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 n2 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 log2 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 n2 jobs in O(x middot (m + n) middot log n) time

[1]  Thomas Stützle,et al.  An Ant Approach to the Flow Shop Problem , 1998 .

[2]  Vittorio Maniezzo,et al.  The Ant System Applied to the Quadratic Assignment Problem , 1999, IEEE Trans. Knowl. Data Eng..

[3]  Alain Hertz,et al.  Ants can colour graphs , 1997 .

[4]  Yi Pan,et al.  Linear Array with a Reconfigurable Pipelined Bus System - Concepts and Applications , 1998, Inf. Sci..

[5]  Martin Middendorf.  Bit Summation on the Reconfigurable Mesh , 1999, IPPS/SPDP Workshops.

[6]  Jerry L. Trahan,et al.  Tighter and Broader Complexity Results for Reconfigurable Models , 1998, Parallel Process. Lett..

[7]  M Dorigo,et al.  Ant colonies for the quadratic assignment problem , 1999, J. Oper. Res. Soc..

[8]  Léon J. M. Rothkrantz,et al.  Ant-Based Load Balancing in Telecommunications Networks , 1996, Adapt. Behav..

[9]  Vittorio Maniezzo,et al.  Exact and Approximate Nondeterministic Tree-Search Procedures for the Quadratic Assignment Problem , 1999, INFORMS J. Comput..

[10]  Marco Dorigo,et al.  Ant Colonies for Adaptive Routing in Packet-Switched Communications Networks , 1998, PPSN.

[11]  T. Stützle,et al.  MAX-MIN Ant System and local search for the traveling salesman problem , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[12]  Rami G. Melhem,et al.  Time-Division Optical Communications in Multiprocessor Arrays , 1993, IEEE Trans. Computers.

[13]  Hartmut Schmeck,et al.  Ant colony optimization for resource-constrained project scheduling , 2000, IEEE Trans. Evol. Comput..

[14]  Koji Nakano.  Prefix-Sums Algorithms on Reconfigurable Meshes , 1995, Parallel Process. Lett..

[15]  Marc Gravel,et al.  PARALLEL IMPLEMENTATION OF AN ANT COLONY OPTIMIZATION METAHEURISTIC WITH OPENMP , 2001 .

[16]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[17]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[18]  Ramachandran Vaidyanathan,et al.  Dynamic reconfiguration - architectures and algorithms , 2003, Series in computer science.

[19]  Daniel Merkle,et al.  Fast Ant Colony Optimization on Runtime Reconfigurable Processor Arrays , 2002, Genetic Programming and Evolvable Machines.