A perturb biogeography based optimization with mutation for global numerical optimization. (English) Zbl 1226.65055

Summary: Biogeography based optimization (BBO) is a new evolutionary optimization algorithm based on the science of biogeography for global optimization. We propose three extensions to BBO. First, we propose a new migration operation based sinusoidal migration model called perturb migration, which is a generalization of the standard BBO migration operator. Then, the Gaussian mutation operator is integrated into perturb biogeography based optimization (PBBO) to enhance its exploration ability and to improve the diversity of population.
Experiments are conducted on 23 benchmark problems of a wide range of dimensions and diverse complexities. Simulation results and comparisons demonstrate the proposed PBBO algorithm using sinusoidal migration model is better, or at least comparable to, the RCBBO based linear model, RCBBO-G, RCBBO-L and evolutionary algorithms from literature when considering the quality of the solutions obtained.


65K05 Numerical mathematical programming methods
90C26 Nonconvex programming, global optimization


Full Text: DOI


[1] Lawler, E.L.; Wood, D.E., Branch-and-bound methods: a survey, Oper. res., 14, 699-719, (1966) · Zbl 0143.42501
[2] Glover, F.; Kochenberger, G., Handbook of meta-heuristics, (2003), Kluwer Boston
[3] Bellman, R., On the theory of dynamic programming, Proc. nat. acad. sci., 38, 716-719, (1952) · Zbl 0047.13802
[4] Snyman, J.A., Practical mathematical optimization: an introduction to basic optimization theory and classical and new gradient-based algorithms, (2004), Kluwer Academic Publishers Dordrect, the Netherlands
[5] Suman, B., Study of simulated annealing based algorithms for multiobjective optimization of a constrained problem, Comput. chem. eng., 8, 1849-1871, (2004)
[6] Horn, J.; Nafpliotis, N.; Goldberg, D.E., A niched Pareto genetic algorithm for multiobjective optimization, Evol. comput., 1, 82-87, (1994)
[7] Reid, D.J., Genetic algorithms in constrained optimization, Mathematical, 3, 87-111, (1996) · Zbl 0852.90118
[8] Kalinlia, A.; Karabogab, N., Artificial immune algorithm for IIR filter design, Eng. appl. artificial intell., 18, 919-929, (2005)
[9] Bergh, F.V.D.; Engelbrecht, A.P., A study of particle swarm optimization particle trajectories, Inform. sci., 176, 937-971, (2006) · Zbl 1093.68105
[10] Clerc, M.; Kennedy, J., The particle swarm-explosion, stability, and convergence in a multidimensional complex space, IEEE trans. evol. comput., 6, 58-73, (2002)
[11] Du, W.; Li, B., Multi-strategy ensemble particle swarm optimization for dynamic optimization, Inform. sci., 178, 3096-3109, (2008) · Zbl 1283.90047
[12] Kennedy, J.; Eberhart, R.C., Particle swarm optimization, Proc. IEEE int. joint conf. neural netw., 4, 942-1948, (1995)
[13] Dorigo, M.; Maniezzo, V.; Colorni, A., The ant system: optimization by a colony of cooperating agents, IEEE trans. syst., man, cybernet.-part B, 26, 1, 29-41, (1996)
[14] Ellabib, I.; Calamai, P.; Basir, O., Exchange strategies for multiple ant colony system, Inform. sci., 177, 1248-1264, (2007)
[15] Zhang, Jingqiao; Sanderson, Arthur C., JADE: adaptive differential evolution with optional external archive, IEEE trans. evol. comput., 13, 5, 945-958, (2009)
[16] Noman, Nasimul; Iba, Hitoshi, Accelerating differential evolution using an adaptive local search, IEEE trans. evol. comput., 12, 1, 07-125, (2008)
[17] Qian, W.Y.; Li, A.J., Adaptive differential evolution algorithm for multiobjective optimization problems, Appl. math. comput., 5, 431-440, (2008) · Zbl 1148.65042
[18] Simon, D., Biogeography-based optimization, IEEE trans. evol. comput., 12, 6, 702-713, (2008)
[19] Simon, D.; Rarick, R.; Ergezer, M.; Du, D., Analytical and numerical comparisons of biogeography-based optimization and genetic algorithms, Inform. sci., (2010)
[20] Zhang, Q.; Muhlenbein, H., On the convergence of a class of estimation of distribution algorithms, IEEE trans. evol. comput., 8, 127-136, (2004)
[21] Zhang, Q.; Sun, J.; Tsang, E.; Ford, J., Hybrid estimation of distribution algorithm for global optimization, Eng. comput., 21, 91-107, (2004) · Zbl 1089.90023
[22] D. Du, D. Simon, M. Ergezer, Biogeography-based optimization combined with evolutionary strategy and immigration refusal, in: IEEE Conference on Systems, Man, and Cybernetics, San Antonio, Texas, October 2009, pp. 1023-1028.
[23] M. Ergezer, D. Simon, D. Du, Oppositional biogeography-based optimization, in: IEEE Conference on Systems, Man, and Cybernetics, San Antonio, Texas, October 2009, pp. 1035-1040.
[24] Boussaı¨d, I.; Chatterjee, A.; Siarry, P.; Ahmed-Nacer, M., Two-stage update biogeography-based optimization using differential evolution algorithm (DBBO), Comput. oper. res., 38, 8, 1188-1198, (2011) · Zbl 1208.90195
[25] Gong, W.; Cai, Z.; Ling, C.; Li, H., A real-coded biogeography-based optimization with mutation, Appl. math. comput., 216, 9, 2749-2758, (2010) · Zbl 1206.90221
[26] Simon, D., A probabilistic analysis of a simplified biogeography-based optimization algorithm, Evol. comput., (2010)
[27] Ma, H., An analysis of the equilibrium of migration models for biogeography-based optimization, Inform. sci., 180, 18, 3444-3464, (2010) · Zbl 1194.92073
[28] Feller, W., An introduction to probability theory and its applications, vol. 2, (1971), Wiley NewYork · Zbl 0219.60003
[29] Yao, X.; Liu, Y.; Lin, G., Evolutionary programming made faster, IEEE trans. evol. comput., 3, 2, 82-102, (1999)
[30] Lee, C.Y.; Yao, X., Evolutionary programming using mutations based on the levy probability distribution, IEEE trans. evol. comput., 8, 1, 1-13, (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.