arXiv subjects

Tias Guns

Publications and source records attributed to Tias Guns.

At least 19 recordsLinked to original sources

arXiv2026

Translating finite-domain integer constraint models to CP/SMT/ILP/PB/SAT solvers with CPMpy

Constraint solving is a declarative approach for solving combinatorial satisfaction and optimization problems. The user specifies their problem through constraints and decision variables, and a generic solver is used to find a solution. Several constraint-solving technologies exist, and certain solvers perform well on certain problems. Therefore, it is useful to try different solvers given a particular application. However, each solving paradigm supports different types of constraints and decision variables. Our goal is to translate high-level constraint satisfaction and optimization problems into any lower-level formalism, including CP, SMT QF-LIA, ILP, PB and (Max)SAT. This allows for comparing different solving technologies for a particular problem, without requiring a user to manually remodel it for each solving paradigm. We define a high-level language of logical and arithmetic operations, and useful additional functions and constraints, which are known as global constraints in the CP community. We then present a modular framework for transforming our high-level modeling language to CP/SMT/ILP/PB and (Max)SAT solvers. While many transformations are partly described in the literature, we observe that they can be implemented through a modular waterfall of smaller components, where lower-level paradigms reuse the transformations of higher-level paradigms. Two recurring challenges are handling the negation of arbitrary subexpressions and avoiding the introduction of auxiliary variables. Additionally, we take special care linearizing non-linear operators for ILP, PB and SAT-solvers. The transformation waterfall is implemented and evaluated in the open-source CPMpy library. Our results show that constraint models significantly change throughout the transformations, and that optimizations to the linearization of constraints are essential for ILP and PB solvers.

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arXiv2026

LLM-Guided Evolutionary Search for Constraint Model Reformulation to Improve Solver Efficiency

Combinatorial problems appear in numerous industrial applications. A common approach is to formulate these problems as declarative constraint models that can subsequently be compiled to and solved by a range of back-end solvers. Recent work shows that Large Language Models (LLMs) can produce correct models from natural language, but even a correct model can be expensive to solve because performance remains sensitive to modelling choices. In this work, we investigate whether LLMs can automate performance-oriented model reformulation. Inspired by Automatic Heuristic Design (AHD), we use an evolutionary framework in which an LLM proposes candidate reformulations that are verified and benchmarked against the user-defined baseline model. We compare AHD-adapted search strategies that control which prior attempts, instructions, and measured feedback enter each prompt. Existing retention strategies prioritize recency or performance, but do not explicitly diversify the context. To cover this gap, we introduce Profile-Diverse Retention (PDR), which applies Maximal Marginal Relevance (MMR) to instance-level runtime vectors to retain behaviourally diverse attempts. We systematically evaluate the strategies on eight CSPLib problems using validation-based final model selection. The results show that: (i) iterative reformulation can produce substantial held-out speedups; (ii) strategies that keep the retained context diverse outperform those that retain only recent or the fastest attempts; and (iii) validation-based selection improves the held-out speedup of every strategy.

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arXiv2026

Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition

Decision-focused learning has shown great promise for addressing predict-then-optimize problems, particularly in the presence of under-specified models. However, its practical deployment is often hindered by high computational costs and limited scalability, as it requires solving a constrained optimization problem for each training instance at every iteration. To address these challenges, we propose a novel framework that incorporates Lagrangian decomposition into the decision-focused learning paradigm. Specifically, we introduce a new surrogate objective along with two loss functions for evaluating and training the underlying prediction model. We further propose two variants of our approach, which offer different trade-offs between computational efficiency and solution quality. Our framework can be seamlessly integrated with standard decision-focused learning methods, including Smart Predict-then-Optimize (SPO+) and Implicit Maximum Likelihood Estimation (IMLE). Through experiments on two standard benchmarks, the multi-dimensional knapsack problem and quadratic portfolio optimization, we demonstrate that our approach achieves competitive performance while remaining amenable to parallelization. In particular, it consistently outperforms traditional decision-focused learning methods on large-scale instances, involving up to eight times more variables than those typically considered in related work. The implementation is available at https://github.com/corail-research/DFL-LD.

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arXiv2026

Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning

Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.g., demand or travel times in delivery problems). A common strategy in such cases is to estimate said parameters via machine learning (ML) models trained to minimize the prediction error, which however is not necessarily aligned with the downstream task-level error. The decision-focused learning (DFL) paradigm overcomes this limitation by training to directly minimize a task loss, e.g. regret. Since the latter has non-informative gradients for combinatorial problems, state-of-the-art DFL methods introduce surrogates and approximations that enable training. But these methods exploit specific assumptions about the problem structures (e.g., convex or linear problems, unknown parameters only in the objective function). We propose an alternative method that makes no such assumptions, it combines stochastic smoothing with score function gradient estimation which works on any task loss. This opens up the use of DFL methods to nonlinear objectives, uncertain parameters in the problem constraints, and even two-stage stochastic optimization. Experiments show that it typically requires more epochs, but that it is on par with specialized methods and performs especially well for the difficult case of problems with uncertainty in the constraints, in terms of solution quality, scalability, or both.

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arXiv2026

Scalable Decision-Focused Learning through Cost-Sensitive Regression

Many real-world combinatorial problems involve uncertain parameters, which can be predicted given contextual features and historical data. These `predict-then-optimize' or `contextual optimization' problems have gained significant attention: end-to-end training methods can now minimize the downstream task cost rather than the predictive error. However, despite their effectiveness, these decision-focused learning (DFL) approaches often rely on repeated solving of the underlying combinatorial optimization problem during training, making them computationally expensive and difficult to scale. We reframe the learning problem as a cost-sensitive multi-output regression problem: multi-output due to the combinatorial problem having multiple uncertain parameters, and cost-sensitive due to the downstream task cost being the real target. Our technical contribution is the formalization of multiple loss function components that follow from this reframing: cost-insensitive normalization, decision-aware asymmetric penalization of over- and underpredictions, and instance-based costs that mimic the true downstream task-based loss locally. These components require zero or one solve per training data instance, while requiring no further solves during training. Experiments show that the combination of loss components achieves comparable downstream task quality to the state of the art, while being significantly more efficient, enabling scaling to problem sizes that have not been tackled before with DFL.

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arXiv2026

DCP-Bench-Open: Evaluating LLMs for Constraint Modelling of Discrete Combinatorial Problems

Discrete Combinatorial Problems (DCPs) are prevalent in industrial decision-making and optimisation. However, while constraint solving technologies for DCPs have advanced significantly, the core process of formalising them, namely constraint modelling, requires significant expertise and remains a bottleneck for wider adoption. Aiming to alleviate this bottleneck, recent studies have explored using Large Language Models (LLMs) to transform combinatorial problem descriptions into executable constraint models. However, the existing evaluation datasets for discrete constraint modelling are often limited to small, homogeneous, or domain-specific problems, which do not capture the diversity of real-world scenarios. This work addresses this gap by introducing DCP-Bench-Open, a novel benchmark that includes a diverse set of well-known discrete combinatorial problems sourced from the Constraint Programming (CP) and Operations Research (OR) communities, structured explicitly for evaluating LLM-driven constraint modelling. With this dataset, and given the variety of modelling frameworks, we compare and evaluate the modelling capabilities of LLMs for three distinct constraint modelling systems, which vary in abstraction level and underlying syntax. Notably, the results show higher performance when modelling with a high-level Python-based framework. Additionally, we systematically evaluate the use of prompt-based and inference-time compute methods across different LLMs, which further increase accuracy, reaching up to 91% on this highly challenging benchmark. DCP-Bench-Open is publicly available.

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arXiv2025

Using Certifying Constraint Solvers for Generating Step-wise Explanations

In the field of Explainable Constraint Solving, it is common to explain to a user why a problem is unsatisfiable. A recently proposed method for this is to compute a sequence of explanation steps. Such a step-wise explanation shows individual reasoning steps involving constraints from the original specification, that in the end explain a conflict. However, computing a step-wise explanation is computationally expensive, limiting the scope of problems for which it can be used. We investigate how we can use proofs generated by a constraint solver as a starting point for computing step-wise explanations, instead of computing them step-by-step. More specifically, we define a framework of abstract proofs, in which both proofs and step-wise explanations can be represented. We then propose several methods for converting a proof to a step-wise explanation sequence, with special attention to trimming and simplification techniques to keep the sequence and its individual steps small. Our results show our method significantly speeds up the generation of step-wise explanation sequences, while the resulting step-wise explanation has a quality similar to the current state-of-the-art.

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arXiv2025

Preference Elicitation for Step-Wise Explanations in Logic Puzzles

Step-wise explanations can explain logic puzzles and other satisfaction problems by showing how to derive decisions step by step. Each step consists of a set of constraints that derive an assignment to one or more decision variables. However, many candidate explanation steps exist, with different sets of constraints and different decisions they derive. To identify the most comprehensible one, a user-defined objective function is required to quantify the quality of each step. However, defining a good objective function is challenging. Here, interactive preference elicitation methods from the wider machine learning community can offer a way to learn user preferences from pairwise comparisons. We investigate the feasibility of this approach for step-wise explanations and address several limitations that distinguish it from elicitation for standard combinatorial problems. First, because the explanation quality is measured using multiple sub-objectives that can vary a lot in scale, we propose two dynamic normalization techniques to rescale these features and stabilize the learning process. We also observed that many generated comparisons involve similar explanations. For this reason, we introduce MACHOP (Multi-Armed CHOice Perceptron), a novel query generation strategy that integrates non-domination constraints with upper confidence bound-based diversification. We evaluate the elicitation techniques on Sudokus and Logic-Grid puzzles using artificial users, and validate them with a real-user evaluation. In both settings, MACHOP consistently produces higher-quality explanations than the standard approach.

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arXiv2025

Solver-Free Decision-Focused Learning for Linear Optimization Problems

Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from contextual features. This gives rise to predict-then-optimize problems, where a machine learning model predicts problem parameters that are then used to make decisions via optimization. A growing body of work on decision-focused learning (DFL) addresses this setting by training models specifically to produce predictions that maximize downstream decision quality, rather than accuracy. While effective, DFL is computationally expensive, because it requires solving the optimization problem with the predicted parameters at each loss evaluation. In this work, we address this computational bottleneck for linear optimization problems, a common class of problems in both DFL literature and real-world applications. We propose a solver-free training method that exploits the geometric structure of linear optimization to enable efficient training with minimal degradation in solution quality. Our method is based on the insight that a solution is optimal if and only if it achieves an objective value that is at least as good as that of its adjacent vertices on the feasible polytope. Building on this, our method compares the estimated quality of the ground-truth optimal solution with that of its precomputed adjacent vertices, and uses this as loss function. Experiments demonstrate that our method significantly reduces computational cost while maintaining high decision quality.

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arXiv2025

Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints

When some parameters of a constrained optimization problem (COP) are uncertain, this gives rise to a predict-then-optimize (PtO) problem, comprising two stages: the prediction of the unknown parameters from contextual information and the subsequent optimization using those predicted parameters. Decision-focused learning (DFL) implements the first stage by training a machine learning (ML) model to optimize the quality of the decisions made using the predicted parameters. When the predicted parameters occur in the constraints, they can lead to infeasible solutions. Therefore, it is important to simultaneously manage both feasibility and decision quality. We develop a DFL framework for predicting constraint parameters in a generic COP. While prior works typically assume that the underlying optimization problem is a linear program (LP) or integer LP (ILP), our approach makes no such assumption. We derive two novel loss functions based on maximum likelihood estimation (MLE): the first one penalizes infeasibility (by penalizing predicted parameters that lead to infeasible solutions), while the second one penalizes suboptimal decisions (by penalizing predicted parameters that make the true optimal solution infeasible). We introduce a single tunable parameter to form a weighted average of the two losses, allowing decision-makers to balance suboptimality and feasibility. We experimentally demonstrate that adjusting this parameter provides decision-makers control over this trade-off. Moreover, across several COP instances, we show that adjusting the tunable parameter allows a decision-maker to prioritize either suboptimality or feasibility, outperforming the performance of existing baselines in either objective.

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arXiv2025

Preference Elicitation for Multi-objective Combinatorial Optimization with Active Learning and Maximum Likelihood Estimation

Real-life combinatorial optimization problems often involve several conflicting objectives, such as price, product quality and sustainability. A computationally-efficient way to tackle multiple objectives is to aggregate them into a single-objective function, such as a linear combination. However, defining the weights of the linear combination upfront is hard; alternatively, the use of interactive learning methods that ask users to compare candidate solutions is highly promising. The key challenges are to generate candidates quickly, to learn an objective function that leads to high-quality solutions and to do so with few user interactions. We build upon the Constructive Preference Elicitation framework and show how each of the three properties can be improved: to increase the interaction speed we investigate using pools of (relaxed) solutions, to improve the learning we adopt Maximum Likelihood Estimation of a Bradley-Terry preference model; and to reduce the number of user interactions, we select the pair of candidates to compare with an ensemble-based acquisition function inspired from Active Learning. Our careful experimentation demonstrates each of these improvements: on a PC configuration task and a realistic multi-instance routing problem, our method selects queries faster, needs fewer queries and synthesizes higher-quality combinatorial solutions than previous CPE methods.

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arXiv2025

Minimizing Surrogate Losses for Decision-Focused Learning using Differentiable Optimization

Decision-focused learning (DFL) trains a machine learning (ML) model to predict parameters of an optimization problem, to directly minimize decision regret, i.e., maximize decision quality. Gradient-based DFL requires computing the derivative of the solution to the optimization problem with respect to the predicted parameters. However, for many optimization problems, such as linear programs (LPs), the gradient of the regret with respect to the predicted parameters is zero almost everywhere. Existing gradient-based DFL approaches for LPs try to circumvent this issue in one of two ways: (a) smoothing the LP into a differentiable optimization problem by adding a quadratic regularizer and then minimizing the regret directly or (b) minimizing surrogate losses that have informative (sub)gradients. In this paper, we show that the former approach still results in zero gradients, because even after smoothing the regret remains constant across large regions of the parameter space. To address this, we propose minimizing surrogate losses -- even when a differentiable optimization layer is used and regret can be minimized directly. Our experiments demonstrate that minimizing surrogate losses allows differentiable optimization layers to achieve regret comparable to or better than surrogate-loss based DFL methods. Further, we demonstrate that this also holds for DYS-Net, a recently proposed differentiable optimization technique for LPs, that computes approximate solutions and gradients through operations that can be performed using feedforward neural network layers. Because DYS-Net executes the forward and the backward pass very efficiently, by minimizing surrogate losses using DYS-Net, we are able to attain regret on par with the state-of-the-art while reducing training time by a significant margin.

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arXiv2024

A Divide-Align-Conquer Strategy for Program Synthesis

A major bottleneck in search-based program synthesis is the exponentially growing search space which makes learning large programs intractable. Humans mitigate this problem by leveraging the compositional nature of the real world: In structured domains, a logical specification can often be decomposed into smaller, complementary solution programs. We show that compositional segmentation can be applied in the programming by examples setting to divide the search for large programs across multiple smaller program synthesis problems. For each example, we search for a decomposition into smaller units which maximizes the reconstruction accuracy in the output under a latent task program. A structural alignment of the constituent parts in the input and output leads to pairwise correspondences used to guide the program synthesis search. In order to align the input/output structures, we make use of the Structure-Mapping Theory (SMT), a formal model of human analogical reasoning which originated in the cognitive sciences. We show that decomposition-driven program synthesis with structural alignment outperforms Inductive Logic Programming (ILP) baselines on string transformation tasks even with minimal knowledge priors. Unlike existing methods, the predictive accuracy of our agent monotonically increases for additional examples and achieves an average time complexity of $\mathcal{O}(m)$ in the number $m$ of partial programs for highly structured domains such as strings. We extend this method to the complex setting of visual reasoning in the Abstraction and Reasoning Corpus (ARC) for which ILP methods were previously infeasible.

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arXiv2024

Generalizing Constraint Models in Constraint Acquisition

Constraint Acquisition (CA) aims to widen the use of constraint programming by assisting users in the modeling process. However, most CA methods suffer from a significant drawback: they learn a single set of individual constraints for a specific problem instance, but cannot generalize these constraints to the parameterized constraint specifications of the problem. In this paper, we address this limitation by proposing GenCon, a novel approach to learn parameterized constraint models capable of modeling varying instances of the same problem. To achieve this generalization, we make use of statistical learning techniques at the level of individual constraints. Specifically, we propose to train a classifier to predict, for any possible constraint and parameterization, whether the constraint belongs to the problem. We then show how, for some classes of classifiers, we can extract decision rules to construct interpretable constraint specifications. This enables the generation of ground constraints for any parameter instantiation. Additionally, we present a generate-and-test approach that can be used with any classifier, to generate the ground constraints on the fly. Our empirical results demonstrate that our approach achieves high accuracy and is robust to noise in the input instances.

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arXiv2024

Exploiting Symmetries in MUS Computation (Extended version)

In eXplainable Constraint Solving (XCS), it is common to extract a Minimal Unsatisfiable Subset (MUS) from a set of unsatisfiable constraints. This helps explain to a user why a constraint specification does not admit a solution. Finding MUSes can be computationally expensive for highly symmetric problems, as many combinations of constraints need to be considered. In the traditional context of solving satisfaction problems, symmetry has been well studied, and effective ways to detect and exploit symmetries during the search exist. However, in the setting of finding MUSes of unsatisfiable constraint programs, symmetries are understudied. In this paper, we take inspiration from existing symmetry-handling techniques and adapt well-known MUS-computation methods to exploit symmetries in the specification, speeding-up overall computation time. Our results display a significant reduction of runtime for our adapted algorithms compared to the baseline on symmetric problems.

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arXiv2024

Trustworthy and Explainable Decision-Making for Workforce allocation

In industrial contexts, effective workforce allocation is crucial for operational efficiency. This paper presents an ongoing project focused on developing a decision-making tool designed for workforce allocation, emphasising the explainability to enhance its trustworthiness. Our objective is to create a system that not only optimises the allocation of teams to scheduled tasks but also provides clear, understandable explanations for its decisions, particularly in cases where the problem is infeasible. By incorporating human-in-the-loop mechanisms, the tool aims to enhance user trust and facilitate interactive conflict resolution. We implemented our approach on a prototype tool/digital demonstrator intended to be evaluated on a real industrial scenario both in terms of performance and user acceptability.

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arXiv2024

Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities

Decision-focused learning (DFL) is an emerging paradigm that integrates machine learning (ML) and constrained optimization to enhance decision quality by training ML models in an end-to-end system. This approach shows significant potential to revolutionize combinatorial decision-making in real-world applications that operate under uncertainty, where estimating unknown parameters within decision models is a major challenge. This paper presents a comprehensive review of DFL, providing an in-depth analysis of both gradient-based and gradient-free techniques used to combine ML and constrained optimization. It evaluates the strengths and limitations of these techniques and includes an extensive empirical evaluation of eleven methods across seven problems. The survey also offers insights into recent advancements and future research directions in DFL. Code and benchmark: https://github.com/PredOpt/predopt-benchmarks

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arXiv2024

Decision-Focused Learning to Predict Action Costs for Planning

In many automated planning applications, action costs can be hard to specify. An example is the time needed to travel through a certain road segment, which depends on many factors, such as the current weather conditions. A natural way to address this issue is to learn to predict these parameters based on input features (e.g., weather forecasts) and use the predicted action costs in automated planning afterward. Decision-Focused Learning (DFL) has been successful in learning to predict the parameters of combinatorial optimization problems in a way that optimizes solution quality rather than prediction quality. This approach yields better results than treating prediction and optimization as separate tasks. In this paper, we investigate for the first time the challenges of implementing DFL for automated planning in order to learn to predict the action costs. There are two main challenges to overcome: (1) planning systems are called during gradient descent learning, to solve planning problems with negative action costs, which are not supported in planning. We propose novel methods for gradient computation to avoid this issue. (2) DFL requires repeated planner calls during training, which can limit the scalability of the method. We experiment with different methods approximating the optimal plan as well as an easy-to-implement caching mechanism to speed up the learning process. As the first work that addresses DFL for automated planning, we demonstrate that the proposed gradient computation consistently yields significantly better plans than predictions aimed at minimizing prediction error; and that caching can temper the computation requirements.

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