The performance of a constraint model can often be improved by converting a subproblem into a single table constraint (referred to as tabulation). Finding subproblems to tabulate is traditionally a manual and time-intensive process, even for expert modellers. This paper presents TabID, an entirely automated method to identify promising subproblems for tabulation in constraint programming. We introduce a diverse set of heuristics designed to identify promising candidates for tabulation, aiming to improve solver performance. These heuristics are intended to encapsulate various factors that contribute to useful tabulation. We also present additional checks to limit the potential drawbacks of suboptimal tabulation. We comprehensively evaluate our approach using benchmark problems from existing literature that previously relied on manual identification by constraint programming experts of constraints to tabulate. We demonstrate that our automated identification and tabulation process achieves comparable, and in some cases improved results. We empirically evaluate the efficacy of our approach on a variety of solvers, including standard CP (Minion and Gecode), clause-learning CP (Chuffed and OR-Tools) and SAT solvers (Kissat). Our findings highlight the substantial potential of fully automated tabulation, suggesting its integration into automated model reformulation tools.

Combinatorial problems are ubiquitous in the world around us. Actually, they are found in all fields of human activity. As illustrations, it may be a question of scheduling the operations to be carried out within an industrial process (production line of a vehicle, an airplane or a satellite), of extracting the recurring patterns in a transaction database (data mining), of organizing the roster of a service (in a hospital, university or industrial environment), of generating molecular structures with good properties (in chemistry or bioinformatics), etc. Solving optimization problems remains a difficult task, especially when the size of the instances of the problems to be solved is large and/or when optimality is desired. In reality, the difficulty is twofold: being able to appropriately write models for encountered problems and being able to effectively solve the different instances of these problems. The main paradigms for optimization, namely mathematical programming, metaheuristics and Constraint Programming (CP), including the Boolean SAT framework, offer varied and interesting tools (languages, libraries, software), and are in a way, quite complementary; each paradigm having its own success stories.

Machine learning models are widely used for real-world applications, such as document analysis and vision. Constrained machine learning problems are problems where learned models have to both be accurate and respect constraints. For continuous convex constraints, many works have been proposed, but learning under combinatorial constraints is still a hard problem. The goal of this paper is to broaden the modeling capacity of constrained machine learning problems by incorporating existing work from combinatorial optimization. We propose first a general framework called BaGeL (Branch, Generate and Learn) which applies Branch and Bound to constrained learning problems where a learning problem is generated and trained at each node until only valid models are obtained. Because machine learning has specific requirements, we also propose an extended table constraint to split the space of hypotheses.

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.

This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of fails in the resolution process, to improve the inferences made during search by the constraint solver by strengthening constraint propagation, and to maintain the level of propagation while reducing the cost of propagating the constraints. Our experimental results show improvements in terms of the resolution speed compared to the original CSPs and a competitiveness to the recent tabulation approach. Besides, our approach can be realized in a preprocessing step, and therefore wouldn't collide with redundancy constraints or parallel computing if implemented.

We describe a constraint-based automated planner named Transition Constraints for Parallel Planning (TCPP). TCPP constructs its constraint model from a redefined version of the domain transition graphs (DTG) of a given planning problem. TCPP encodes state transitions in the redefined DTGs by using table constraints with cells containing don't cares or wild cards. TCPP uses Minion the constraint solver to solve the constraint model and returns a parallel plan. We empirically compare TCPP with the other state-of-the-art constraint-based parallel planner PaP2. PaP2 encodes action successions in the finite state automata (FSA) as table constraints with cells containing sets of values. PaP2 uses SICStus Prolog as its constraint solver. We also improve PaP2 by using dont cares and mutex constraints. Our experiments on a number of standard classical planning benchmark domains demonstrate TCPP's efficiency over the original PaP2 running on SICStus Prolog and our reconstructed and enhanced versions of PaP2 running on Minion.

Table constraints are very useful for modeling combinatorial constrained problems, and thus play an important role in Constraint Programming (CP). During the last decade, many algorithms have been proposed for enforcing the property known as Generalized Arc Consistency (GAC) on such constraints. A state-of-the art GAC algorithm called Compact-Table (CT), which has been recently proposed, significantly outperforms all previously proposed algorithms. In this paper, we extend this algorithm in order to deal with both short supports and negative tables, i.e., tables that contain universal values and conflicts. Our experimental results show the interest of using this fast general algorithm.

We present a planner named Transition Constraints for Parallel Planning (TCPP). TCPP constructs a new constraint model from domain transition graphs (DTG) of a given planning problem. TCPP encodes the constraint model by using table constraints that allow don't cares or wild cards as cell values. TCPP uses Minion the constraint solver to solve the constraint model and returns the parallel plan. Empirical results exhibit the efficiency of our planning system over state-of-the-art constraint-based planners.

One of the most widely studied classes of constraints in constraint programming (CP) is that of table constraints. Numerousspecialized filtering algorithms, enforcing the wellknown property called generalized arc consistency (GAC),have been developed for such constraints. Among the most successful GAC algorithms for table constraints, we find variants of simple tabular reduction (STR), like STR2. In this paper,we propose an extension of STR-based algorithms that achieves full pairwise consistency (FPWC), a consistency stronger than GAC and max restricted pairwise consistency (maxRPWC). Our approach involves counting the number of occurrences of specific combinations of values in constraint intersections. Importantly, the worst-case time complexity of one call to the basic filtering procedure at the heart of our new algorithm is quite close to that of STR algorithms. Experiments demonstrate that our method can outperform STR2 in many classes of problems, being significantly faster in some cases. Also, it is clearly superior to maxRPWC+, an algorithm that has been recently proposed.

In this paper, we propose an extension of our Mining for SAT framework to Constraint satisfaction Problem (CSP). We consider n-ary extensional constraints (table constraints). Our approach aims to reduce the size of the CSP by exploiting the structure of the constraints graph and of its associated microstructure. More precisely, we apply itemset mining techniques to search for closed frequent itemsets on these two representation. Using Tseitin extension, we rewrite the whole CSP to another compressed CSP equivalent with respect to satisfiability. Our approach contrast with previous proposed approach by Katsirelos and Walsh, as we do not change the structure of the constraints.