Showing papers by "Barry O'Sullivan published in 2023"

Breaking Symmetry for Knowledge Compilation

Abstract: Constraint programming is a powerful paradigm for solving combinatorial problems. Diagnosis, planning, and product configuration, are example use-cases. While reasoning about the solution space of combinatorial problems is usually intractable, compilation methods are often used to pre-compute a representation that can answer queries in time that is polynomial in the representation size. Symmetry breaking constraints can be added to a combinatorial problem to eliminate symmetries and reduce the number of states to be explored. Finding compact representations is often the bottleneck of compilation methods. One approach that is sometimes used is partial compilation whereby a subset of the solutions of a set of constraints are compiled, e.g. those that are considered most important or most likely to be useful. In this paper we investigate if breaking symmetries always leads to a smaller compiled representation. We considered four compilers and four highly symmetrical problems. A reduction is observed in all the problems for the compilation size when we break symmetries, with top-down compilers seeing greater reduction.

Using Machine Learning Classifiers in SAT Branching [Extended Abstract]

Abstract: The Boolean Satisfiability Problem (SAT) can be framed as a binary classification task. Recently, numerous machine and deep learning techniques have been successfully deployed to predict whether a CNF has a solution. However, these approaches do not provide a variables assignment when the instance is satisfiable and have not been used as part of SAT solvers. In this work, we investigate the possibility of using a machine-learning SAT/UNSAT classifier to assign a truth value to a variable. A heuristic solver can be created by iteratively assigning one variable to the value that leads to higher predicted satisfiability. We test our approach with and without probing features and compare it to a heuristic assignment based on the variable's purity. We consider as objective the maximisation of the number of literals fixed before making the CNF unsatisfiable. The preliminary results show that this iterative procedure can consistently fix variables without compromising the formula's satisfiability, finding a complete assignment in almost all test instances.

The role of genetic algorithms in production scheduling

Abstract: The objective of this paper is to demonstrate the applicability of genetic algorithms to flowshop production scheduling. A summary of various conventional approaches to scheduling theory is presented, along with a discussion of the advantages and disadvantages associated with these methods. A description of the genetic algorithm proposed by this research is described in detailed. The proposed algorithm is compared to a typical heuristic (Least-Work-Remaining first) on a test problem. The proposed approach for implementing a genetic algorithm for production scheduling proves to be quite promising.

SAT Feature Analysis for Machine Learning Classification Tasks

Abstract: The extraction of meaningful features from CNF instances is crucial to applying machine learning to SAT solving, enabling algorithm selection and configuration for solver portfolios and satisfiability classification. While many approaches have been proposed for feature extraction, their relevance to these tasks is unclear. Their applicability and comparison of the information extracted and the computational effort needed are complicated by the lack of working or updated implementations, negatively affecting reproducibility. In this paper, we analyse the performance of five sets of features presented in the literature on SAT/UNSAT and problem category classification over a dataset of 3000 instances across ten problem classes distributed equally between SAT and UNSAT. To increase reproducibility and encourage research in this area, we released a Python library containing an updated and clear implementation of structural, graph-based, statistical and probing features presented in the literature for SAT CNF instances; and we define a clear pipeline to compare feature sets in a given learning task robustly. We analysed which of the computed features are relevant for the specific task and the tradeoff they provide between accuracy and computational effort. The results of the analysis provide insights into which features mostly affect an instance's satisfiability and which can be used to identify the problem's type. These insights can be used to develop more effective solver portfolios and satisfiability classification algorithms.