Mohamed El Halaby

Mohamed El Halaby

Due to the good performance of current SAT (satisfiability) and Max-SAT (maximum ssatisfiability) solvers, many real-life optimization problems such as scheduling can be solved by encoding them into Max-SAT. In this paper we tackle the course timetabling problem of the department of mathematics, Cairo University by encoding it into Max-SAT. Generating timetables for the department by hand has proven to be cumbersome and the generated timetable almost always contains conflicts. We show how the constraints can be modelled as a Max-SAT instance.

Mohamed El Halaby

The Maximum Satisfiability (MaxSAT) problem is the problem of finding a truth assignment that maximizes the number of satisfied clauses of a given Boolean formula in Conjunctive Normal Form (CNF). Many exact solvers for MaxSAT have been developed during recent years, and many of them were presented in the well-known SAT conference. Algorithms for MaxSAT generally fall into two categories: (1) branch and bound algorithms and (2) algorithms that use successive calls to a SAT solver (SAT- based), which this paper in on. In practical problems, SAT-based algorithms have been shown to be more efficient. This paper provides an experimental investigation to compare the performance of recent SAT-based and branch and bound algorithms on the benchmarks of the MaxSAT Evaluations.

Mohamed El Halaby, Areeg Abdalla

In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to Łukasiewicz logic. The MaxSAT problem for a set of formulae Φ is the problem of finding an assignment to the variables in Φ that satisfies the maximum number of formulae. Three possible solutions (encodings) are proposed to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem (WCSP). Like its Boolean counterpart, the extended fuzzy MaxSAT will have numerous applications in optimization problems that involve vagueness.