Two Phase Optimization Method Based on Meta heuristic Algorithms, Big Bang-Big Crunch and Black Hole

Document Type : Original Paper

Authors

Department of Mathematics, Faculty of Science, Zanjan University, Zanjan, Iran

Abstract

This research proposes a two-phase algorithm whose main idea is based on meta heuristic algorithms, Big Bang and Black Hole. In the first phase of this algorithm, the artificial ants scan the reticulated rectangular region in parallel directions. The best points in the ant’s navigations are used as starting points for the second stage of this algorithm. Big Bang and Black Hole algorithms, as an exploitation phase, try to investigate more accurate answers in the neighborhood of the starting points by reducing the neighborhood radius. Numerical examples confirm that this algorithm is capable to achieve an optimal solution with the desired accuracy and low computational costs.

Keywords

Main Subjects

References

[1] Biradar, Sh. Hote, Y. V. Saxena, S. Reduced-order modeling of linear time invariant systems using big bang big crunch optimization and time moment matching method, Applied Mathematical Modelling, 40(15) (2016) 7225–7244.
[2] Coley, D. A. An Introduction to genetic algorithm for scientist and engineering, World Scientific Publishing Co, 1999.
[3] Dorigo, M. Maria Gambardella, L. Ant colony system; A cooperative learning approach to the traveling salesman problem, IEEE Transactions on Evolutionary Computation, 1(1) (1997) 53–66.
[4] Dorigo, M. Maniezzo, V. Colorni, A. The ant system: optimization by a colony of cooperating agents, IEEE Transactions on Systems, Man, and Cybernetics–Part B, 26(1) (1996) 29–41.
[5] Erol, O.K. Eksin, I. A new optimization method: Big Bang-Big Crunch, Journal of Advances in Engineering Software, 37 (2006) 106–111.
[6] Gutjahr, W. J. Convergence Analysis of Metaheuristics, Matheuristics: Hybridizing Metaheuristics and Mathematical Programming, Springer US, (2010) 159–187.
[7] Hatamlou, A. Black hole: A new heuristic optimization approach for data clustering, Information Sciences 222 (2013) 175–184.
[8] kennedy,J. Eberhart, R. Particle swarm optimization, IEEE International Conference on Neural Networks, 4 (1995) 1942–1948.
[9] Krikpatrick, S. Gelatt, C.D. Vecchi, M.P. Optimization by simulated annealing, Science, New Series, 220 (4598) (1983) 671–680.
[10] Liu, Y. Passino, K.M. Biomimicry of social foraging bacteria for distributed optimization: models, principles and emergent behaviors, Journal of Optimization Theory and Applications, 115(3) (2002) 603–628.
[11] Madi, M. Markovi, D. Radovanovi, M. Comparison of metaheuristic algorithms for solving machining optimization problems , Facta universitatis - series: Mechanical Engineering, 11(1) (2013) 29–44.
[12] Prayogo, D. Cheng, M.Y. Wu, Y. W. Arief Herdany, A. Prayogo, H. Differential Big Bang –Big Crunch algorithm for construction–engineering design optimization, Automation in Construction, 85 (2018) 290–304.
[13] Tarasewich, P. McMullen, P.R. Swarm intelligence: power in numbers, Communication of ACM, 45 (2002) 62–67.
[14] Zhang, J. Liu, K. Tan, Y. and He, X. Random black hole particle swarm optimization and its application, IEEE conference neural networks and signal processing, (2008) 359–365.
Journal of Advanced Mathematical Modeling
Volume 11, Issue 3
September 2021
Pages 515-530

Files

History

  • Receive Date: 24 May 2021
  • Revise Date: 05 August 2021
  • Accept Date: 15 August 2021

Share

How to cite

Statistics