**A Multilevel Evolutionary Algorithm Applied to the Maximum Satisfiability Problems** A Multilevel Evolutionary Algorithm Applied to the

DOI: 10.5772/intechopen.72843

Noureddine Bouhmala, Kjell Ivar Øvergård and Karina Hjelmervik Noureddine Bouhmala, Kjell Ivar Øvergård

Maximum Satisfiability Problems

Additional information is available at the end of the chapter and Karina Hjelmervik Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72843

#### Abstract

The maximum satisfiability problem that is known to be nondeterministic polynomial (NP) complete plays a central role problem in many applications in the fields of very large-scale integration (VLSI) computer-aided design, computing theory, artificial intelligence, and defense. Given a set of m clauses and n Boolean variables, the maximum satisfiability problem refers to the task of finding an assignment of values to the variables that maximizes the number of satisfied clauses (or minimizes the number of unsatisfied clauses) In this chapter, a multilevel evolutionary algorithm is proposed for the maximum satisfiability problem. The multilevel process works by grouping the variables defining the problem to form clusters, uses the clusters to define a new problem, and is repeated until the problem size falls below some threshold. The coarsest problem is then given an initial assignment of values to variables and the assignment is successively refined on all the problems starting with the coarsest and ending with the original.

Keywords: maximum satisfiability problem, genetic algorithm, multilevel paradigm, discrete optimization, effect size
