An ACO-RFD hybrid method to solve NP-complete problems

Abstract

In this paper we hybridize ant colony optimization (ACO) and river formation dynamics (RFD), two related swarm intelligence methods. In ACO, ants form paths (problem solutions) by following each other's pheromone trails and reinforcing trails at best paths until eventually a single path is followed. On the other hand, RFD is based on copying how drops form rivers by eroding the ground and depositing sediments. In a rough sense, RFD can be seen as a gradient-oriented version of ACO. Several previous experiments have shown that the gradient orientation of RFD makes this method solve problems in a different way as ACO. In particular, RFD typically performs deeper searches, which in turn makes it find worse solutions than ACO in the first execution steps in general, though RFD solutions surpass ACO solutions after some more time passes. In this paper we try to get the best features of both worlds by hybridizing RFD and ACO. We use a kind of ant-drop hybrid and consider both pheromone trails and altitudes in the environment. We apply the hybrid method, as well as ACO and RFD, to solve two NP-hard problems where ACO and RFD fit in a different manner: the traveling salesman problem (TSP) and the problem of the minimum distances tree in a variable-cost graph (MDV). We compare the results of each method and we analyze the advantages of using the hybrid approach in each case.