Reducing chaos in SAT-like search: finding solutions close to a given one

Motivated by our own industrial users, we attack the following challenge that is crucial in many practical planning, scheduling or timetabling applications. Assume that a solver has found a solution for a given hard problem and, due to unforeseen circumstances (e.g., rescheduling), or after an analysis by a committee, a few more constraints have to be added and the solver has to be re-run. Then it is almost always important that the new solution is “close” to the original one. The activity-based variable selection heuristics used by SAT solvers make search chaotic, i.e., extremely sensitive to the initial conditions. Therefore, re-running with just one additional clause added at the end of the input usually gives a completely different solution. We show that naive approaches for finding close solutions do not work at all, and that solving the Boolean optimization problem is far too inefficient: to find a reasonably close solution, state-of-the-art tools typically require much more time than was needed to solve the original problem. Here we propose the first (to our knowledge) approach that obtains close solutions quickly. In fact, it typically finds the optimal (i.e., closest) solution in only 25% of the time the solver took in solving the original problem. Our approach requires no deep theoretical or conceptual innovations. Still, it is non-trivial to come up with and will certainly be valuable for researchers and practitioners facing the same problem.Postprint (published version

ROAD-R: The autonomous driving dataset with logical requirements

Neural networks have proven to be very powerful at computer vision tasks. However, they often exhibit unexpected behaviours, violating known requirements expressing background knowledge. This calls for models (i) able to learn from the requirements, and (ii) guaranteed to be compliant with the requirements themselves. Unfortunately, the development of such models is hampered by the lack of datasets equipped with formally specified requirements. In this paper, we introduce the ROad event Awareness Dataset with logical Requirements (ROAD-R), the first publicly available dataset for autonomous driving with requirements expressed as logical constraints. Given ROAD-R, we show that current state-of-the-art models often violate its logical constraints, and that it is possible to exploit them to create models that (i) have a better performance, and (ii) are guaranteed to be compliant with the requirements themselves

Solving hard industrial combinatorial problems with SAT

The topic of this thesis is the development of SAT-based techniques and tools for solving industrial combinatorial problems. First, it describes the architecture of state-of-the-art SAT and SMT Solvers based on the classical DPLL procedure. These systems can be used as black boxes for solving combinatorial problems. However, sometimes we can increase their efficiency with slight modifications of the basic algorithm. Therefore, the study and development of techniques for adjusting SAT Solvers to specific combinatorial problems is the first goal of this thesis. Namely, SAT Solvers can only deal with propositional logic. For solving general combinatorial problems, two different approaches are possible: - Reducing the complex constraints into propositional clauses. - Enriching the SAT Solver language. The first approach corresponds to encoding the constraint into SAT. The second one corresponds to using propagators, the basis for SMT Solvers. Regarding the first approach, in this document we improve the encoding of two of the most important combinatorial constraints: cardinality constraints and pseudo-Boolean constraints. After that, we present a new mixed approach, called lazy decomposition, which combines the advantages of encodings and propagators. The other part of the thesis uses these theoretical improvements in industrial combinatorial problems. We give a method for efficiently scheduling some professional sport leagues with SAT. The results are promising and show that a SAT approach is valid for these problems. However, the chaotical behavior of CDCL-based SAT Solvers due to VSIDS heuristics makes it difficult to obtain a similar solution for two similar problems. This may be inconvenient in real-world problems, since a user expects similar solutions when it makes slight modifications to the problem specification. In order to overcome this limitation, we have studied and solved the close solution problem, i.e., the problem of quickly finding a close solution when a similar problem is considered

Some Computational Aspects of DISTANCE-SAT

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