Adjusted Artificial Bee Colony Algorithm for the Minimum Weight Triangulation

The minimum weight triangulation is a well-known NP-hard problem often used for the construction of triangulated random network models of land contours. Since it is an intractable problem, the required computational time for an exhaustive search algorithm grows exponentially with the number of points in 2D space. Nature-inspired swarm intelligence algorithms are prominent and efficient optimization techniques for solving that kind of problems. In this paper, we adjusted the artificial bee colony algorithm for the minimum weight triangulation problem. Our adjusted algorithm has been implemented and tested on several randomly generated instances of points in the plane. The performance of our proposed method was compared to the performance of other stochastic optimization algorithms, as well as with the exhaustive search for smaller instances. The simulation results show that our proposed algorithm in almost all cases outperforms other compared algorithms.