Fuzzy Ant Supervised by PSO and simplified ant supervised PSO applied to TSP

Bio-inspired techniques and swarm intelligence are used to solve complex problems. In this paper, two new variants of AS-PSO (Ant Supervised by Particle Swarm optimization) meta-heuristic are proposed and applied to a classical travelling salesman benchmark problem. The new variants are Fuzzy-AS-PSO and Simplified AS-PSO (S-AS-PSO). AS-PSO is a hierarchical meta-heuristic based on the ant colony optimisation (ACO) and particle swarm optimization (PSO), in which ACO is the heuristic and PSO is the meta-heuristic. The paper reviews the initial formulation; and introduces a new focus as well as two new variants. AS-PSO is an adaptive heuristic, since the user is not asked to fit any parameter values. In AS-PSO, the ACO algorithm is in charge of the problem solving, while the PSO is managing the optimality of the ACO parameters. The Simplified AS-PSO, S-AS-PSO, is a variant that uses simplified PSO while in Fuzzy AS-PSO; the fuzzy PSO is used as a meta-heuristic. The paper also includes an application of the new AS-PSO variants to the travelling Salesman Problem (TSP) and is compared with the ACO results.