Genetic Algorithms for Hunting Snakes in Hypercubes: Fitness Function Analysis and Open Questions

Abstract

Hunting for snakes of maximum length in hypercubes has been addressed with non-heuristic methods for hypercubes of dimension less than eight. Above that dimension the problem is intractable because the search grows exponentially with the dimension, which make it an NP-hard problem. Heuristic methods, like genetic algorithms, have been used to solve this kind of problem. We propose different fitness functions to find snakes in hypercubes of dimension greater than three and pose some open questions regarding the number of maximum length snakes in a hypercube of dimension d.