Vasco Manquinho

ECAI Conference 2023 Conference Paper

Graph Neural Networks for Mapping Variables Between Programs

• Pedro Orvalho
• Jelle Piepenbrock
• Mikolás Janota
• Vasco Manquinho

Automated program analysis is a pivotal research domain in many areas of Computer Science — Formal Methods and Artificial Intelligence, in particular. Due to the undecidability of the problem of program equivalence, comparing two programs is highly challenging. Typically, in order to compare two programs, a relation between both programs’ sets of variables is required. Thus, mapping variables between two programs is useful for a panoply of tasks such as program equivalence, program analysis, program repair, and clone detection. In this work, we propose using graph neural networks (GNNs) to map the set of variables between two programs based on both programs’ abstract syntax trees (ASTs). To demonstrate the strength of variable mappings, we present three use-cases of these mappings on the task of program repair to fix well-studied and recurrent bugs among novice programmers in introductory programming assignments (IPAs). Experimental results on a dataset of 4166 pairs of incorrect/correct programs show that our approach correctly maps 83% of the evaluation dataset. Moreover, our experiments show that the current state-of-the-art on program repair, greatly dependent on the programs’ structure, can only repair about 72% of the incorrect programs. In contrast, our approach, which is solely based on variable mappings, can repair around 88. 5%.

SAT Conference 2023 Conference Paper

UpMax: User Partitioning for MaxSAT

• Pedro Orvalho
• Vasco Manquinho
• Ruben Martins

It has been shown that Maximum Satisfiability (MaxSAT) problem instances can be effectively solved by partitioning the set of soft clauses into several disjoint sets. The partitioning methods can be based on clause weights (e. g. , stratification) or based on graph representations of the formula. Afterwards, a merge procedure is applied to guarantee that an optimal solution is found. This paper proposes a new framework called UpMax that decouples the partitioning procedure from the MaxSAT solving algorithms. As a result, new partitioning procedures can be defined independently of the MaxSAT algorithm to be used. Moreover, this decoupling also allows users that build new MaxSAT formulas to propose partition schemes based on knowledge of the problem to be solved. We illustrate this approach using several problems and show that partitioning has a large impact on the performance of unsatisfiability-based MaxSAT algorithms.

SAT Conference 2022 Conference Paper

SAT-Based Leximax Optimisation Algorithms

• Miguel Cabral
• Mikolás Janota
• Vasco Manquinho

In several real-world problems, it is often the case that the goal is to optimise several objective functions. However, usually there is not a single optimal objective vector. Instead, there are many optimal objective vectors known as Pareto-optima. Finding all Pareto-optima is computationally expensive and the number of Pareto-optima can be too large for a user to analyse. A compromise can be made by defining an optimisation criterion that integrates all objective functions. In this paper we propose several SAT-based algorithms to solve multi-objective optimisation problems using the leximax criterion. The leximax criterion is used to obtain a Pareto-optimal solution with a small trade-off between the objective functions, which is suitable in problems where there is an absence of priorities between the objective functions. Experimental results on the Multi-Objective Package Upgradeability Optimisation problem show that the SAT-based algorithms are able to outperform the Integer Linear Programming (ILP) approach when using non-commercial ILP solvers. Additionally, experimental results on selected instances from the MaxSAT evaluation adapted to the multi-objective domain show that our approach outperforms the ILP approach using commercial solvers.

AAAI Conference 2019 Conference Paper

Concurrency Debugging with MaxSMT

• Miguel Terra-Neves
• Nuno Machado
• Ines Lynce
• Vasco Manquinho

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.

IJCAI Conference 2019 Conference Paper

Integrating Pseudo-Boolean Constraint Reasoning in Multi-Objective Evolutionary Algorithms

• Miguel Terra-Neves
• Inês Lynce
• Vasco Manquinho

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.

AAAI Conference 2018 Conference Paper

Enhancing Constraint-Based Multi-Objective Combinatorial Optimization

• Miguel Terra-Neves
• Inês Lynce
• Vasco Manquinho

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.

IJCAI Conference 2018 Conference Paper

Multi-Objective Optimization Through Pareto Minimal Correction Subsets

• Miguel Terra-Neves
• Inês Lynce
• Vasco Manquinho

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.

IJCAI Conference 2018 Conference Paper

Stratification for Constraint-Based Multi-Objective Combinatorial Optimization

• Miguel Terra-Neves
• Inês Lynce
• Vasco Manquinho

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.

SAT Conference 2017 Conference Paper

Introducing Pareto Minimal Correction Subsets

• Miguel Terra-Neves
• Inês Lynce
• Vasco Manquinho

Abstract 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, one of them being 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, a first definition of Pareto Minimal Correction Subsets (Pareto-MCSs) is proposed with the goal of 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. An experimental evaluation considers the multi-objective virtual machine consolidation problem. Results show that the proposed Pareto-MCS approach outperforms the state-of-the-art approaches.

SAT Conference 2015 Conference Paper

Exploiting Resolution-Based Representations for MaxSAT Solving

• Miguel Terra-Neves
• Ruben Martins
• Mikolás Janota
• Inês Lynce
• Vasco Manquinho

Abstract Most recent MaxSAT algorithms rely on a succession of calls to a SAT solver in order to find an optimal solution. In particular, several algorithms take advantage of the ability of SAT solvers to identify unsatisfiable subformulas. Usually, these MaxSAT algorithms perform better when small unsatisfiable subformulas are found in early iterations of the algorithm. However, this is not the case in many problem instances, since the whole formula is given to the SAT solver in each call. In this paper, we propose to partition the MaxSAT formula using a resolution-based graph representation. Partitions are then iteratively joined by using a proximity measure extracted from the graph representation of the formula. The algorithm ends when only one partition remains and the optimal solution is found. Experimental results show that this new approach further enhances a state of the art MaxSAT solver to optimally solve a larger set of industrial problem instances.

ECAI Conference 2014 Conference Paper

Efficient Autarkies

• João Marques-Silva 0001
• Alexey Ignatiev
• António Morgado 0001
• Vasco Manquinho
• Inês Lynce

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.

SAT Conference 2014 Conference Paper

Open-WBO: A Modular MaxSAT Solver,

• Ruben Martins
• Vasco Manquinho
• Inês Lynce

Abstract This paper presents open-wbo, a new MaxSAT solver. open-wbo has two main features. First, it is an open-source solver that can be easily modified and extended. Most MaxSAT solvers are not available in open-source, making it hard to extend and improve current MaxSAT algorithms. Second, open-wbo may use any MiniSAT-like solver as the underlying SAT solver. As many other MaxSAT solvers, open-wbo relies on successive calls to a SAT solver. Even though new techniques are proposed for SAT solvers every year, for many MaxSAT solvers it is hard to change the underlying SAT solver. With open-wbo, advances in SAT technology will result in a free improvement in the performance of the solver. In addition, the paper uses open-wbo to evaluate the impact of using different SAT solvers in the performance of MaxSAT algorithms.

ECAI Conference 2014 Conference Paper

Progression in Maximum Satisfiability

• Alexey Ignatiev
• António Morgado 0001
• Vasco Manquinho
• Inês Lynce
• João Marques-Silva 0001

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.

SAT Conference 2013 Conference Paper

Community-Based Partitioning for MaxSAT Solving

• Ruben Martins
• Vasco Manquinho
• Inês Lynce

Abstract Unsatisfiability-based algorithms for Maximum Satisfiability (MaxSAT) have been shown to be very effective in solving several classes of problem instances. These algorithms rely on successive calls to a SAT solver, where an unsatisfiable subformula is identified at each iteration. However, in some cases, the SAT solver returns unnecessarily large subformulas. In this paper a new technique is proposed to partition the MaxSAT formula in order to identify smaller unsatisfiable subformulas at each call of the SAT solver. Preliminary experimental results analyze the effect of partitioning the MaxSAT formula into communities. This technique is shown to significantly improve the unsatisfiability-based algorithm for different benchmark sets.

ECAI Conference 2012 Conference Paper

On Partitioning for Maximum Satisfiability

• Ruben Martins
• Vasco Manquinho
• Inês Lynce

Partitioning formulas is motivated by the expectation to identify easy to solve subformulas, even though at the cost of having more formulas to solve. In this paper we suggest to apply partitioning to Maximum Satisfiability (MaxSAT), the optimization version of the well-known Satisfiability (SAT) problem. The use of partitions can be naturally combined with unsatisfiability-based algorithms for MaxSAT that are built upon successive calls to a SAT solver, where each call identifies an unsatisfiable subformula. One of the drawbacks of these algorithms results from the SAT solver returning large unsatisfiable subformulas. However, when using partitions, the solver is more likely to identify smaller unsatisfiable subformulas. Experimental results show that the use of partitions in MaxSAT significantly improves the performance of unsatisfiability-based algorithms.

SAT Conference 2010 Conference Paper

Improving Unsatisfiability-Based Algorithms for Boolean Optimization

• Vasco Manquinho
• Ruben Martins
• Inês Lynce

Abstract Recently, several unsatisfiability-based algorithms have been proposed for Maximum Satisfiability (MaxSAT) and other Boolean Optimization problems. These algorithms are based on being able to iteratively identify and relax unsatisfiable sub-formulas with the use of fast Boolean satisfiability solvers. It has been shown that this approach is very effective for several classes of instances, but it can perform poorly on others for which classical Boolean optimization algorithms find it easy to solve. This paper proposes the use of Pseudo-Boolean Optimization (PBO) solvers as a preprocessor for unsatisfiability-based algorithms in order to increase its robustness. Moreover, the use of constraint branching, a well-known technique from Integer Linear Programming, is also proposed into the unsatisfiability-based framework. Experimental results show that the integration of these features in an unsatisfiability-based algorithm results in an improved and more effective solver for Boolean optimization problems.

SAT Conference 2009 Conference Paper

Algorithms for Weighted Boolean Optimization

• Vasco Manquinho
• João Marques-Silva 0001
• Jordi Planes

Abstract The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT). In the recent past, different algorithms have been proposed for PBO and for MaxSAT, despite the existence of straightforward mappings from PBO to MaxSAT, and vice-versa. This papers proposes Weighted Boolean Optimization (WBO), a new unified framework that aggregates and extends PBO and MaxSAT. In addition, the paper proposes a new unsatisfiability-based algorithm for WBO, based on recent unsatisfiability-based algorithms for MaxSAT. Besides standard MaxSAT, the new algorithm can also be used to solve weighted MaxSAT and PBO, handling pseudo-Boolean constraints either natively or by translation to clausal form. Experimental results illustrate that unsatisfiability-based algorithms for MaxSAT can be orders of magnitude more efficient than existing dedicated algorithms. Finally, the paper illustrates how other algorithms for either PBO or MaxSAT can be extended to WBO.

LPAR Conference 2008 Conference Paper

Symmetry Breaking for Maximum Satisfiability

• João Marques-Silva 0001
• Inês Lynce
• Vasco Manquinho

Abstract Symmetries are intrinsic to many combinatorial problems including Boolean Satisfiability (SAT) and Constraint Programming (CP). In SAT, the identification of symmetry breaking predicates (SBPs) is a well-known, often effective, technique for solving hard problems. The identification of SBPs in SAT has been the subject of significant improvements in recent years, resulting in more compact SBPs and more effective algorithms. The identification of SBPs has also been applied to pseudo-Boolean (PB) constraints, showing that symmetry breaking can also be an effective technique for PB constraints. This paper extends further the application of SBPs, and shows that SBPs can be identified and used inMaximum Satisfiability (MaxSAT), as well as in its most well-known variants, including partial MaxSAT, weighted MaxSAT and weighted partial MaxSAT. As with SAT and PB, symmetry breaking predicates for MaxSAT and variants are shown to be effective for a representative number of problem domains, allowing solving problem instances that current state of the art MaxSAT solvers could not otherwise solve.

SAT Conference 2008 Conference Paper

Towards More Effective Unsatisfiability-Based Maximum Satisfiability Algorithms

• João Marques-Silva 0001
• Vasco Manquinho

Abstract The MaxSAT problem and some of its well-known variants find an increasing number of practical applications in a wide range of areas. Examples include different optimization problems in system design and verification. However, most MaxSAT problem instances from these practical applications are too hard for existing branch and bound algorithms. One recent alternative to branch and bound MaxSAT algorithms is based on unsatisfiable subformula identification. A number of different unsatisfiability-based MaxSAT algorithms have been developed, which are effective at solving different classes of problem instances. All MaxSAT algorithms based on unsatisfiable subformula identification require using additional Boolean variables, either to allow relaxing some of the clauses or to encode cardinality constraints used by these algorithms. As a result, these algorithms may require using a significant number of additional Boolean variables, that can exceed the original number of variables for some problem instances. This paper proposes techniques for effectively reducing the number of auxiliary variables that must be used in unsatisfiability-based MaxSAT algorithms. Experimental results indicate that the techniques for reducing the number of auxiliary variables are effective, and contribute to more efficient MaxSAT algorithms.

SAT Conference 2006 Conference Paper

Counting Models in Integer Domains

• António Morgado 0001
• Paulo J. Matos
• Vasco Manquinho
• João Marques-Silva 0001

Abstract This paper addresses the problem of counting models in integer linear programming (ILP) using Boolean Satisfiability (SAT) techniques, and proposes two approaches to solve this problem. The first approach consists of encoding ILP instances into pseudo-Boolean (PB) instances. Moreover, the paper introduces a model counter for PB constraints, which can be used for counting models in PB as well as in ILP. A second alternative approach consists of encoding instances of ILP into instances of SAT. A two-step procedure is proposed, consisting of first mapping the ILP instance into PB constraints and then encoding the PB constraints into SAT. One key observation is that not all existing PB to SAT encodings can be used for counting models. The paper provides conditions for PB to SAT encodings that can be safely used for model counting, and proves that some of the existing encodings are safe for model counting while others are not. Finally, the paper provides experimental results, comparing the PB and SAT approaches, as well as existing alternative solutions.

SAT Conference 2005 Conference Paper

On Applying Cutting Planes in DLL-Based Algorithms for Pseudo-Boolean Optimization

• Vasco Manquinho
• João Marques-Silva 0001

Abstract The utilization of cutting planes is a key technique in Integer Linear Programming (ILP). However, cutting planes have seldom been applied in Pseudo-Boolean Optimization (PBO) algorithms derived from the Davis-Logemann-Loveland (DLL) procedure for Propositional Satisfiability (SAT). This paper proposes the utilization of cutting planes in a DLL-style PBO algorithm, which incorporates the most effective techniques for PBO. We propose the utilization of cutting planes both during preprocessing and during the search process. Moreover, we also establish conditions that enable clause learning and non-chronological backtracking in the presence of conflicts involving constraints generated by cutting plane techniques. The experimental results, obtained on a large number of classes of instances, indicate that the integration of cutting planes with backtrack search is an extremely effective technique for PBO.

SAT Conference 2004 Conference Paper

Using Lower-Bound Estimates in SAT-Based Pseudo-Boolean Optimization

• Vasco Manquinho
• João Marques-Silva 0001

Linear Pseudo-Boolean constraints offer a much more compact formalism to express significant boolean problems in several areas, ranging from Artificial Intelligence to Electronic Design Automation. This paper proposes a new algorithm for the Pseudo-Boolean Optimization Problem (PBO) which integrates features from recent advances in Boolean Satisfiability (SAT) and classical branch and bound algorithms. Moreover, the paper shows that the utilization of lower bound estimates can improve the overall performance of PBO solvers for different classes of instances. In addition, the paper describes how to apply nonchronological backtracking in the presence of conflicts that result from the bounding process. Finally, the paper also shows how the notion of Unique Implication Points (UIP), widely used in modern SAT solvers, can be generalized for PBO.

ECAI Conference 2000 Conference Paper

Search Pruning Conditions for Boolean Optimization

• Vasco Manquinho
• João Marques-Silva 0001