle that exhibits highly symmetrical and combinatorial nature. In this paper, we pose the questions derived from the puzzle, but with more difficulty and generality. In addition, we also present a constraint programming model for the proposed questions, which can provide the answers to our first two questions. The purpose of this paper is to share our preliminary result and problems to encourage researchers in both group theory and constraint communities to consider this topic further.

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 evaluate the approach on five different problems that involve combinations of the linear and the alldifferent constraints. We also compare our algorithm to other relevant approaches. The experimental results show a great potential of the proposed improvement.

Designing a search heuristic for constraint programming that is reliable across problem domains has been an important research topic in recent years. This paper concentrates on one family of candidates: counting-based search. Such heuristics seek to make branching decisions that preserve most of the solutions by determining what proportion of solutions to each individual constraint agree with that decision. Whereas most generic search heuristics in constraint programming rely on local information at the level of the individual variable, our search heuristics are based on more global information at the constraint level. We design several algorithms that are used to count the number of solutions to specific families of constraints and propose some search heuristics exploiting such information. The experimental part of the paper considers eight problem domains ranging from well-established benchmark puzzles to rostering and sport scheduling. An initial empirical analysis identifies heuristic maxSD as a robust candidate among our proposals. We then evaluate the latter against the state of the art, including the latest generic search heuristics, restarts, and discrepancy-based tree traversals. Experimental results show that counting-based search generally outperforms other generic heuristics.

Constraint solvers are complex pieces of software which require many design decisions to be made by the implementer based on limited information. These decisions affect the performance of the finished solver significantly [16]. Once a design decision has been made, it cannot easily be reversed, although a different decision may be more appropriate for a particular problem. We investigate using machine learning to make these decisions automatically depending on the problem to solve. We use the alldifferent constraint as a case study. Our system is capable of making nontrivial, multilevel decisions that improve over always making a default choice and can be implemented as part of a general-purpose constraint solver.

Programs to solve so-called constraint problems are complex pieces of software which require many design decisions to be made more or less arbitrarily by the implementer. These decisions affect the performance of the finished solver significantly [13]. Once a design decision has been made, it cannot easily be reversed, although a different decision may be more appropriate for a particular problem. We investigate using machine learning to make these decisions automatically depending on the problem to solve with the alldifferent constraint as an example. Our system is capable of making nontrivial, multilevel decisions that improve over always making a default choice.

Constraint Programming (CP)[21] is a powerful technique for spec ifying Constraint Satisfaction Problems (CSPs) based on allowing a constraintprogrammer to model problems in terms of high-level constraints. Using such global constraints allows easier specification of problems but also allows for faster solve rs that take advantage of the structure in the problem. The classica l approach to CSP solving is to explore the search tree of all possible assignment s to the variables in a depth-first search backtracking manner, guided by v arious heuristics, until a solution is found or proven not to exist. One of the most basic techniques for reducing the number of search tree nodes explore d is to perform domain propagation at each node. In order to get as much domain propagation as possible we wish for each constraint to remove from the variable d omains all values that cannot participate in a solution to that constraint.

MINLP problems are hard constrained optimization problems, with nonlinear constraints and mixed discrete continuous variables. They can be solved using a Branch-and-Bound scheme combining several methods, such as linear programming, interval analysis, and cutting methods. Our goal is to integrate constraint programming techniques in this framework. Firstly, global constraints can be introduced to reformulate MINLP problems thus leading to clean models and more precise computations. Secondly, interval-based approximation techniques for nonlinear constraints can be improved by taking into account the integrality of variables early. These methods have been implemented in an interval solver and we present experimental results from a set of MINLP instances.

Powerful consistency techniques, such as AC* and FDAC*, have been developed for Weighted Constraint Satisfaction Problems (WCSPs) to reduce the space in solution search, but are restricted to only unary and binary constraints.  On the other hand, van Hoeve et al developed efficient graph-based algorithms for handling soft constraints as classical constraint optimization problems. We prove that naively incorporating van Hoeve's method into the WCSP framework can enforce a strong form of varnothing-Inverse Consistency, which can prune infeasible values and deduce good lower bound estimates.  We further show how Van Hoeve's method can be modified so as to handle cost projection and extension to maintain the stronger AC* and FDAC* generalized for non-binary constraints.  Using the soft allDifferent constraint as a testbed, preliminary results demonstrate that our proposal gives improvements up to an order of magnitude both in terms of time and pruning.