A genetic algorithm for straight-line embedding of a cycle onto a given set of points inside simple polygons

TL;DR

This paper introduces a genetic algorithm to embed a cycle onto points inside simple polygons with minimal intersections, addressing a complex geometric problem with a novel mutation strategy.

Contribution

It presents a new genetic algorithm with a specialized mutation operation for embedding cycles inside polygons, improving efficiency over traditional methods.

Findings

The proposed genetic algorithm reduces intersections effectively.

The mutation operation significantly improves algorithm performance.

Experimental results demonstrate superior efficiency of the new method.

Abstract

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.