  In this paper, we have examined the problem of embedding a cycle of n
vertices onto a given set of n points inside a simple polygon. The goal of the
problem is that the cycle must be embedded without bends and does not intersect
itself and the polygon. This problem is a special case of the open problem of
finding a (s, X, t) - simple Hamiltonian path inside a simple polygon that does
not intersect itself and the sides of the polygon. The complexity of the
problem is examined in this paper is open, but it has been proved that similar
problems are NP-complete. We have presented a metaheuristic algorithm based on
a genetic algorithm for straight-line embedding of a cycle with the minimum
numbers of intersections, onto a given set of points inside simple polygons.
The efficiency of the proposed genetic algorithm is due to the definition of
the mutation operation, which removes it if there is an intersection between
the embedded edges of the cycle. The experimental results show that the results
of the version of the algorithm that uses this mutation operation are much more
efficient than the version that uses only the usual two-points mutation
operation.
