Constraint Programming Research Articles

Finding Complete Impossible Differential Attacks on AndRX Ciphers and Efficient Distinguishers for ARX Designs

The impossible differential (ID) attack is one of the most important cryptanalytic techniques for block ciphers. There are two phases to finding an ID attack: searching for the distinguisher and building a key recovery upon it. Previous works only focused on automated distinguisher discovery, leaving key recovery as a manual post-processing task, which may lead to a suboptimal final complexity. At EUROCRYPT 2023, Hadipour et al. introduced a unified constraint programming (CP) approach based on satisfiability for finding optimal complete ID attacks in strongly aligned ciphers. While this approach was extended to weakly-aligned designs like PRESENT at ToSC 2024, its application to ARX and AndRX ciphers remained as future work. Moreover, this method only exploited ID distinguishers with direct contradictions at the junction of two deterministic transitions. In contrast, some ID distinguishers, particularly for ARX and AndRX designs, may not be detectable by checking only the existence of direct contradictions.This paper fills these gaps by extending Hadipour et al.’s method to handle indirect contradictions and adapting it for ARX and AndRX designs. We also present a similar method for identifying zero-correlation (ZC) distinguishers. Moreover, we extend our new model for finding ID distinguishers to a unified optimization problem that includes both the distinguisher and the key recovery for AndRX designs. Our method improves ID attacks and introduces new distinguishers for several ciphers, such as SIMON, SPECK, Simeck, ChaCha, Chaskey, LEA, and SipHash. For example, we achieve a one-round improvement in ID attacks against SIMON-64-96, SIMON-64-128, SIMON-128-128, SIMON-128-256 and a two-round improvement against SIMON-128- 192. These results significantly contribute to our understanding of the effectiveness of automated tools in the cryptanalysis of different design paradigms.

An implementation of nonmonotonic reasoning with c-representations using an SMT solver

A qualitative conditional “If A then usually B” establishes a plausible connection between the antecedent A and the consequent B. As a semantics for conditional knowledge bases containing such conditionals, ranking functions order possible worlds by mapping them to a degree of plausibility. c-Representations are special ranking functions that are obtained by assigning individual integer impacts to the conditionals in a knowledge base R and by defining the rank of each possible world as the sum of these impacts of falsified conditionals. c-Inference is the nonmonotonic inference relation taking all c-representations of a given knowledge base R into account. In this paper, we show how c-inference can be realized as a satisfiability modulo theories problem (SMT), which allows an implementation by an appropriate SMT solver. Moreover, we show that this leads to the first implementation fully realizing c-inference because it does not require a predefined upper limit for the impacts assigned to the conditionals. We develop a transformation of the constraint satisfaction problem characterizing c-inference into a solvable-equivalent SMT problem, prove its correctness, and illustrate it by a running example. Furthermore, we provide a corresponding implementation using the SMT solver Z3. We develop and implement a randomized generation scheme for knowledge bases and queries, and evaluate our SMT-based implementation of c-inference with respect to such randomly generated knowledge bases. Our evaluation demonstrates the feasibility of our approach as well as the superiority in comparison to former implementations of c-inference.

The Dial-a-Tour Problem

This article delves into the Dial-a-Tour Problem (DATP) frequently encountered in local travel agencies, known for their personalized and hands-on customer service. In the DATP, multiple tourist groups are efficiently matched with different vehicles using vanpooling, maximizing vehicle occupancy while ensuring seamless transfers to the local attractions included in their booked tours. Each tourist group is picked up from and returned to their respective hotels after their journey. The predetermined locations and the sequence of visits for each tour are known in advance. Therefore, the primary objective is to minimize the number of vehicles required to fulfill all requests and maintain the desired level of service.To tackle this challenge, the article presents a comprehensive approach. It introduces a mixed-integer linear model, two constraint programming formulations, and a novel operator called the k-buffer insertion operator. This operator serves as the centerpiece of a descent heuristic proposed in the study.Extensive evaluation across a diverse range of randomly generated instances underscores the superiority of the proposed constraint programming formulations over the mixed integer linear programming model. However, it is noteworthy that the proposed heuristic surpasses even the most effective constraint programming formulation. This highlights its remarkable efficiency in solving real-size instances within notably brief computation times. Such prowess underscores the practical utility of this heuristic in effectively tackling the complexities inherent in the Dial-a-Tour Problem.

A Graph-Neural-Network-Powered Solver Framework for Graph Optimization Problems.

Backtracking combined with branching heuristics is a prevalent approach for tackling constraint satisfaction problems (CSPs) and combinatorial optimization problems (COPs). While branching heuristics specifically designed for certain problems can be theoretically efficient, they are often complex and difficult to implement in practice. On the other hand, general branching heuristics can be applied across various problems, but at the risk of suboptimality. We introduce a solver framework that leverages the Shannon entropy in branching heuristics to bridge the gap between generality and specificity in branching heuristics. This enables backtracking to follow the path of least uncertainty, based on probability distributions that conform to problem constraints. We employ graph neural network (GNN) models with loss functions derived from the probabilistic method to learn these probability distributions. We have evaluated our approach by its applications to two NP-hard problems: the (minimum) dominating-clique problem and the edge-clique-cover problem. Compared with the state-of-the-art solvers for both problems, our solver framework outputs competitive results. Specifically, for the (minimum) dominating-clique problem, our approach generates fewer branches than the solver presented by Culberson et al. (2005). For the edge-clique-cover problem, our approach produces smaller-sized edge clique covers (ECCs) than the solvers referenced by Conte et al. (2020) and Kellerman (1973).

The dual-resource-constrained re-entrant flexible flow shop a constraint programming approach and a hybrid genetic algorithm

ABSTRACT The dual-resource-constrained re-entrant flexible flow shop scheduling problem represents a specialised variant of the flow shop scheduling problem, inspired by real-world scenarios in screen printing industries. Besides the well-known flow shop structure, stages consist of identical parallel machines and operations may re-enter the same stage multiple times before completion. Moreover, each machine must be operated by a skilled worker, making it a dual-resource-constrained problem according to the existing literature. The objective is to minimise the total length of the production schedule. To address this problem, our study employs two methods: a constraint programming model and a hybrid genetic algorithm with a single-level solution representation and an efficient decoding heuristic. To evaluate the performance of our methods, we conducted a computational study using different problem instances. Our findings demonstrate that the proposed hybrid genetic algorithm consistently delivers high-quality solutions, particularly for large instances, while also maintaining a short computational time. Additionally, our methods improve existing benchmark results for instances from the literature for a subclass of the problem. Furthermore, we provide managerial insights into how dual-resource constraints affect the solution quality and the efficiency associated with different workforce configurations in the described production setting.

State estimation for constant-time labeled automata under dense time

In this paper, we focus on state estimation for constant-time labeled automata in a dense time context, i.e., the time constraints of the automata can be given according to real numbers. Given a sequence of timed observations (i.e., pairs of logical observations with their time stamps) collected from a system within a finite time window, a state estimation method is proposed to find the set of states in which the system might reside by the end of the time window. By using both labeling and timing information as well as the structure of the system, we can express any finite time evolution from one state to another into constraint satisfaction problems (CSPs). This structural analysis is independent of all collected sequences of timed observations and can be achieved offline, although its cost is exponential with respect to the number of states in the system. Consequently, two algorithms are designed to perform state estimation under a single observation and no observation, respectively, by solving a finite number of CSPs generated according to the system’s structural information. Both algorithms can be jointly used in an iterative approach to perform state estimation for any sequence of timed observations. In such a case, the number of generated CSPs in the algorithms increases linearly with respect to the length of the observed sequence.

Clustering bike sharing stations using Quantum Machine Learning: A case study of Toronto, Canada

Quantum Machine Learning (QML) is a field that combines the principles of Quantum Computing (QC) and Machine Learning (ML). QC works by taking advantage of the properties of quantum physics, such as superposition and entanglement. To fully realize the potential of this technology, more research is necessary, as the field of QML is still in its early stages. Since QC technologies and devices continue to develop quickly, it is important to identify the use cases and applications that benefit the most. This paper investigates the potentials of QC, and more specifically, Quantum Annealing (QA), for clustering real-world data in transportation systems. The Bike Sharing System (BSS) is used as a case study applying a clustering model on QA computers. The main contribution of this research is to introduce a hybrid model to cluster stations in a BSS by solving it as a Constraint Satisfaction Problem (CSP) problem with different methods on a QA computer using a real-time dataset. In addition to the practical contribution, this research also offers theoretical advancements in the field of computational optimization by defining a new topology for the input data that is compatible with QC topology (e.g., Chimera topology). The goal of real-time clustering BSS stations based on dynamic and static datasets is, in fact, to assist decision-makers in better managing and minimizing the risk of bike unavailability at each station and rebalancing bikes shared. Three different methods have been used to determine the number of clusters, and Euclidean, Manhattan, Pearson, and Spearman dissimilarity functions have been applied to cluster the stations. The evaluation is done using the magnitude vs. cardinality approach. The distribution of the stations, magnitude, and cardinality of the results indicate the potential to use QC for clustering for a real-world application, e.g., BSS.

Automated Verification of Higher-Order Probabilistic Programs via a Dependent Refinement Type System

Verification of higher-order probabilistic programs is a challenging problem. We present a verification method that supports several quantitative properties of higher-order probabilistic programs. Usually, extending verification methods to handle the quantitative aspects of probabilistic programs often entails extensive modifications to existing tools, reducing compatibility with advanced techniques developed for qualitative verification. In contrast, our approach necessitates only small amounts of modification, facilitating the reuse of existing techniques and implementations. On the theoretical side, we propose a dependent refinement type system for a generalised higher-order fixed point logic (HFL). Combined with continuation-passing style encodings of properties into HFL, our dependent refinement type system enables reasoning about several quantitative properties, including weakest pre-expectations, expected costs, moments of cost, and conditional weakest pre-expectations for higher-order probabilistic programs with continuous distributions and conditioning. The soundness of our approach is proved in a general setting using a framework of categorical semantics so that we don’t have to repeat similar proofs for each individual problem. On the empirical side, we implement a type checker for our dependent refinement type system that reduces the problem of type checking to constraint solving. We introduce admissible predicate variables and integrable predicate variables to constrained Horn clauses (CHC) so that we can soundly reason about the least fixed points and samplings from probability distributions. Our implementation demonstrates that existing CHC solvers developed for non-probabilistic programs can be extended to a solver for the extended CHC with only small efforts. We also demonstrate the ability of our type checker to verify various concrete examples.

On the Complexity of Symmetric vs. Functional PCSPs

The complexity of the promise constraint satisfaction problem \(\operatorname{(PCSP)}(\mathbf{A},\mathbf{B})\) is largely unknown, even for symmetric \(\mathbf{A}\) and \(\mathbf{B}\) , except for the case when \(\mathbf{A}\) and \(\mathbf{B}\) are Boolean. First, we establish a dichotomy for \(\operatorname{PCSP}(\mathbf{A},\mathbf{B})\) where \(\mathbf{A},\mathbf{B}\) are symmetric, \(\mathbf{B}\) is functional (i.e., any \(r-1\) elements of an \(r\) -ary tuple uniquely determines the last one), and \((\mathbf{A},\mathbf{B})\) satisfies technical conditions we introduce called dependency and additivity . This result implies a dichotomy for \(\operatorname{PCSP}(\mathbf{A},\mathbf{B})\) with \(\mathbf{A},\mathbf{B}\) symmetric and \(\mathbf{B}\) functional if (i) \(\mathbf{A}\) is Boolean, or (ii) \(\mathbf{A}\) is a hypergraph of a small uniformity, or (iii) \(\mathbf{A}\) has a relation \(R^{\mathbf{A}}\) of arity at least three such that the hypergraph diameter of \((A,R^{\mathbf{A}})\) is at most one. Second, we show that for \(\operatorname{PCSP}(\mathbf{A},\mathbf{B})\) , where \(\mathbf{A}\) and \(\mathbf{B}\) contain a single relation, \(\mathbf{A}\) satisfies a technical condition called balancedness , and \(\mathbf{B}\) is arbitrary, the combined basic linear programming relaxation and the affine integer programming (AIP) relaxation is no more powerful than the (in general strictly weaker) \({{\rm AIP}}\) relaxation. Balanced \(\mathbf{A}\) include symmetric \(\mathbf{A}\) or, more generally, \(\mathbf{A}\) preserved by a transitive permutation group.

Industrial multi-resource flexible job shop scheduling with partially necessary resources

This paper is dedicated to the study of industrial extensions of the flexible job shop scheduling problem with multiple resources in order to propose an alternative to expensive optimization software for small to medium-sized manufacturing companies. In this context, we propose a generic model able to tackle some constraints often found in industrial scheduling problems. This model tackles partially necessary resources by decomposing operations into stages. Instances are solved by a simulated annealing metaheuristic which is further improved using efficient conditions to filter non-interesting solutions. We compare our approach to a constraint programming model using a commercial solver. Extensive experiments and statistical analysis show that our method is competitive and of practical use in the industrial context.

Polynomial Time Linear Programs for Hard Constraint Satisfaction Problems

Polynomial Time Linear Programs for Hard Constraint Satisfaction Problems

Advanced constraint programming formulations for additive manufacturing machine scheduling problems

In comparison with traditional subtractive manufacturing techniques, additive manufacturing (AM) enables fabricating complex parts through a layer-by-layer process. AM makes it possible to produce one-piece and lightweight functional products, which are traditionally made from several parts. This paper introduces constraint programming (CP) models to minimise makespan in single, parallel identical and parallel unrelated AM machine scheduling environments for selective laser melting. Alternative CP formulations are explored to improve efficiency. The proposed CP model significantly benefits from the introduction of interval variables to replace binary assignment variables, and pre-definitions to narrow the search space, resulting in increased search performance. A computational study has been conducted to compare the performance of our proposed CP model with both a mixed-integer programming and a genetic algorithm from existing literature, evaluating improvements made to its search capability. Computational results indicate that the proposed CP model can obtain high-quality solutions in a timely manner even for several large-size instances.

Projection methods for finding the greatest element of the intersection of max-closed convex sets

We focus on the problem of finding the greatest element of the intersection of max-closed convex sets. For this purpose, we analyze the famous method of cyclic projections and show that, if this method is suitably initialized and applied to max-closed convex sets, it converges to the greatest element of their intersection. Moreover, we propose another projection method, called the decreasing projection, which turns out both theoretically and practically preferable to Euclidean projections in this particular case. Next, we argue that several known algorithms, such as Bellman-Ford and Floyd-Warshall algorithms for shortest paths or Gauss-Seidel variant of value iteration in Markov decision processes, can be interpreted as special cases of iteratively applying decreasing projections onto certain max-closed convex sets. Finally, we link decreasing projections (and thus also the aforementioned algorithms) to bounds consistency in constraint programming.

Real-time Physically Guided Hair Interpolation

Strand-based hair simulations have recently become increasingly popular for a range of real-time applications. However, accurately simulating the full number of hair strands remains challenging. A commonly employed technique involves simulating a subset of guide hairs to capture the overall behavior of the hairstyle. Details are then enriched by interpolation using linear skinning. Hair interpolation enables fast real-time simulations but frequently leads to various artifacts during runtime. As the skinning weights are often pre-computed, substantial variations between the initial and deformed shapes of the hair can cause severe deviations in fine hair geometry. Straight hairs may become kinked, and curly hairs may become zigzags. This work introduces a novel physical-driven hair interpolation scheme that utilizes existing simulated guide hair data. Instead of directly operating on positions, we interpolate the internal forces from the guide hairs before efficiently reconstructing the rendered hairs based on their material model. We formulate our problem as a constraint satisfaction problem for which we present an efficient solution. Further practical considerations are addressed using regularization terms that regulate penetration avoidance and drift correction. We have tested various hairstyles to illustrate that our approach can generate visually plausible rendered hairs with only a few guide hairs and minimal computational overhead, amounting to only about 20% of conventional linear hair interpolation. This efficiency underscores the practical viability of our method for real-time applications.

The Two-Echelon for Meat Products Location-Routing Problem with Picking Up and Delivery by Using Constraint Programming

The Two-Echelon for Meat Products Location-Routing Problem with Picking Up and Delivery by Using Constraint Programming

A constraint programming framework for preliminary mission analysis: Applications for constellation-servicing active debris removal

Constraint Programming is a classical artificial intelligence paradigm characterised by its flexibility for the modelling of complex problems. In the field of space operations, this approach has been successfully used for mission planning and scheduling. This manuscript proposes a framework that leverages the strengths of Constraint Programming for the preliminary analysis of space missions, introducing some modifications to tailor it to the application at hand. Specifically, it uses constraint propagation and search techniques to thoroughly explore the configuration space of a mission in an efficient manner. Consequently, it is able to quantify the performance of precomputed mission choices with respect to the mission requirements, as well as generate new ones that optimise such performance. The proposed methodology has been particularised for two application cases involving active debris removal missions for large constellations in low Earth orbit, namely, a chaser case and a mothership case. The chaser case considers a servicing satellite that rendezvouses with the failed satellites of the constellation and directly transports them to a disposal orbit. The mothership case comprises a servicing satellite that installs deorbiting kits in each of the failed satellites, except for the one removed in the last place. This way, the servicing satellite will only transport this object, while the deorbiting kits will carry out the disposal of the rest of them. This methodology has been successfully used to evaluate a preliminary mission analysis of both application cases developed under ESA’s Sunrise project.

Applying constraint programming to minimal lottery designs

AbstractWe develop and deploy a set of constraints for the purpose of calculating minimal sizes of lottery designs. Specifically, we find the minimum number of tickets of size six which are needed to match at least two balls on any draw of size six, whenever there are at most 70 balls.

An adapted constraint‐programming formulation of the resource‐constrained project scheduling problem applied to the identical parallel machines group shop and mixed shop scheduling problems

AbstractIn this paper, we study the group shop and the mixed shop scheduling problems with single and identical parallel machines at each workstation with the makespan criterion. We adapted a constraint programming formulation previously presented for the classical resource‐constrained project scheduling problem. The effectiveness of our approach is evident in the fact that it achieved optimality in 107 out of 130 classical group shop scheduling problem instances and in 320 classical mixed shop scheduling problem instances. In the last set, we obtained 13 new optimal solutions.

A Constraint Programming Approach for Discrete Time–Cost Tradeoff Problems in a Time-Constrained Activity Network

The discrete time-cost tradeoff problem (DTCTP) is a well-researched topic in the field of operations research. The majority of existing DTCTP models are based on traditional activity networks, which permit the execution of an activity as soon as all its predecessors have been completed. This assumption is reasonable, but it is important to note that there are always exceptions. The main work of this study was threefold. Firstly, we expanded the analysis of the DTCTP to encompass time-constrained activity networks (DTCTPTC), which encompassed three different types of time constraints. The first constraint was the time-window constraint, which limited the time interval during which an activity could be executed. The second constraint was the time-schedule constraint, which specified the times at which an activity could begin execution. The third constraint was the time-switch constraint, which required project activities to start at specific times and remain inactive during designated time periods. Secondly, a constraint programming (CP) model was developed for the purpose of solving the DTCTPTC. The model employed interval variables to define the activity and its potential time constraints, while CP expressions were utilized to ensure the feasibility of the solution. The objective was to identify the optimal execution mode for each activity, the optimal start times for time-scheduled activities, and the optimal work/rest patterns for time-switch activities, with the aim of minimizing the total cost of the project. Finally, the efficacy of the proposed CP model was validated through two case studies based on two illustrative projects of varying sizes. The outcomes were then compared against existing algorithms. The results demonstrated that time constraints were important factors affecting schedule optimization, and the proposed CP model had the ability to solve large-scale DTCTPTC.

Scheduling of Automated Wet-Etch Stations with One Robot in Semiconductor Manufacturing via Constraint Answer Set Programming

Scheduling and optimization have a central place in the research area of computing because it is increasingly important to achieve fully automated production processes to adjust manufacturing systems to the requirements of Industry 4.0. In this paper, we demonstrate how an automated wet-etch scheduling problem for the semiconductor industry can be solved by constraint answer set programming (CASP) and its solver called clingcon. A successful solution to this problem is achieved, and we found that for all tested problems, CASP is faster and obtains smaller makespan values for seven of the eight problems tested than the solutions based on mixed integer linear programming and constraint paradigms. The considered scheduling problem includes a robot for lot transfers between baths. CASP is a hybrid approach in automated reasoning that combines different research areas such as answer set programming, constraint processing, and Satisfiability Modulo Theories. For a long time, exact methods such as constraint programming have displayed difficulties in solving real large-scale problem instances. Currently, the performance of state-of-the-art constraint solvers is comparatively better than a decade ago, and some complex combinatorial problems can be better solved. These theoretical and technical achievements open new horizons for declarative programming applications such as logistics.