A clique in a graph is a set of vertices that are all connected to each

other. A maximum clique is a clique of maximum size. A graph may have

more than one maximum cliques. The problem of finding a maximum

clique is a strongly hard NP-hard problem. It is not possible to find an

approximation algorithm which finds a maximum clique that is a constant

factor of the optimum solution. In this work, we present a genetic algorithm

for the maximum clique problem that is able to find optimum or

close to optimum solutions to most DIMACS graphs. The genetic algorithm

uses new crossover mechanisms which are able to find reasonably

good cliques which can then be used in other applications downstream.

We also provide C++ code for our algorithm. Results show that our algorithm

is able to find maximum cliques for most DIMACS instances, and

if not, close to optimum solutions for the other instances.