Jean-Charles Régin

Alexandre Bonlarron, Aurélie Calabrèse, Pierre Kornprobst et al.

This paper introduces a new approach to generating strongly constrained texts. We consider standardized sentence generation for the typical application of vision screening. To solve this problem, we formalize it as a discrete combinatorial optimization problem and utilize multivalued decision diagrams (MDD), a well-known data structure to deal with constraints. In our context, one key strength of MDD is to compute an exhaustive set of solutions without performing any search. Once the sentences are obtained, we apply a language model (GPT-2) to keep the best ones. We detail this for English and also for French where the agreement and conjugation rules are known to be more complex. Finally, with the help of GPT-2, we get hundreds of bona-fide candidate sentences. When compared with the few dozen sentences usually available in the well-known vision screening test (MNREAD), this brings a major breakthrough in the field of standardized sentence generation. Also, as it can be easily adapted for other languages, it has the potential to make the MNREAD test even more valuable and usable. More generally, this paper highlights MDD as a convincing alternative for constrained text generation, especially when the constraints are hard to satisfy, but also for many other prospects.

Giovanni Gatti Pinheiro, Michael Defoin-Platel, Jean-Charles Regin

Correctly estimating how demand respond to prices is fundamental for airlines willing to optimize their pricing policy. Under some conditions, these policies, while aiming at maximizing short term revenue, can present too little price variation which may decrease the overall quality of future demand forecasting. This problem, known as earning while learning problem, is not exclusive to airlines, and it has been investigated by academia and industry in recent years. One of the most promising methods presented in literature combines the revenue maximization and the demand model quality into one single objective function. This method has shown great success in simulation studies and real life benchmarks. Nevertheless, this work needs to be adapted to certain constraints that arise in the airline revenue management (RM), such as the need to control the prices of several active flights of a leg simultaneously. In this paper, we adjust this method to airline RM while assuming unconstrained capacity. Then, we show that our new algorithm efficiently performs price experimentation in order to generate more revenue over long horizons than classical methods that seek to maximize revenue only.

Margaux Schmied, Jean-Charles Regin

The success of Constraint Programming relies partly on the global constraints and implementation of the associated filtering algorithms. Recently, new ideas emerged to improve these implementations in practice, especially regarding the all different constraint. In this paper, we consider the cardinality constraint with costs. The cardinality constraint is a generalization of the all different constraint that specifies the number of times each value must be taken by a given set of variables in a solution. The version with costs introduces an assignment cost and bounds the total sum of assignment costs. The arc consistency filtering algorithm of this constraint is difficult to use in practice, as it systematically searches for many shortest paths. We propose a new approach that works with upper bounds on shortest paths based on landmarks. This approach can be seen as a preprocessing. It is fast and avoids, in practice, a large number of explicit computations of shortest paths.

Alexandre Bonlarron, Florian Régin, Elisabetta De Maria et al.

Large Language Models (LLMs) excel at generating fluent text but struggle to enforce external constraints because they generate tokens sequentially without explicit control mechanisms. GenCP addresses this limitation by combining LLM predictions with Constraint Programming (CP) reasoning, formulating text generation as a Constraint Satisfaction Problem (CSP). In this paper, we improve GenCP by integrating Masked Language Models (MLMs) for domain generation, which allows bidirectional constraint propagation that leverages both past and future tokens. This integration bridges the gap between token-level prediction and structured constraint enforcement, leading to more reliable and constraint-aware text generation. Our evaluation on COLLIE benchmarks demonstrates that incorporating domain preview via MLM calls significantly improves GenCP's performance. Although this approach incurs additional MLM calls and, in some cases, increased backtracking, the overall effect is a more efficient use of LLM inferences and an enhanced ability to generate feasible and meaningful solutions, particularly in tasks with strict content constraints.

Alexandre Bonlarron, Jean-Charles Régin

This paper presents NgramMarkov, a variant of the Markov constraints. It is dedicated to text generation in constraint programming (CP). It involves a set of n-grams (i.e., sequence of n words) associated with probabilities given by a large language model (LLM). It limits the product of the probabilities of the n-gram of a sentence. The propagator of this constraint can be seen as an extension of the ElementaryMarkov constraint propagator, incorporating the LLM distribution instead of the maximum likelihood estimation of n-grams. It uses a gliding threshold, i.e., it rejects n-grams whose local probabilities are too low, to guarantee balanced solutions. It can also be combined with a "look-ahead" approach to remove n-grams that are very unlikely to lead to acceptable sentences for a fixed-length horizon. This idea is based on the MDDMarkovProcess constraint propagator, but without explicitly using an MDD (Multi-Valued Decision Diagram). The experimental results show that the generated text is valued in a similar way to the LLM perplexity function. Using this new constraint dramatically reduces the number of candidate sentences produced, improves computation times, and allows larger corpora or smaller n-grams to be used. A real-world problem has been solved for the first time using 4-grams instead of 5-grams.

Jordan Demeulenaere, Renaud Hartert, Christophe Lecoutre et al.

In this paper, we describe Compact-Table (CT), a bitwise algorithm to enforce Generalized Arc Consistency (GAC) on table con- straints. Although this algorithm is the default propagator for table constraints in or-tools and OscaR, two publicly available CP solvers, it has never been described so far. Importantly, CT has been recently improved further with the introduction of residues, resetting operations and a data-structure called reversible sparse bit-set, used to maintain tables of supports (following the idea of tabular reduction): tuples are invalidated incrementally on value removals by means of bit-set operations. The experimentation that we have conducted with OscaR shows that CT outperforms state-of-the-art algorithms STR2, STR3, GAC4R, MDD4R and AC5-TC on standard benchmarks.

Anthony Palmieri, Jean-Charles Régin, Pierre Schaus

We consider the problem of selecting the best variable-value strategy for solving a given problem in constraint programming. We show that the recent Embarrassingly Parallel Search method (EPS) can be used for this purpose. EPS proposes to solve a problem by decomposing it in a lot of subproblems and to give them on-demand to workers which run in parallel. Our method uses a part of these subproblems as a simple sample as defined in statistics for comparing some strategies in order to select the most promising one that will be used for solving the remaining subproblems. For each subproblem of the sample, the parallelism helps us to control the running time of the strategies because it gives us the possibility to introduce timeouts by stopping a strategy when it requires more than twice the time of the best one. Thus, we can deal with the great disparity in solving times for the strategies. The selections we made are based on the Wilcoxon signed rank tests because no assumption has to be made on the distribution of the solving times and because these tests can deal with the censored data that we obtain after introducing timeouts. The experiments we performed on a set of classical benchmarks for satisfaction and optimization problems show that our method obtain good performance by selecting almost all the time the best variable-value strategy and by almost never choosing a variable-value strategy which is dramatically slower than the best one. Our method also outperforms the portfolio approach consisting in running some strategies in parallel and is competitive with the multi armed bandit framework.

Guillaume Perez, Jean-Charles Régin

We study the relations between Multi-valued Decision Diagrams (MDD) and tuples (i.e. elements of the Cartesian Product of variables). First, we improve the existing methods for transforming a set of tuples, Global Cut Seeds, sequences of tuples into MDDs. Then, we present some in-place algorithms for adding and deleting tuples from an MDD. Next, we consider an MDD constraint which is modified during the search by deleting some tuples. We give an algorithm which adapts MDD-4R to these dynamic and persistent modifications. Some experiments show that MDD constraints are competitive with Table constraints.