A Maximum Satisfiability Based Approach to Bi-Objective Boolean Optimization

Many real-world problem settings give rise to NP-hard combinatorial optimization problems. This results in a need for non-trivial algorithmic approaches for finding optimal solutions to such problems. Many such approaches—ranging from probabilistic and meta-heuristic algorithms to declarative programming—have been presented for optimization problems with a single objective. Less work has been done on approaches for optimization problems with multiple objectives. We present BiOptSat, an exact declarative approach for finding so-called Pareto-optimal solutions to bi-objective optimization problems. A bi-objective optimization problem arises for example when learning interpretable classifiers and the size, as well as the classification error of the classifier should be taken into account as objectives. Using propositional logic as a declarative programming language, we seek to extend the progress and success in maximum satisfiability (MaxSAT) solving to two objectives. BiOptSat can be viewed as an instantiation of the lexicographic method and makes use of a single SAT solver that is preserved throughout the entire search procedure. It allows for solving three tasks for bi-objective optimization: finding a single Pareto-optimal solution, finding one representative solution for each Pareto point, and enumerating all Pareto-optimal solutions. We provide an open-source implementation of five variants of BiOptSat, building on different algorithms proposed for MaxSAT. Additionally, we empirically evaluate these five variants, comparing their runtime performance to that of three key competing algorithmic approaches. The empirical comparison in the contexts of learning interpretable decision rules and bi-objective set covering shows practical benefits of our approach. Furthermore, for the best-performing variant of BiOptSat, we study the effects of proposed refinements to determine their effectiveness

MaxSAT-Based Bi-Objective Boolean Optimization

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Rapid generation of chromosome-specific alphoid DNA probes using the polymerase chain reaction

Non-isotopic in situ hybridization of chromosome-specific alphoid DNA probes has become a potent tool in the study of numerical aberrations of specific human chromosomes at all stages of the cell cycle. In this paper, we describe approaches for the rapid generation of such probes using the polymerase chain reaction (PCR), and demonstrate their chromosome specificity by fluorescence in situ hybridization to normal human metaphase spreads and interphase nuclei. Oligonucleotide primers for conserved regions of the alpha satellite monomer were used to generate chromosome-specific DNA probes from somatic hybrid cells containing various human chromosomes, and from DNA libraries from sorted human chromosomes. Oligonucleotide primers for chromosome-specific regions of the alpha satellite monomer were used to generate specific DNA probes for the pericentromeric heterochromatin of human chromosomes 1, 6, 7, 17 and X directly from human genomic DNA

MaxSAT-Based Bi-Objective Boolean Optimization

We explore a maximum satisfiability (MaxSAT) based approach to bi-objective optimization. Bi-objective optimization refers to the task of finding so-called Pareto-optimal solutions in terms of two objective functions. Bi-objective optimization problems naturally arise in various real-world settings. For example, in the context of learning interpretable representations, such as decision rules, from data, one wishes to balance between two objectives, the classification error and the size of the representation. Our approach is generally applicable to bi-objective optimizations which allow for propositional encodings. The approach makes heavy use of incremental Boolean satisfiability (SAT) solving and draws inspiration from modern MaxSAT solving approaches. In particular, we describe several variants of the approach which arise from different approaches to MaxSAT solving. In addition to computing a single representative solution per each point of the Pareto front, the approach allows for enumerating all Pareto-optimal solutions. We empirically compare the efficiency of the approach to recent competing approaches, showing practical benefits of our approach in the contexts of learning interpretable classification rules and bi-objective set covering

Preprocessing in SAT-Based Multi-Objective Combinatorial Optimization

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