A New Heuristic for the Hamiltonian Circuit Problem

Abstract

In this research work, we have discussed a new heuristic for the Hamiltonian circuit problem. Our heuristic initially builds a small cycle in the given graph and incrementally expands the cycle by adding shorter cycles to it. We added features to our base heuristic to deal with the problems encountered during preliminary experiments. Most of our efforts were directed at cubic Cayley graphs but we also considered random, knight tour and geometric graphs. Our experimental results were mixed. In some but not all cases the enhancements improved performance. Runtime of our heuristic was generally not competitive with existing heuristics but this may be due to inefficient implementation. However, our experiments against geometric graphs were very successful and the performance was better than the Hertel’s SCHA algorithm, even in terms of runtime.