To efficiently solve exact discrete optimization problems, branch and bound algorithms require tight bounds. In constraint programming, for optimization, soft arc consistencies typically derive much stronger bounds than those offered by domain or bound consistencies applied to a cost variable. The reason is that soft local consistencies exchange marginal cost information between variables whereas domain consistencies rely only on shrinking domains, which is less informative. However, CP solvers equipped with soft arc consistencies have so far offered limited support for efficient processing of global constraints. In this work, we show how we can efficiently enforce soft local consistency over the AllDifferent constraint, relying on algorithms for the Linear Assignment Problem (LAP). We implement this propagator in toulbar2, the state-of-the-art weighted CP solver exploiting soft local consistencies for bounding. We show that, equipped with this new propagator, toulbar2 outperforms state-of-the-art domain consistency-based CP as well as integer programming solvers for the Quadratic Assignment Problem and shows better performance for miniCOP instances of the 2024 XCSP competition with AllDifferent constraints.

Background: In the ongoing quest for hybridizing discrete reasoning with neural nets, there is an increasing interest in neural architectures that can learn how to solve discrete reasoning or optimisation problems from natural inputs, a task that Large Language Models seem to struggle with. Objectives: We introduce a differentiable neuro-symbolic architecture and a loss function dedicated to learning how to solve NP-hard reasoning problems. Methods: Our new probabilistic loss allows for learning both the constraints and the objective – possibly non-linear – of a combinatorial problem. Thus, it delivers a complete model that can be scrutinized and completed with side constraints. By pushing the combinatorial solver out of the training loop, our architecture also offers scalable training while exact inference gives access to maximum accuracy. Results: We empirically show that it can efficiently learn how to solve NP-hard reasoning problems from natural inputs. On three variants of the Sudoku benchmark – symbolic, visual, and many-solution –, our approach requires a fraction of data and training time of other hybrid methods. On a visual Min-Cut/Max-cut task, it optimizes the regret as well as a Decision-Focused-Learning regret-dedicated loss. Finally, it efficiently learns the energy optimisation formulation of the large real-world problem of designing proteins.

The use of discrete optimization, including Constraint Programming, for designing objects that we completely understand is quite usual. In this talk, I'll show how designing specific biomolecules (proteins) raises new challenges, requiring solving problems that combine precise design targets, approximate laws, and design rules that can be deep-learned from data.

In the ongoing quest for hybridizing discrete reasoning with neural nets, there is an increasing interest in neural architectures that can learn how to solve discrete reasoning or optimization problems from natural inputs. In this paper, we introduce a scalable neural architecture and loss function dedicated to learning the constraints and criteria of NP-hard reasoning problems expressed as discrete Graphical Models. We empirically show our loss function is able to efficiently learn how to solve NP-hard reasoning problems from natural inputs as the symbolic, visual or many-solutions Sudoku problems as well as the energy optimization formulation of the protein design problem, providing data efficiency, interpretability, and a posteriori control over predictions.

In this paper, we extend a Burer-Monteiro style method to compute low rank Semi-Definite Programming (SDP) bounds for the MAP problem on discrete graphical models with an arbitrary number of states and arbitrary pairwise potentials. We consider both a penalized constraint approach and a dedicated Block Coordinate Descent (BCD) approach which avoids large penalty coefficients in the cost matrix. We show our algorithm is decreasing. Experiments show that the BCD approach compares favorably to the penalized approach and to usual linear bounds relying on convergent message passing approaches.

Graphical models (GMs) define a family of mathematical models aimed at the concise description of multivariate functions using decomposability. We restrict ourselves to functions of discrete variables but try to cover a variety of models that are not always considered as "Graphical Models", ranging from functions with Boolean variables and Boolean co-domain (used in automated reasoning) to functions over finite domain variables and integer or real co-domains (usual in machine learning and statistics). We use a simple algebraic semi-ring based framework for generality, define associated queries, relationships between graphical models, complexity results, and families of algorithms, with their associated guarantees.

MOTIVATION: Structure-based computational protein design (CPD) plays a critical role in advancing the field of protein engineering. Using an all-atom energy function, CPD tries to identify amino acid sequences that fold into a target structure and ultimately perform a desired function. The usual approach considers a single rigid backbone as a target, which ignores backbone flexibility. Multistate design (MSD) allows instead to consider several backbone states simultaneously, defining challenging computational problems. RESULTS: We introduce efficient reductions of positive MSD problems to Cost Function Networks with two different fitness definitions and implement them in the Pompd (Positive Multistate Protein design) software. Pompd is able to identify guaranteed optimal sequences of positive multistate full protein redesign problems and exhaustively enumerate suboptimal sequences close to the MSD optimum. Applied to nuclear magnetic resonance and back-rubbed X-ray structures, we observe that the average energy fitness provides the best sequence recovery. Our method outperforms state-of-the-art guaranteed computational design approaches by orders of magnitudes and can solve MSD problems with sizes previously unreachable with guaranteed algorithms. AVAILABILITY AND IMPLEMENTATION: https://forgemia.inra.fr/thomas.schiex/pompd as documented Open Source. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

In many applications of constraint programming, it is often impossible to capture all the relevant information in one numerical criterion. In this case, it is useful to produce a set of high quality yet diverse solutions. In this paper, motivated by a Computational Protein Design application, we consider the general problem of producing a diverse set of high-quality solutions of a given Weighted Constraint Satisfaction Problem, with guarantees both on solution quality and diversity. We use weighted automata decomposed in functions of bounded arity, incremental CFN solving, a simple form of predictive bounding and compressed representations of distance constraints for improved efficiency. We show that this approach can be successfully applied to a variety of problems that include both Protein Design Problems but also large Bayesian networks represented as Cost Function Networks. We also show that our approach has the capacity to enumerate so-called local delta-modes and that it does provide improved protein designs.

MOTIVATION: Structure-based Computational Protein design (CPD) plays a critical role in advancing the field of protein engineering. Using an all-atom energy function, CPD tries to identify amino acid sequences that fold into a target structure and ultimately perform a desired function. Energy functions remain however imperfect and injecting relevant information from known structures in the design process should lead to improved designs. RESULTS: We introduce Shades, a data-driven CPD method that exploits local structural environments in known protein structures together with energy to guide sequence design, while sampling side-chain and backbone conformations to accommodate mutations. Shades (Structural Homology Algorithm for protein DESign), is based on customized libraries of non-contiguous in-contact amino acid residue motifs. We have tested Shades on a public benchmark of 40 proteins selected from different protein families. When excluding homologous proteins, Shades achieved a protein sequence recovery of 30% and a protein sequence similarity of 46% on average, compared with the PFAM protein family of the target protein. When homologous structures were added, the wild-type sequence recovery rate achieved 93%. AVAILABILITY AND IMPLEMENTATION: Shades source code is available at https://bitbucket.org/satsumaimo/shades as a patch for Rosetta 3.8 with a curated protein structure database and ITEM library creation software. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The geometry and properties of the fitness landscapes of Computational Protein Design (CPD) are not well understood, due to the difficulty for sampling methods to access the NP-hard optima and explore their neighborhoods. In this paper, we enumerate all solutions within a 2 kcal/mol energy interval of the optimum of two CPD problems. We compute the number of local minima, the size of the attraction basins, and the local optima network. We provide various features in order to characterize the fitness landscapes, in particular the multimodality, and the ruggedness of the fitness landscape. Results show some key differences in the fitness landscapes and help to understand the successes and failures of metaheuristics on CPD problems. Our analysis gives some previously inaccessible and valuable information on the problem structure related to the optima of the CPD instances (multi-funnel structure), and could lead to the development of more efficient metaheuristic methods.

Motivation: Accurate and economic methods to predict change in protein binding free energy upon mutation are imperative to accelerate the design of proteins for a wide range of applications. Free energy is defined by enthalpic and entropic contributions. Following the recent progresses of Artificial Intelligence-based algorithms for guaranteed NP-hard energy optimization and partition function computation, it becomes possible to quickly compute minimum energy conformations and to reliably estimate the entropic contribution of side-chains in the change of free energy of large protein interfaces. Results: Using guaranteed Cost Function Network algorithms, Rosetta energy functions and Dunbrack's rotamer library, we developed and assessed EasyE and JayZ, two methods for binding affinity estimation that ignore or include conformational entropic contributions on a large benchmark of binding affinity experimental measures. If both approaches outperform most established tools, we observe that side-chain conformational entropy brings little or no improvement on most systems but becomes crucial in some rare cases. Availability and implementation: as open-source Python/C++ code at sourcesup.renater.fr/projects/easy-jayz. Supplementary information: Supplementary data are available at Bioinformatics online.

Virtual Arc Consistency (VAC) is a recent local consistency for processing cost function networks (aka weighted constraint networks) that exploits a simple but powerful connection with standard constraint networks. It has allowed to close hard frequency assignment benchmarks and is capable of directly solving networks of sub modular functions. The algorithm enforcing VAC is an iterative algorithm that solves a sequence of standard constraint networks. This algorithm has been improved by exploiting the idea of dynamic arc consistency between each iteration, leading to the dynamic VAC algorithm. When VAC is maintained during search, the difference between two adjacent nodes in the search tree is also limited. In this paper, we show that the incrementality of Dynamic VAC can also be useful when maintaining VAC during search and we present results showing that maintaining dynamic VAC during search can effectively accelerate search.

UNLABELLED: It is now easy and increasingly usual to produce oriented RNA-Seq data as a prokaryotic genome is being sequenced. However, this information is usually just used for expression quantification. EuGene-PP is a fully automated pipeline for structural annotation of prokaryotic genomes integrating protein similarities, statistical information and any oriented expression information (RNA-Seq or tiling arrays) through a variety of file formats to produce a qualitatively enriched annotation including coding regions but also (possibly antisense) non-coding genes and transcription start sites. AVAILABILITY AND IMPLEMENTATION: EuGene-PP is an open-source software based on EuGene-P integrating a Galaxy configuration. EuGene-PP can be downloaded at eugene.toulouse.inra.fr.

MOTIVATION: The main challenge for structure-based computational protein design (CPD) remains the combinatorial nature of the search space. Even in its simplest fixed-backbone formulation, CPD encompasses a computationally difficult NP-hard problem that prevents the exact exploration of complex systems defining large sequence-conformation spaces. RESULTS: We present here a CPD framework, based on cost function network (CFN) solving, a recent exact combinatorial optimization technique, to efficiently handle highly complex combinatorial spaces encountered in various protein design problems. We show that the CFN-based approach is able to solve optimality a variety of complex designs that could often not be solved using a usual CPD-dedicated tool or state-of-the-art exact operations research tools. Beyond the identification of the optimal solution, the global minimum-energy conformation, the CFN-based method is also able to quickly enumerate large ensembles of suboptimal solutions of interest to rationally build experimental enzyme mutant libraries. AVAILABILITY: The combined pipeline used to generate energetic models (based on a patched version of the open source solver Osprey 2.0), the conversion to CFN models (based on Perl scripts) and CFN solving (based on the open source solver toulbar2) are all available at http://genoweb.toulouse.inra.fr/~tschiex/CPD

As (Lee et al., 2012) have shown, weighted constraint satisfaction problems can benefit from the introduction of global cost functions, leading to a new Cost Function Programming paradigm. In this paper, we explore the possibility of decomposing global cost functions in such a way that enforcing soft local consistencies on the decomposition offers guarantees on the level of consistency enforced on the original global cost function. We show that directional arc consistency and virtual arc consistency offer such guarantees. We conclude by experiments on decomposable cost functions showing that decompositions may be very useful to easily integrate efficient global cost functions in solvers.

BACKGROUND: Detecting duplication segments within completely sequenced genomes provides valuable information to address genome evolution and in particular the important question of the emergence of novel functions. The usual approach to gene duplication detection, based on all-pairs protein gene comparisons, provides only a restricted view of duplication. RESULTS: In this paper, we introduce ReD Tandem, a software using a flow based chaining algorithm targeted at detecting tandem duplication arrays of moderate to longer length regions, with possibly locally weak similarities, directly at the DNA level. On the A. thaliana genome, using a reference set of tandem duplicated genes built using TAIR,(a) we show that ReD Tandem is able to predict a large fraction of recently duplicated genes (dS < 1) and that it is also able to predict tandem duplications involving non coding elements such as pseudo-genes or RNA genes. CONCLUSIONS: ReD Tandem allows to identify large tandem duplications without any annotation, leading to agnostic identification of tandem duplications. This approach nicely complements the usual protein gene based which ignores duplications involving non coding regions. It is however inherently restricted to relatively recent duplications. By recovering otherwise ignored events, ReD Tandem gives a more comprehensive view of existing evolutionary processes and may also allow to improve existing annotations.

SUMMARY: Transcriptome sequencing represents a fundamental source of information for genome-wide studies and transcriptome analysis and will become increasingly important for expression analysis as new sequencing technologies takes over array technology. The identification of the protein-coding region in transcript sequences is a prerequisite for systematic amino acid-level analysis and more specifically for domain identification. In this article, we present FrameDP, a self-training integrative pipeline for predicting CDS in transcripts which can adapt itself to different levels of sequence qualities. AVAILABILITY: FrameDP for Linux (web-server and underlying pipeline) is available at {{http://iant.toulouse.inra.fr/FrameDP}} for direct use or a standalone installation.

The Weighted Constraint Satisfaction Problem (WCSP) framework allows representing and solving problems involving both hard constraints and cost functions. It has been applied to various problems, including resource allocation, bioinformatics, scheduling, etc. To solve such problems, solvers usually rely on branch-and-bound algorithms equipped with local consistency filtering, mostly soft arc consistency. However, these techniques are not well suited to solve problems with very large domains. Motivated by the resolution of an RNA gene localization problem inside large genomic sequences, and in the spirit of bounds consistency for large domains in crisp CSPs, we introduce soft bounds arc consistency, a new weighted local consistency specifically designed for WCSP with very large domains. Compared to soft arc consistency, BAC provides significantly improved time and space asymptotic complexity. In this paper, we show how the semantics of cost functions can be exploited to further improve the time complexity of BAC. We also compare both in theory and in practice the efficiency of BAC on a WCSP with bounds consistency enforced on a crisp CSP using cost variables. On two different real problems modeled as WCSP, including our RNA gene localization problem, we observe that maintaining bounds arc consistency outperforms arc consistency and also improves over bounds consistency enforced on a constraint model with cost variables.

BACKGROUND: In the last decade, sequencing projects have led to the development of a number of annotation systems dedicated to the structural and functional annotation of protein-coding genes. These annotation systems manage the annotation of the non-protein coding genes (ncRNAs) in a very crude way, allowing neither the edition of the secondary structures nor the clustering of ncRNA genes into families which are crucial for appropriate annotation of these molecules. RESULTS: LeARN is a flexible software package which handles the complete process of ncRNA annotation by integrating the layers of automatic detection and human curation. CONCLUSION: This software provides the infrastructure to deal properly with ncRNAs in the framework of any annotation project. It fills the gap between existing prediction software, that detect independent ncRNA occurrences, and public ncRNA repositories, that do not offer the flexibility and interactivity required for annotation projects. The software is freely available from the download section of the website http://bioinfo.genopole-toulouse.prd.fr/LeARN.

MOTIVATION: Genome maps are fundamental to the study of an organism and essential in the process of genome sequencing which in turn provides the ultimate map of the genome. The increased number of genomes being sequenced offers new opportunities for the mapping of closely related organisms. We propose here an algorithmic formalization of a genome comparison approach to marker ordering. RESULTS: In order to integrate a comparative mapping approach in the algorithmic process of map construction and selection, we propose to extend the usual statistical model describing the experimental data, here radiation hybrids (RH) data, in a statistical framework that models additionally the evolutionary relationships between a proposed map and a reference map: an existing map of the corresponding orthologous genes or markers in a closely related organism. This has concretely the effect of exploiting, in the process of map selection, the information of marker adjacencies in the related genome when the information provided by the experimental data is not conclusive for the purpose of ordering. In order to compute efficiently the map, we proceed to a reduction of the maximum likelihood estimation to the Traveling Salesman Problem. Experiments on simulated RH datasets as well as on a real RH dataset from the canine RH project show that maps produced using the likelihood defined by the new model are significantly better than maps built using the traditional RH model. AVAILABILITY: The comparative mapping approach is available in the last version of de Givry,S. et al. [(2004) Bioinformatics, 21, 1703-1704, www.inra.fr/mia/T/CarthaGene], a free (the LKH part is free for academic use only) mapping software in C++, including LKH (Helsgaun,K. (2000) Eur. J. Oper. Res., 126, 106-130, www.dat.ruc.dk/keld/research/LKH) for maximum likelihood computation.

Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express "simple" decision problems, while others are designed to take into account uncertainties, unfeasible decisions, and utilities. Even in a single formalism, several variants are often proposed to model different types of uncertainty (probability, possibility...) or utility (additive or not). In this article, we introduce an algebraic graphical model that encompasses a large number of such formalisms: (1) we first adapt previous structures from Friedman, Chu and Halpern for representing uncertainty, utility, and expected utility in order to deal with generic forms of sequential decision making; (2) on these structures, we then introduce composite graphical models that express information via variables linked by "local" functions, thanks to conditional independence; (3) on these graphical models, we finally define a simple class of queries which can represent various scenarios in terms of observabilities and controllabilities. A natural decision-tree semantics for such queries is completed by an equivalent operational semantics, which induces generic algorithms. The proposed framework, called the Plausibility-Feasibility-Utility (PFU) framework, not only provides a better understanding of the links between existing formalisms, but it also covers yet unpublished frameworks (such as possibilistic influence diagrams) and unifies formalisms such as quantified boolean formulas and influence diagrams. Our backtrack and variable elimination generic algorithms are a first step towards unified algorithms.

MOTIVATION: Searching RNA gene occurrences in genomic sequences is a task whose importance has been renewed by the recent discovery of numerous functional RNA, often interacting with other ligands. Even if several programs exist for RNA motif search, none exists that can represent and solve the problem of searching for occurrences of RNA motifs in interaction with other molecules. RESULTS: We present a constraint network formulation of this problem. RNA are represented as structured motifs that can occur on more than one sequence and which are related together by possible hybridization. The implemented tool MilPat is used to search for several sRNA families in genomic sequences. Results show that MilPat allows to efficiently search for interacting motifs in large genomic sequences and offers a simple and extensible framework to solve such problems. New and known sRNA are identified as H/ACA candidates in Methanocaldococcus jannaschii. AVAILABILITY: http://carlit.toulouse.inra.fr/MilPaT/MilPat.pl.

UNLABELLED: CAR(H)(T)A GENE: is an integrated genetic and radiation hybrid (RH) mapping tool which can deal with multiple populations, including mixtures of genetic and RH data. CAR(H)(T)A GENE: performs multipoint maximum likelihood estimations with accelerated expectation-maximization algorithms for some pedigrees and has sophisticated algorithms for marker ordering. Dedicated heuristics for framework mapping are also included. CAR(H)(T)A GENE: can be used as a C++ library, through a shell command and a graphical interface. The XML output for companion tools is integrated. AVAILABILITY: The program is available free of charge from www.inra.fr/bia/T/CarthaGene for Linux, Windows and Solaris machines (with Open Source). CONTACT: [email protected].

BACKGROUND: Alternative splicing (AS) is now considered as a major actor in transcriptome/proteome diversity and it cannot be neglected in the annotation process of a new genome. Despite considerable progresses in term of accuracy in computational gene prediction, the ability to reliably predict AS variants when there is local experimental evidence of it remains an open challenge for gene finders. RESULTS: We have used a new integrative approach that allows to incorporate AS detection into ab initio gene prediction. This method relies on the analysis of genomically aligned transcript sequences (ESTs and/or cDNAs), and has been implemented in the dynamic programming algorithm of the graph-based gene finder EuGENE. Given a genomic sequence and a set of aligned transcripts, this new version identifies the set of transcripts carrying evidence of alternative splicing events, and provides, in addition to the classical optimal gene prediction, alternative optimal predictions (among those which are consistent with the AS events detected). This allows for multiple annotations of a single gene in a way such that each predicted variant is supported by a transcript evidence (but not necessarily with a full-length coverage). CONCLUSIONS: This automatic combination of experimental data analysis and ab initio gene finding offers an ideal integration of alternatively spliced gene prediction inside a single annotation pipeline.

Many AI synthesis problems such as planning, scheduling or design may be encoded in a constraint satisfaction problem (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, for many real tasks, the set of constraints to consider may evolve because of the environment or because of user interactions. The problem considered here is the solution maintenance problem in such a dynamic CSP (DCSP). The authors propose a new class of constraint recording algorithms called Nogood Recording that may be used for solving both static and dynamic CSPs. It offers an interesting compromise, polynomially bounded in space, between an ATMS-like approach and the usual static constraint satisfaction algorithms.

The ATMS resolution mechanisms have been formalized, using the concept of DK-tree. We propose in this paper a new and simple approach based on the fixed point theory and an original demonstration of the completeness of these mechanisms. We first introduce the basic definitions of terms, sets and functions which are used in the paper and build a lattice. Then, the basic formal tools to describe the ATMS mechanisms are introduced: The notion of DK-clash (in fact, the inference rule), and a monotonic function, which represents the deduction process and whose least fixed point corresponds to the output of an ATMS. We prove the soundness and the completeness (for specific clauses) of these mechanisms. This demonstration brings to light an original and interesting property, whose applications are discussed at the end of the paper.