A Genetic-Based Approach for Satisfiability Problems

Abstract

We present a genetic-based approach to solve SAT problem and NP-complete problems. The main idea of the approach presented here is to exploit the fact that, although all NP-complete problems are equally difficult in a general computational sense, some have much better genetic representations than others, leading to much more successful use of genetic-based algorithm on some NP-complete problems than on others. Since any NP-complete problem can be mapped into any other one in polynomial time by a transformation, the approach described here consists of identifying and finding a canonical or generic NP-complete problem on which genetic algorithm work well, and solving other NP-complete problems indirectly by translating them onto the canonical problem. We presented some initial results where we have the Boolean Satisfiability Problem (SAT) as a canonical problem, and results on Hamiltonian Circuit problem which represent a family of NP-complete problems, it can be solved efficiently by mapping them first onto SAT problems.