Abstract
This paper presents glowworm swarm optimization (GSO), a novel algorithm for the simultaneous computation of multiple optima of multimodal functions. The algorithm shares a few features with some better known swarm intelligence based optimization algorithms, such as ant colony optimization and particle swarm optimization, but with several significant differences. The agents in GSO are thought of as glowworms that carry a luminescence quantity called luciferin along with them. The glowworms encode the fitness of their current locations, evaluated using the objective function, into a luciferin value that they broadcast to their neighbors. The glowworm identifies its neighbors and computes its movements by exploiting an adaptive neighborhood, which is bounded above by its sensor range. Each glowworm selects, using a probabilistic mechanism, a neighbor that has a luciferin value higher than its own and moves toward it. These movements—based only on local information and selective neighbor interactions—enable the swarm of glowworms to partition into disjoint subgroups that converge on multiple optima of a given multimodal function. We provide some theoretical results related to the luciferin update mechanism in order to prove the bounded nature and convergence of luciferin levels of the glowworms. Experimental results demonstrate the efficacy of the proposed glowworm based algorithm in capturing multiple optima of a series of standard multimodal test functions and more complex ones, such as stair-case and multiple-plateau functions. We also report the results of tests in higher dimensional spaces with a large number of peaks. We address the parameter selection problem by conducting experiments to show that only two parameters need to be selected by the user. Finally, we provide some comparisons of GSO with PSO and an experimental comparison with Niche-PSO, a PSO variant that is designed for the simultaneous computation of multiple optima.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bonabeau, E., Dorigo, M., & Theraulaz, G. (1999). Swarm intelligence: from natural to artificial systems. New York: Oxford University Press.
Brits, R., Engelbrecht, A. P., & van den Bergh, F. (2002). A niching particle swarm optimizer. In Proceedings of the 4th Asia-Pacific conference on simulated evolution and learning (pp. 692–696).
Clerc (2007). Particle swarm optimization. London: ISTE Ltd.
Dorigo, M., & Gambardella, L. M. (1997). Ant colony system: a cooperative learning approach to the travelling salesman problem. IEEE Transactions on Evolutionary Computation, 1(1), 53–66.
Dorigo, M., & Stützle (2004). Ant colony optimization. Cambridge: MIT Press.
Dorigo, M., Maniezzo, V., & Colorni, A. (1996). The ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 26(1), 29–41.
Dorigo, M., Trianni, V., Sahin, E., Gross, R., Labella, T. H., Baldassarre, G., Nolfi, S., Deneubourg, J.-L., Mondada, F., Floreano, D., & Gambardella, L. M. (2004). Evolving self-organizing behaviors for a swarm-bot. Autonomous Robots, 17(2–3), 223–245.
Dréo, J., & Siarry, P. (2004). Continuous interacting ant colony algorithm based on dense hierarchy. Future Generations Computer Systems, 20, 841–856.
Fevrier, V., & Patricia, M. (2007). Parallel evolutionary computing using a cluster for mathematical function optimization. In Proceedings of the annual meeting of the North American fuzzy information processing society (pp. 598–603). Piscataway: IEEE Press.
Fronczek, J. W., & Prasad, N. R. (2005). Bio-inspired sensor swarms to detect leaks in pressurized systems. In Proceedings of IEEE international conference on systems, man and cybernetics (pp. 1967–1972). Piscataway: IEEE Press.
Kennedy, J. (2000). Stereotyping: improving particle swarm performance with cluster analysis. In Proceedings of the congress on evolutionary computation (pp. 1507–1512). Piscataway: IEEE Press.
Kennedy, J., & Eberhart, R. C. (1995). Particle swarm optimization. In Proceedings of the IEEE international conference on neural networks (pp. 1942–1948). Piscataway: IEEE Press.
Krishnanand, K. N. (2007). Glowworm swarm optimization: a multimodal function optimization paradigm with applications to multiple signal source localization tasks. PhD thesis, Department of Aerospace Engineering, Indian Institute of Science.
Krishnanand, K. N., & Ghose, D. (2005). Detection of multiple source locations using a glowworm metaphor with applications to collective robotics. In Proceedings of IEEE swarm intelligence symposium (pp. 84–91). Piscataway: IEEE Press.
Krishnanand, K. N., & Ghose, D. (2006a). Glowworm swarm based optimization algorithm for multimodal functions with collective robotics applications. Multiagent and Grid Systems, 2(3), 209–222.
Krishnanand, K. N., & Ghose, D. (2006b). Theoretical foundations for multiple rendezvous of glowworm-inspired mobile agents with variable local-decision domains. In Proceedings of American control conference (pp. 3588–3593). Piscataway: IEEE Press.
Krishnanand, K. N., & Ghose, D. (2008). Theoretical foundations for rendezvous of glowworm-inspired agent swarms at multiple locations. Robotics and Autonomous Systems, 56(7), 549–569.
Krishnanand, K. N., Amruth, P., Guruprasad, M. H., Bidargaddi, S. V., & Ghose, D. (2006a). Rendezvous of glowworm-inspired robot swarms at multiple source locations: a sound source based real-robot implementation. In M. Dorigo et al. (Eds.), Lecture notes in computer science : Vol. 4150. Ant colony optimization and swarm intelligence (pp. 259–269). Berlin: Springer.
Krishnanand, K. N., Amruth, P., Guruprasad, M. H., Bidargaddi, S. V., & Ghose, D. (2006b). Glowworm-inspired robot swarm for simultaneous taxis toward multiple radiation sources. In Proceedings of IEEE international conference on robotics and automation (pp. 958–963). Piscataway: IEEE Press.
Mühlenbein, H., Schomisch, D., & Born, J. (1991). The parallel genetic algorithm as function optimizer. Parallel Computing, 17(6–7), 619–632.
Muller, S. D., Marchetto, J., & Koumoutsakos, S. A. P. (2002). Optimization based on bacterial chemotaxis. IEEE Transactions on Evolutionary Computation, 6(6), 16–29.
Parsopoulos, K., & Vrahatis, M. N. (2004). On the computation of all global minimizers through particle swarm optimization. IEEE Transactions on Evolutionary Computation, 8(3), 211–224.
Poli, R., Kennedy, J., & Blackwell, T. (2007). Particle swarm optimization: an overview. Swarm Intelligence, 1(1), 33–57.
Reutskiy, S. Y., & Chen, C. S. (2006). Approximation of multivariate functions and evaluation of particular solutions using Chebyshev polynomial and trigonometric basis functions. International Journal for Numerical Methods in Engineering, 67(13), 1811–1829.
Singh, G., & Deb, K. (2006). Comparison of multi-modal optimization algorithms based on evolutionary algorithms. In Proceedings of the genetic and evolutionary computation conference (pp. 1305–1312). New York: ACM Press.
Singh, K. A., Mukherjee, A., & Tiwari, M. K. (2004). Incorporating kin selection in simulated annealing algorithm and its performance evaluation. European Journal of Operational Research, 158, 34–45.
Törn, A., & Zilinskas, A. (1989). Global optimization. New York: Springer.
Tyler, J. (1994). Glow-worms. Sevenoaks: Tyler-Scagell.
Zarzhitsky, D., Spears, D. F., & Spears, W. M. (2005). Swarms for chemical plume tracing. In Proceedings of IEEE Swarm Intelligence Symposium (pp. 249–256). Piscataway: IEEE Press.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is partially supported by a project grant from the Ministry of Human Resources Development, India and by DRDO-IISc Mathematical Engineering Program.
Rights and permissions
About this article
Cite this article
Krishnanand, K.N., Ghose, D. Glowworm swarm optimization for simultaneous capture of multiple local optima of multimodal functions. Swarm Intell 3, 87–124 (2009). https://doi.org/10.1007/s11721-008-0021-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11721-008-0021-5