Ant Colony Optimal Algorithm: Fast Ants on the Optical Pipelined R-Mesh

In this paper, we demonstrate how to implement and improve two ant colony optimization (ACO) algorithms on the optical pipelined reconfigurable mesh (PR-mesh): the generic ACO and the fast ant colony optimization (FACO) algorithm. The run-time complexity of our improved generic ACO algorithm, with x generations each generation having m ants, on an n times n PR-mesh is O((x middot m + n)log n), which outperforms the currently best known electrical model implemented in (Merkle and Middendorf, 2002) with run-time complexity of O(x middot (m + n)log n). Our FACO algorithm on PR-mesh yields O(((z/(n*middot;log
²
n)) + n/log n) middot log log n) run-time complexity for n
²
jobs while the existing FACO algorithm on the electrical model yields a run-time complexity of O((z + n)log* n) but can only handle log
²
n jobs, where z is the total number of ants from all generations. In addition, we propose a theoretical FACO algorithm on a three dimensional PR-mesh solving n
²
jobs in O(x middot (m + n) middot log n) time