Abstract In the last decade, numerous algorithms for single-objective Boolean optimization have been proposed that rely on the iterative usage of a highly effective Propositional Satisfiability (SAT) solver. But the use of SAT solvers in Multi-Objective Combinatorial Optimization (MOCO) algorithms is scarce. Due to the shortage of efficient tools for MOCO, many real-world applications formulated as multi-objective are cast as single-objective, using either a linear combination or by setting a preference order among the objectives. In this paper, we extend the state of the art of MOCO solvers with three novel unsatisfiability-based algorithms. The first two are core-guided MOCO solvers. The third is a hitting set MOCO solver. Experimental results in several sets of benchmark instances show that our new unsatisfiability-based algorithms can outperform and complement other SAT-based, state-of-the-art algorithms for MOCO.

Abstract The issue of fairness is a well-known challenge in Machine Learning (ML) that has gained increased importance with the emergence of Large Language Models (LLMs) and generative AI. Algorithmic bias can manifest during the training of ML models due to the presence of sensitive attributes, such as gender or racial identity. One approach to mitigate bias is to avoid making decisions based on these protected attributes. However, indirect discrimination can still occur if sensitive information is inferred from proxy attributes. To prevent this, there is a growing interest in detecting potential proxy attributes before training ML models. In this case study, we report on the use of Inductive Logic Programming (ILP) to discover proxy attributes in training datasets, with a focus on the ML classification problem. While ILP has established applications in program synthesis and data curation, we demonstrate that it can also advance the state of the art in proxy attribute discovery by removing the need for prior domain knowledge. Our evaluation shows that this approach is effective at detecting potential sources of indirect discrimination, having successfully identified proxy attributes in several well-known datasets used in fairness-awareness studies.

Following the successful use of Propositional Satisfiability (SAT) algorithms in Boolean optimization (e.g., Maximum Satisfiability), several SAT-based algorithms have been proposed for Multi-Objective Combinatorial Optimization (MOCO). However, these new algorithms either provide a small subset of the Pareto front or follow a more exploratory search procedure and the solutions found are usually distant from the Pareto front. We extend the state of the art with a new SAT-based MOCO solver, Slide and Drill (Slide&Drill), that hones an upper bound set of the exact solution. Moreover, we show that Slide&Drill neatly complements proposed UNSAT-SAT algorithms for MOCO. These algorithms can work in tandem over the same shared "blackboard" formula, in order to enable a faster convergence. Experimental results in several sets of benchmark instances show that Slide&Drill can outperform other SAT-based algorithms for MOCO, in particular when paired with previously proposed UNSAT-SAT algorithms.

This paper proposes an iterative Maximum Satisfiability (MaxSAT) approach designed to solve train scheduling optimization problems. The generation of railway timetables is known to be intractable for a single track. We consider hundreds of trains on interconnected multi-track railway networks with complex connections between trains. Furthermore, the proposed algorithm is incremental to reduce the impact of time discretization. The performance of our approach is evaluated with the real-world Swiss Federal Railway (SBB) Crowd Sourcing Challenge benchmark and Periodic Event Scheduling Problems benchmark (PESPLib). The execution time of the proposed approach is shown to be, on average, twice as fast as the best existing solution for the SBB instances. In addition, we achieve a significant improvement over SAT-based solutions for solving the PESPLib instances. We also analyzed real schedule data from Switzerland and the Netherlands to create a disruption generator based on probability distributions. The novel incremental algorithm allows solving the train scheduling problem under disruptions with better performance than traditional algorithms.

To keep up with changes in requirements, frameworks, and coding practices, software organizations might need to migrate code from one language to another. Source-to-source migration, or transpilation, is often a complex, manual process. Transpilation requires expertise both in the source and target language, making it highly laborious and costly. Languages models for code generation and transpilation are becoming increasingly popular. However, despite capturing code-structure well, code generated by language models is often spurious and contains subtle problems. We propose BatFix , a novel approach that augments language models for transpilation by leveraging program repair and synthesis to fix the code generated by these models. BatFix takes as input both the original program, the target program generated by the machine translation model, and a set of test cases and outputs a repaired program that passes all test cases. Experimental results show that our approach is agnostic to language models and programming languages. BatFix can locate bugs spawning multiple lines and synthesize patches for syntax and semantic bugs for programs migrated from Java to C++ and Python to C++ from multiple language models, including, OpenAI’s Codex .

Software developers often struggle to update APIs, leading to manual, time-consuming, and error-prone processes. We introduce Melt, a new approach that generates lightweight API migration rules directly from pull requests in popular library repositories. Our key insight is that pull requests merged into open-source libraries are a rich source of information sufficient to mine API migration rules. By leveraging code examples mined from the library source and automatically generated code examples based on the pull requests, we infer transformation rules in Comby, a language for structural code search and replace. Since inferred rules from single code examples may be too specific, we propose a generalization procedure to make the rules more applicable to client projects. Melt rules are syntax-driven, interpretable, and easily adaptable. Moreover, unlike previous work, our approach enables rule inference to seamlessly integrate into the library workflow, removing the need to wait for client code migrations. We evaluated Melt on pull requests from four popular libraries, successfully mining 461 migration rules from code examples in pull requests and 114 rules from auto-generated code examples. Our generalization procedure increases the number of matches for mined rules by 9×. We applied these rules to client projects and ran their tests, which led to an overall decrease in the number of warnings and fixing some test cases demonstrating MELT's effectiveness in real-world scenarios.

Abstract In the last decade, numerous algorithms for single-objective Boolean optimization have been proposed that rely on the iterative usage of a highly effective Propositional Satisfiability (SAT) solver. But the use of SAT solvers in Multi-Objective Combinatorial Optimization (MOCO) algorithms is still scarce. Due to this shortage of efficient tools for MOCO, many real-world applications formulated as multi-objective are simplified to single-objective, using either a linear combination or a lexicographic ordering of the objective functions to optimize. In this paper, we extend the state of the art of MOCO solvers with two novel unsatisfiability-based algorithms. The first is a core-guided MOCO solver. The second is a hitting set-based MOCO solver. Experimental results in several sets of benchmark instances show that our new unsatisfiability-based algorithms can outperform state-of-the-art SAT-based algorithms for MOCO.

Based on environmental and species monitoring data, Species Distribution Modelling (SDM) tries to build a model to predict the distribution of a species across a geographic area. These models can then be used to manage the activities in the area in order to prevent negative economic and environmental impacts. In marine ecosystems, SDM can be used to regulate fishing practices or manage protected areas. This paper presents DeepData, a new no-code web-based machine learning platform to facilitate the work of marine biologists with SDM. The DeepData tool enables to automate SDM, by automating the creation and validation of the model by marine biologists. Biologists mostly use probabilistic algorithms, such as maximum entropy, generalized linear models and generalized additive models. The DeepData tool also allows the use of machine learning algorithms, such as classification and regression trees, random forests and support vector machines. Moreover, besides the usage of machine learning algorithms, other steps in SDM, such as data preparation and model evaluation, are also discussed in the paper. Furthermore, a concrete explanation of the use of the DeepData tool is presented, as well as the details of implementation and evaluation.

Congestion Control Algorithms (CCAs) impact numerous desirable Internet properties such as performance, stability, and fairness. Hence, the networking community invests substantial effort into studying whether new algorithms are safe for wide-scale deployment. However, operators today are continuously innovating and some deployed CCAs are unpublished - either because the CCA is in beta or because it is considered proprietary. How can the networking community evaluate these new CCAs when their inner workings are unknown?

With the growth of the open-source data science community, both the number of data science libraries and the number of versions for the same library are increasing rapidly. To match the evolving APIs from those libraries, open-source organizations often have to exert manual effort to refactor the APIs used in the code base. Moreover, due to the abundance of similar open-source libraries, data scientists working on a certain application may have an abundance of libraries to choose, maintain and migrate between. The manual refactoring between APIs is a tedious and error-prone task. Although recent research efforts were made on performing automatic API refactoring between different languages, previous work relies on statistical learning with collected pairwise training data for the API matching and migration. Using large statistical data for refactoring is not ideal because such training data will not be available for a new library or a new version of the same library. We introduce Synthesis for Open-Source API Refactoring (SOAR), a novel technique that requires no training data to achieve API migration and refactoring. SOAR relies only on the documentation that is readily available at the release of the library to learn API representations and mapping between libraries. Using program synthesis, SOAR automatically computes the correct configuration of arguments to the APIs and any glue code required to invoke those APIs. SOAR also uses the interpreter's error messages when running refactored code to generate logical constraints that can be used to prune the search space. Our empirical evaluation shows that SOAR can successfully refactor 80% of our benchmarks corresponding to deep learning models with up to 44 layers with an average run time of 97.23 seconds, and 90% of the data wrangling benchmarks with an average run time of 17.31 seconds.

Abstract Form validators based on regular expressions are often used on digital forms to prevent users from inserting data in the wrong format. However, writing these validators can pose a challenge to some users. We presentForest, a regular expression synthesizer for digital form validations.Forestproduces a regular expression that matches the desired pattern for the input values and a set of conditions over capturing groups that ensure the validity of integer values in the input. Our synthesis procedure is based on enumerative search and uses a Satisfiability Modulo Theories (SMT) solver to explore and prune the search space. We propose a novel representation for regular expressions synthesis, multi-tree, which induces patterns in the examples and uses them to split the problem through a divide-and-conquer approach. We also present a new SMT encoding to synthesize capture conditions for a given regular expression. To increase confidence in the synthesized regular expression, we implement user interaction based on distinguishing inputs. We evaluatedForeston real-world form-validation instances using regular expressions. Experimental results show thatForestsuccessfully returns the desired regular expression in 70% of the instances and outperformsRegel, a state-of-the-art regular expression synthesizer.

Charts are commonly used for data visualization. Generating a chart usually involves performing data transformations, including data pre-processing and aggregation. These tasks can be cumbersome and time-consuming, even for experienced data scientists. Reproducing existing charts can also be a challenging task when information about data transformations is no longer available.

Current Maximum Satisfiability (MaxSAT) algorithms based on successive calls to a powerful Satisfiability (SAT) solver are now able to solve real-world instances in many application domains. Moreover, replacing the SAT solver with a Satisfiability Modulo Theories (SMT) solver enables effective MaxSMT algorithms. However, MaxSMT has seldom been used in debugging multi-threaded software.Multi-threaded programs are usually non-deterministic due to the huge number of possible thread operation schedules, which makes them much harder to debug than sequential programs. A recent approach to isolate the root cause of concurrency bugs in multi-threaded software is to produce a report that shows the differences between a failing and a non-failing execution. However, since they rely solely on heuristics, these reports can be unnecessarily large. Hence, reports may contain operations that are not relevant to the bug’s occurrence.This paper proposes the use of MaxSMT for the generation of minimal reports for multi-threaded software with concurrency bugs. The proposed techniques report situations that the existing techniques are not able to identify. Experimental results show that using MaxSMT can significantly improve the accuracy of the generated reports and, consequently, their usefulness in debugging the root cause of concurrency bugs.

Constraint-based reasoning methods thrive in solving problem instances with a tight solution space. On the other hand, evolutionary algorithms are usually effective when it is not hard to satisfy the problem constraints. This dichotomy has been observed in many optimization problems. In the particular case of Multi-Objective Combinatorial Optimization (MOCO), new recently proposed constraint-based algorithms have been shown to outperform more established evolutionary approaches when a given problem instance is hard to satisfy. In this paper, we propose the integration of constraint-based procedures in evolutionary algorithms for solving MOCO. First, a new core-based smart mutation operator is applied to individuals that do not satisfy all problem constraints. Additionally, a new smart improvement operator based on Minimal Correction Subsets is used to improve the quality of the population. Experimental results clearly show that the integration of these operators greatly improves multi-objective evolutionary algorithms MOEA/D and NSGAII. Moreover, even on problem instances with a tight solution space, the newly proposed algorithms outperform the state-of-the-art constraint-based approaches for MOCO.

Minimal Correction Subsets (MCSs) have been successfully applied to find approximate solutions to several real-world single-objective optimization problems. However, only recently have MCSs been used to solve Multi-Objective Combinatorial Optimization (MOCO) problems. In particular, it has been shown that all optimal solutions of MOCO problems with linear objective functions can be found by an MCS enumeration procedure. In this paper, we show that the approach of MCS enumeration can also be applied to MOCO problems where objective functions are divisions of linear expressions. Hence, it is not necessary to use a linear approximation of these objective functions. Additionally, we also propose the integration of diversification techniques on the MCS enumeration process in order to find better approximations of the Pareto front of MOCO problems. Finally, experimental results on the Virtual Machine Consolidation (VMC) problem show the effectiveness of the proposed techniques.

New constraint-based algorithms have been recently proposed to solve Multi-Objective Combinatorial Optimization (MOCO) problems. These new methods are based on Minimal Correction Subsets (MCSs) or P-minimal models and have shown to be successful at solving MOCO instances when the constraint set is hard to satisfy. However, if the constraints are easy to satisfy, constraint-based tools usually do not perform as well as stochastic methods. For solving such instances, algorithms should focus on dealing with the objective functions. This paper proposes the integration of stratification techniques in constraint-based algorithms for MOCO. Moreover, it also shows how to diversify the stratification among the several objective criteria in order to better approximate the Pareto front of MOCO problems. An extensive experimental evaluation on publicly available MOCO instances shows that the new algorithm is competitive with stochastic methods and it is much more effective than existing constraint-based methods.

A Minimal Correction Subset (MCS) of an unsatisfiable constraint set is a minimal subset of constraints that, if removed, makes the constraint set satisfiable. MCSs enjoy a wide range of applications, such as finding approximate solutions to constrained optimization problems. However, existing work on applying MCS enumeration to optimization problems focuses on the single-objective case. In this work, Pareto Minimal Correction Subsets (Pareto-MCSs) are proposed for approximating the Pareto-optimal solution set of multi-objective constrained optimization problems. We formalize and prove an equivalence relationship between Pareto-optimal solutions and Pareto-MCSs. Moreover, Pareto-MCSs and MCSs can be connected in such a way that existing state-of-the-art MCS enumeration algorithms can be used to enumerate Pareto-MCSs. Finally, experimental results on the multi-objective virtual machine consolidation problem show that the Pareto-MCS approach is competitive with state-of-the-art algorithms.

The most successful parallel SAT and MaxSAT solvers follow a portfolio approach, where each thread applies a different algorithm (or the same algorithm configured differently) to solve a given problem instance. The main goal of building a portfolio is to diversify the search process being carried out by each thread. As soon as one thread finishes, the instance can be deemed solved. In this paper we present a new open source distributed solver for MaxSAT solving that addresses two issues commonly found in multicore parallel solvers, namely memory contention and scalability. Preliminary results show that our nonportfolio distributed MaxSAT solver outperforms its sequential version and is able to solve more instances in several instance sets as the number of processes increases.

Linear search algorithms have been shown to be particularly effective for solving partial Maximum Satisfiability (MaxSAT) problem instances. These algorithms start by adding a new relaxation variable to each soft clause and solving the resulting formula with a SAT solver. Whenever a Model is found, a new constraint on the relaxation variables is added such that Models with a greater or equal value are excluded. However, if the problem instance has a large number of relaxation variables, then adding a new constraint over these variables can lead to the exploration of a much larger search space. This article proposes new algorithms to improve the performance of linear search algorithms for MaxSAT by using Models found by the SAT solver to partition the relaxation variables. These algorithms add a new constraint on a subset of relaxation variables, thus intensifying the search on that subspace. In addition, the proposed algorithms are further enhanced by using incremental approaches where learned clauses are kept between calls to the SAT solver. Experimental results show that Model-based algorithms can outperform a classic linear search algorithm in several problem instances. Moreover, incremental approaches further improve the performance of linear search and Model-based algorithms for MaxSAT. Overall, Model-based algorithms are competitive with state-of-the-art MaxSAT solvers, and can improve their performance when solving problem instances with a large number of soft clauses.

Maximum Satisfiability (MaxSAT) is a well-known optimization version of Propositional Satisfiability (SAT), that finds a wide range of relevant practical applications. Despite the significant progress made in MaxSAT solving in recent years, many practically relevant problem instances require prohibitively large run times, and many cannot simply be solved with existing algorithms. One approach for solving MaxSAT is based on iterative SAT solving, which may optionally be guided by unsatisfiable cores. A difficulty with this class of algorithms is the possibly large number of times a SAT solver is called, e.g. for instances with very large clause weights. This paper proposes the use of geometric progressions to tackle this issue, thus allowing, for the vast majority of problem instances, to reduce the number of calls to the SAT solver. The new approach is also shown to be applicable to core-guided MaxSAT algorithms. Experimental results, obtained on a large number of problem instances, show gains when compared to state-of-the-art implementations of MaxSAT algorithms.

Autarkies are partial truth assignments that satisfy all clauses having literals in the assigned variables. Autarkies provide important information in the analysis of unsatisfiable formulas. Indeed, clauses satisfied by autarkies cannot be included in minimal explanations or in minimal corrections of unsatisfiability. Computing the maximum autarky allows identifying all such clauses. In recent years, a number of alternative approaches have been proposed for computing a maximum autarky. This paper develops new models for representing autarkies, and proposes new algorithms for computing the maximum autarky. Experimental results, obtained on a large number of problem instances, show orders of magnitude performance improvements over existing approaches, and solving instances that could not otherwise be solved.

Cardinality constraints appear in many practical problems and have been well studied in the past. There are many CNF encodings for cardinality constraints, although it is not clear which encodings perform better. Indeed, different encodings can perform well over different problems. This paper examines a large number of cardinality encodings and evaluates their performance for solving the problem of Maximum Satisfiability (MaxSAT). Taking advantage of the diversification of cardinality encodings, we propose to exploit those encodings in parallel MaxSAT solving. Our parallel solver, pMAX, simultaneously searches in the lower and upper bound of the optimum value, and different cardinality encodings are used in each thread to increase the diversification of the search. Moreover, learned clauses are shared between threads during the search. Experimental results show that our parallel solver outperforms other sequential and parallel state-of-the-art MaxSAT solvers.

The extraction of a Minimal Unsatisfiable Core (MUC) in a Constraint Satisfaction Problem (CSP) aims to identify a subset of constraints that make a CSP instance unsatisfiable. Recent work has addressed the identification of a Minimal Set of Unsatisf

The last two decades progresses have led Propositional Satisfiability (SAT) to be a competitive practical approach to solve a wide range of industrial and academic problems. Thanks to these advances, the size and difficulty of the SAT instances have grown significantly. The demand for more computational power led to the creation of new computer architectures and paradigms composed by multiple machines connected by a network to act as one machine, like clusters and grids. However, extra computing power is not coming anymore from higher processor frequencies, but rather from a growing number of computing cores and processors. It becomes clear that exploiting this new architecture is essential for the evolution of SAT solvers. Search space splitting is probably the most commonly used strategy to explore the parallelism provided by the search space. However, it is not clear how to find the relevant set of variables to divide the search space. This paper extends a method based on the VSIDS heuristic to find the initial set of partition variables. A drawback of search space splitting is load balancing. To overcome this problem, we propose the use of a hybrid approach between search space splitting and portfolio. Preliminary results show that both these techniques improve the performance of the solver and reveal that combining search space splitting and portfolio approaches can lead to better results.

The installation of software packages depends on the correct resolution of dependencies and conflicts between packages. This problem is NP-complete and, as expected, is a hard task. Moreover, today's technology still does not address this problem in an acceptable way. This paper introduces a new approach to solving the software dependency problem in a Linux environment, devising a way for solving dependencies according to available packages and user preferences. This work introduces the "apt-pbo" tool, the first publicly available tool that solves dependencies in a complete and optimal way.

Boolean satisfiability (SAT) finds a wide range of practical applications, including Artificial Intelligence and, more recently, Bioinformatics. Although encoding some combinatorial problems using Boolean logic may not be the most intuitive solution, the efficiency of state-of-the-art SAT solvers often makes it worthwhile to consider encoding a problem to SAT. One representative application of SAT in Bioinformatics is haplotype inference. The problem of haplotype inference under the assumption of pure parsimony consists in finding the smallest number of haplotypes that explains a given set of genotypes. The original formulations for solving the problem of Haplotype Inference by Pure Parsimony (HIPP) were based on Integer Linear Programming. More recently, solutions based on SAT have been shown to be remarkably more efficient. This paper provides an overview of SAT-based approaches for solving the HIPP problem and identifies current research directions.

Recent advances in prepositional satisfiability (SAT) include studying the hidden structure of unsatisfiable formulas, i.e. explaining why a given formula is unsatisfiable. Although theoretical work on the topic has been developed in the past, only recently two empirical successful approaches have been proposed: extracting unsatisfiable cores and identifying strong backdoors. An unsatisfiable core is a subset of clauses that defines a subformula that is also unsatisfiable, whereas a strong backdoor defines a subset of variables which assigned with all values allow concluding that the formula is unsatisfiable. The contribution of This work is two-fold. First, we study the relation between the search complexity of unsatisfiable random 3-SAT formulas and the sizes of unsatisfiable cores and strong backdoors. For this purpose, we use an existing algorithm which uses an approximated approach for calculating these values. Second, we introduce a new algorithm that optimally reduces the size of unsatisfiable cores and strong backdoors, thus giving more accurate results. Experimental results indicate that the search complexity of unsatisfiable random 3-SAT formulas is related with the size of unsatisfiable cores and strong backdoors.

Preprocessing is an often used approach for solving hard instances of propositional satisfiability (SAT). Preprocessing can be used for reducing the number of variables and for drastically modifying the set of clauses, either by eliminating irrelevant clauses or by inferring new clauses. Over the years, a large number of formula manipulation techniques has been proposed, that in some situations have allowed solving instances not otherwise solvable with state-of-the-art SAT solvers. This paper proposes probing-based preprocessing, an integrated approach for preprocessing propositional formulas, that for the first time integrates in a single algorithm most of the existing formula manipulation techniques. Moreover, the new unified framework can be used to develop new techniques. Preliminary experimental results illustrate that probing-based preprocessing can be effectively used as a preprocessing tool in state-of-the-art SAT solvers.