Krill herd: A new bio-inspired optimization algorithm.

*(English)*Zbl 1266.65092Summary: A novel biologically-inspired algorithm, namely krill herd (KH) is proposed for solving optimization tasks. The KH algorithm is based on the simulation of the herding behavior of krill individuals. The minimum distances of each individual krill from food and from highest density of the herd are considered as the objective function for the krill movement. The time-dependent position of the krill individuals is formulated by three main factors: (i) movement induced by the presence of other individuals (ii) foraging activity, and (iii) random diffusion. For more precise modeling of the krill behavior, two adaptive genetic operators are added to the algorithm. The proposed method is verified using several benchmark problems commonly used in the area of optimization. Further, the KH algorithm is compared with eight well-known methods in the literature. The KH algorithm is capable of efficiently solving a wide range of benchmark optimization problems and outperforms the exciting algorithms.

##### MSC:

65K05 | Numerical mathematical programming methods |

90C15 | Stochastic programming |

90C59 | Approximation methods and heuristics in mathematical programming |

##### Keywords:

krill herd; biologically-inspired algorithm; optimization; metaheuristic; benchmarking; numerical examples##### Software:

Krill herd
PDF
BibTeX
XML
Cite

\textit{A. H. Gandomi} and \textit{A. H. Alavi}, Commun. Nonlinear Sci. Numer. Simul. 17, No. 12, 4831--4845 (2012; Zbl 1266.65092)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Yang, X.-S., Nature-inspired metaheuristic algorithms, (2008), Luniver Press |

[2] | Gandomi AH. Yang X-S, Alavi AH. Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Engineering with Computers, in press. DOI 10.1007/s00366-011-0241-y. |

[3] | Talbi, E.G., Metaheuristics: from design to implementation, (2009), John Wiley & Sons Hoboken, New Jersey, USA · Zbl 1190.90293 |

[4] | Geem, Z.W.; Kim, J.-H.; Loganathan, G.V., A new heuristic optimization algorithm: harmony search, Simulation, 76, 2, 60-68, (2001) |

[5] | Kaveh, A.; Talatahari, S., A novel heuristic optimization method: charged system search, Acta mech, 213, 267-289, (2010) · Zbl 1397.65094 |

[6] | Zang, H.; Zhang, S.; Hapeshi, K., A review of nature-inspired algorithms, J bionic eng, 7, S232-S237, (2010) |

[7] | Tang, W.J.; Wu, Q.H., Biologically inspired optimization: a review, Trans inst meas control, 31, 495-515, (2009) |

[8] | Goldberg, D.E., Genetic algorithms in search, optimization and machine learning, (1989), Addison-Wesley Reading, MA · Zbl 0721.68056 |

[9] | Koza, J.R., Genetic programming: on the programming of computers by natural selection, (1992), MIT Press Cambridge, MA · Zbl 0850.68161 |

[10] | Fogel, L.J.; Owens, A.J.; Walsh, M.J., Artificial intelligence thorough simulated evolution, (1966), John Wiley & Sons, Ltd. Chichester, UK · Zbl 0148.40701 |

[11] | Storn, R.; Price, K.V., Differential evolutionâ€”A simple and efficient heuristic for global optimization over continuous spaces, J global optim, 11, 4, 341-359, (1997) · Zbl 0888.90135 |

[12] | Khatib, W.; Fleming, P., The stud GA: A mini revolution?, () |

[13] | Gandomi, A.H.; Alavi, A.H., Multi-stage genetic programming: a new strategy to nonlinear system modeling, Inf sci, 181, 23, 5227-5239, (2011) |

[14] | Gandomi, A.H.; Alavi, A.H., A new multi-gene genetic programming approach to nonlinear system modeling. part I: materials and structural engineering problems, Neural comput appl, 21, 1, 171-187, (2012) |

[15] | Simon, D., Biogeography-based optimization, IEEE trans evolut comput, 12, 702-713, (2008) |

[16] | Eberhart, R.C.; Kennedy, J., A new optimizer using particle swarm theory, () |

[17] | Dorigo, M.; Maniezzo, V.; Colorni, A., The ant system: optimization by a colony of cooperating agents, IEEE trans syst man cybern B, 26, 1, 29-41, (1996) |

[18] | Yang, X.S.; Gandomi, A.H., Bat algorithm: a novel approach for global engineering optimization, Eng comput, 29, 5, (2012) |

[19] | Passino, K.M., Biomimicry of bacterial foraging for distributed optimization and control, IEEE control syst mag, 22, 53-67, (2002) |

[20] | Gregory, R.; Paton, R.C.; Saunders, J.R.; Wu, Q.H., Parallelising a model of bacterial interaction and evolution, Biosystems, 76, 121-131, (2004) |

[21] | Vlachos, C.; Paton, R.C.; Saunders, J.R.; Wu, Q.H., A rule-based approach to the modelling of bacterial ecosystems, Biosystems, 84, 49-72, (2005) |

[22] | Flierl, G.; Grunbaum, D.; Levin, S.; Olson, D., From individuals to aggregations: the interplay between behavior and physics, J theor biol, 196, 397-454, (1999) |

[23] | Okubo, A., Dynamical aspects of animal grouping: swarms, schools, flocks, and herds, Adv biophys, 22, 1-94, (1986) |

[24] | Hofmann, E.E.; Haskell, A.G.E.; Klinck, J.M.; Lascara, C.M., Lagrangian modelling studies of antarctic krill (euphasia superba) swarm formation, ICES J mar sci, 61, 617-631, (2004) |

[25] | Hardy, A.C.; Gunther, E.R., The plankton of the south Georgia whaling grounds and adjacent waters, 1926-1927, Disc rep, 11, 1-456, (1935) |

[26] | Marr, J.W.S., The natural history and geography of the antarctic krill (euphausia superba dana), Disc rep, 32, 33-464, (1962) |

[27] | Nicol, S., Living krill, zooplankton and experimental investigations, Proceedings of the international workshop on understanding living krill for improved management and stock assessment marine and freshwater behaviour and physiology, 36, 4, 191-205, (2003) |

[28] | Murphy, E.J.; Morris, D.J.; Watkins, J.L.; Priddle, J., Scales of interaction between antarctic krill and the environment, (), 120-130 |

[29] | Miller, D.G.M.; Hampton, I., Krill aggregation characteristics: spatial distribution patterns from hydroacoustic observations, Polar biol, 10, 125-134, (1989) |

[30] | Price, H.J., Swimming behavior of krill in response to algal patches: a mesocosm study, Limnol oceanogr, 34, 649-659, (1989) |

[31] | Morin A, Okubo A, Kawasaki K. Acoustic data analysis and models of krill spatial distribution. Scientific Committee for the Conservation of Antarctic Marine Living Resources, Selected Scientific Papers, Part I; 1988. p.311-29. |

[32] | Yao, X.; Liu, Y.; Lin, G., Evolutionary programming made faster, IEEE trans evolut comput, 3, 82-102, (1999) |

[33] | Ma, H., An analysis of the equilibrium of migration models for biogeography-based optimization, Inf sci, 180, 3444-3464, (2010) · Zbl 1194.92073 |

[34] | Gandomi, A.H.; Yang, X.S.; Talatahari, S.; Deb, S., Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization, Comput math appl., 63, 1, 191-200, (2012) · Zbl 1238.90109 |

[35] | Wolpert, D.H.; Macready, W.G., No free lunch theorems for optimization, IEEE trans evol comput, 1, 1, 67-82, (1997) |

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.