Abstract
EigenAnt is a bare-bones ant colony optimization algorithm that has been proven to converge to the optimal solution under certain conditions. In this paper, we extend EigenAnt to the sequential ordering problem (SOP), comparing its performance to Gambardella et al.’s enhanced ant colony system (EACS), a model that has been found to have state-of-the-art performance on the SOP. Our experimental results, using the SOPLIB2006 instance library, indicate that there is no statistically significant difference in performance between our proposed method and the state-of-the-art EACS method.
Similar content being viewed by others
References
Abdelbar AM (2008) Stubborn ants. In: Proceedings SIS-08, St. Louis, pp 1–5
Abdelbar AM (2012) Is there a computational advantage to representing evaporation rate in ant colony optimization as a Gaussian random variable?. In: Proceedings GECCO-12, Philadelphia, pp 1–8
Abdelbar AM, Wunsch DC (2012) Improving the performance of MAX-MIN ant system on the TSP using stubborn ants. In: Proceedings GECCO-12, Philadelphia, pp 1395–1396
Anghinolfi D, Montemanni R, Paolucci M, Gambardella LM (2009) A particle swarm optimization approach for the sequential ordering problem. In: Proceedings MIC-09. Hamburg, Germany
Anghinolfi D, Montemanni R, Paolucci M, Gambardella LM (2011) A hybrid particle swarm optimization approach for the sequential ordering problem. Comput Operat Res 38(7):1076–1085
Ascheuer N (1995) Hamiltonian path problems in the on-line optimization of flexible manufacturing systems, PhD Thesis, Technische Universität Berlin
Bentley JJ (1992) Fast algorithms for geometric traveling salesman problems. ORSA J Comput 4(4):387–411
Bullnheimer B, Hartl RF, Strauss C (1999) An improved ant system algorithm for the vehicle routing problem. Ann Operat Res 89:25–38
Chen S, Smith S (1996) Commonality and genetic algorithms, Technical Report CMURI-TR-96-27, Robotic Institute, Carnegie Mellon University
Chica M, Cordón O, Damas S, Bautista J (2011) A new diversity induction mechanism for a multi-objective ant colony algorithm to solve a real-world time and space assembly line balancing problem. Memet Comput 3:15–24
Cordón O, de Viana IF, Herrera F (2002) Analysis of the best-worst ant system and its variants on the TSP. Mathw Soft Comput 9(2–3):177–192
Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. Mach Learn Res 7:1–30
Dorigo M, Gambardella LM (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evolut Comput 1(1):35–66
Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperative agents. IEEE Trans Syst Man Cybern 26(1):29–41
Dorigo M, Stützle T (2004) Ant colony optimization. MIT Press, Cambridge
Dorigo M, Stützle T (2010) Ant colony optimization: overview and recent advances. In: Gendreau M, Potvin Y (eds) Handbook of metaheuristics, 2nd edn. Springer, New York, pp 227–263
Escudero LF (1988) An inexact algorithm for the sequential ordering problem. Eur J Operat Res 37:232–253
Ezzat A, Abdelbar AM (2013) A less-exploitative variation of the enhanced ant colony system applied to SOP. In: Proceedings CEC-2013, Canćun, Mexico, pp 1917–1924
Gambardella LM, Dorigo M (2000) An ant colony system hybridized with a new local search for the sequential ordering problem. INFORMS J Comput 12(3):237–255
Gambardella LM, Montemanni R, Weyland D (2012) Coupling ant colony systems with strong local searches. Eur J Operat Res 220(3):831–843
Guerriero F, Mancini M (2003) A cooperative parallel rollout algorithm for the sequential ordering problem. Parallel Comput 29(5):663–677
Jackson DE, Bicak M, Holcombe M (2011) Decentralized communication, trail connectivity and emergent benefits of ant pheromone trail networks. Memet Comput 3:25–32
Jayadeva, Shah S, Bhaya A, Kothari R, Chandra S (2013) Ants find the shortest path: a mathematical proof. Swarm Intell 7(1):43–62
Kindervater G, Savelsbergh M (1997) Vehicle routing: handling edge exchanges. In: Aarts EHL, Lenstra JK (eds) Local search in combinatorial optimization. Wiley, Chichester, pp 337–360
Lin S (1965) Computer solutions of the traveling salesman problem. Bell Syst Tech J 44:2245–2269
Lin S, Kernighan BW (1973) An effective heuristic algorithm for the traveling-salesman problem. Operat Res 21:498–516
Montemanni R. SOPLIB2006 Problem Instance Library. http://www.idsia.ch/~roberto/SOPLIB06.zip
Montemanni R, Smith DH, Gambardella LM (2007) Ant colony systems for large sequential ordering problems. In: Proceedings SIS-07, Honolulu, pp 60–67
Montemanni R, Smith DH, Gambardella LM (2008) A heuristic manipulation technique for the sequential ordering problem. Comput Operat Res 35(12):3931–3944
Montemanni R, Smith DH, Rizzoli AE, Gambardella LM (2009) Sequential ordering problems for crane scheduling in port terminals. Int J Simul Process Model 5(4):348–361
Or I (1976) Traveling salesman-type combinatorial problems and their relation to the logistics of regional blood banking, PhD Thesis, Dept. of Industrial Engineering and Management Sciences, Northwestern University
Otero FEB, Freitas AA, Johnson CG (2010) A hierarchical multi-label classification ant colony algorithm for protein function prediction. Memet Comput 2:165–181
Pullyblank W, Timlin M (1991) Precedence constrained routing and helicopter scheduling: heuristic design, Technical Report RC17154 (#76032). IBM T.J. Watson Research Center
Savelsbergh MWP (1990) An efficient implementation of local search algorithms for constrained routing problems. Eur J Operat Res 47:75–85
Seo DI, Moon BR (2003) A hybrid genetic algorithm based on complete graph representation for the sequential ordering problem. In: Proceedings GECCO-03, Chicago, pp 669–680
Stützle T. ACOTSP: a software package for various ant colony optimization algorithms applied to the symmetric traveling salesman problem. http://www.aco-metaheuristic.org/aco-code/
Stützle T, Hoos H (2000) MAX-MIN ant system. Future Gener Comput Syst 16(8):889–914
Acknowledgments
The partial support of the National Science Foundation, the Missouri University of Science and Technology Center for Infrastructure Engineering Studies and Intelligent Systems Center, and the Mary K. Finley Missouri Endowment are gratefully acknowledged. We would like to thank Jayadeva for providing the Matlab source code for the EigenAnt algorithm. Although our implementation, in C, did not directly incorporate this code, having access to it was useful in validating our implementation.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ezzat, A., Abdelbar, A.M. & Wunsch, D.C. A bare-bones ant colony optimization algorithm that performs competitively on the sequential ordering problem. Memetic Comp. 6, 19–29 (2014). https://doi.org/10.1007/s12293-013-0129-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12293-013-0129-z