A Hybrid PBIL-Based Krill Herd Algorithm

When krill herd (KH) is used to solve complicated multimodal functions, sometimes it fails to find the best solutions and cannot converge fast. Herein, we propose a hybrid KH method, called PBILKH, by integrating the KH with the population-based incremental learning (PBIL). In addition, a type of elitism is applied to memorize the krill with the best fitness when finding the best solution. The effectiveness of the PBILKH is verified by various benchmarks and experimental results demonstrate that our PBILKH is well capable of overtaking the KH algorithm and other optimization methods in solving nonlinear problems.

[1]  Zong Woo Geem,et al.  A New Heuristic Optimization Algorithm: Harmony Search , 2001, Simul..

[2]  Amir Hossein Gandomi,et al.  Krill herd algorithm for optimum design of truss structures , 2013, Int. J. Bio Inspired Comput..

[3]  Michèle Sebag,et al.  Extending Population-Based Incremental Learning to Continuous Search Spaces , 1998, PPSN.

[4]  Xin-She Yang,et al.  Binary bat algorithm , 2013, Neural Computing and Applications.

[5]  Dan Simon,et al.  Biogeography-Based Optimization , 2022 .

[6]  Amir Hossein Gandomi,et al.  A new improved krill herd algorithm for global numerical optimization , 2014, Neurocomputing.

[7]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[8]  Amir Hossein Gandomi,et al.  Chaotic Krill Herd algorithm , 2014, Inf. Sci..

[9]  Antero Arkkio,et al.  A hybrid PBIL-based harmony search method , 2011, Neural Computing and Applications.

[10]  Zhihua Cui,et al.  Monarch butterfly optimization , 2015, Neural Computing and Applications.

[11]  Sakti Prasad Ghoshal,et al.  Optimal design of non-uniform circular antenna arrays using PSO with wavelet mutation , 2014, Int. J. Bio Inspired Comput..

[12]  Gaige Wang,et al.  A Novel Hybrid Bat Algorithm with Harmony Search for Global Numerical Optimization , 2013, J. Appl. Math..

[13]  Xiangtao Li,et al.  An opposition-based differential evolution algorithm for permutation flow shop scheduling based on diversity measure , 2013, Adv. Eng. Softw..

[14]  Minghao Yin,et al.  Animal migration optimization: an optimization algorithm inspired by animal migration behavior , 2014, Neural Computing and Applications.

[15]  Seyed Mohammad Mirjalili,et al.  Multi-Verse Optimizer: a nature-inspired algorithm for global optimization , 2015, Neural Computing and Applications.

[16]  Amir Hossein Alavi,et al.  An effective krill herd algorithm with migration operator in biogeography-based optimization , 2014 .

[17]  Amir Hossein Gandomi,et al.  Hybrid krill herd algorithm with differential evolution for global numerical optimization , 2014, Neural Computing and Applications.

[18]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[19]  Xin-She Yang,et al.  Cuckoo search: recent advances and applications , 2013, Neural Computing and Applications.

[20]  Minghao Yin,et al.  Application of Differential Evolution Algorithm on Self-Potential Data , 2012, PloS one.

[21]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[22]  Amir Hossein Gandomi,et al.  A multi-stage particle swarm for optimum design of truss structures , 2013, Neural Computing and Applications.

[23]  Amir Hossein Alavi,et al.  An introduction of Krill Herd algorithm for engineering optimization , 2015 .

[24]  Shumeet Baluja,et al.  A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning , 1994 .

[25]  Gai-Ge Wang,et al.  A New Improved Firefly Algorithm for Global Numerical Optimization , 2014 .

[26]  Xiangtao Li,et al.  Self-adaptive constrained artificial bee colony for constrained numerical optimization , 2012, Neural Computing and Applications.

[27]  Zhao Xinchao A perturbed particle swarm algorithm for numerical optimization , 2010 .

[28]  Luo Liu,et al.  A hybrid meta-heuristic DE/CS Algorithm for UCAV path planning , 2012 .

[29]  Jianbin Qiu,et al.  Model Reduction for Discrete-Time Markovian Jump Systems with Deficient Mode Information , 2013 .

[30]  Qidi Wu,et al.  Bat algorithm with Gaussian walk , 2014, Int. J. Bio Inspired Comput..

[31]  Hong Duan,et al.  Path Planning for Uninhabited Combat Aerial Vehicle Using Hybrid Meta-Heuristic DE/BBO Algorithm , 2012 .

[32]  Amir Hossein Gandomi,et al.  Chaotic cuckoo search , 2015, Soft Computing.

[33]  A. Gandomi,et al.  A novel improved accelerated particle swarm optimization algorithm for global numerical optimization , 2014 .

[34]  Amir Hossein Gandomi,et al.  Multi-stage genetic programming: A new strategy to nonlinear system modeling , 2011, Inf. Sci..

[35]  Seyed Mohammad Mirjalili,et al.  The Ant Lion Optimizer , 2015, Adv. Eng. Softw..

[36]  Andrew Lewis,et al.  Let a biogeography-based optimizer train your Multi-Layer Perceptron , 2014, Inf. Sci..

[37]  Amir Hossein Gandomi,et al.  Stud krill herd algorithm , 2014, Neurocomputing.

[38]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[39]  Amir Hossein Gandomi,et al.  Hybridizing harmony search algorithm with cuckoo search for global numerical optimization , 2014, Soft Computing.

[40]  H. H. Newman The Theory of Evolution , 1917, Botanical Gazette.

[41]  Jianhua Wu,et al.  An effective global harmony search algorithm for reliability problems , 2011, Expert Syst. Appl..

[42]  Xiangtao Li,et al.  Parameter estimation for chaotic systems by hybrid differential evolution algorithm and artificial bee colony algorithm , 2014 .

[43]  Xin-She Yang,et al.  Nature-Inspired Metaheuristic Algorithms , 2008 .

[44]  Amir Hossein Gandomi,et al.  Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization , 2012, Comput. Math. Appl..

[45]  Dexuan Zou,et al.  A novel global harmony search algorithm for reliability problems , 2010, Comput. Ind. Eng..

[46]  John Maynard Smith,et al.  The Theory of Evolution , 1958 .

[47]  Amir Hossein Alavi,et al.  Structural Optimization Using Krill Herd Algorithm , 2013 .

[48]  Xiangtao Li,et al.  Enhancing the performance of cuckoo search algorithm using orthogonal learning method , 2013, Neural Computing and Applications.

[49]  A. Gandomi,et al.  Mixed variable structural optimization using Firefly Algorithm , 2011 .

[50]  Xinchao Zhao,et al.  An improved discrete immune optimization algorithm based on PSO for QoS-driven web service composition , 2012, Appl. Soft Comput..

[51]  Xiangtao Li,et al.  A perturb biogeography based optimization with mutation for global numerical optimization , 2011, Appl. Math. Comput..

[52]  Minghao Yin,et al.  A novel objective function for job-shop scheduling problem with fuzzy processing time and fuzzy due date using differential evolution algorithm , 2011 .

[53]  Simon Fong,et al.  A heuristic optimization method inspired by wolf preying behavior , 2015, Neural Computing and Applications.

[54]  Gai-Ge Wang,et al.  An Effective Hybrid Firefly Algorithm with Harmony Search for Global Numerical Optimization , 2013, TheScientificWorldJournal.

[55]  Amir Hossein Gandomi,et al.  A chaotic particle-swarm krill herd algorithm for global numerical optimization , 2013, Kybernetes.

[56]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[57]  Amir Hossein Alavi,et al.  Levy-flight krill herd algorithm , 2013 .

[58]  Xin-She Yang,et al.  Discrete cuckoo search algorithm for the travelling salesman problem , 2014, Neural Computing and Applications.

[59]  Minghao Yin,et al.  Multiobjective Binary Biogeography Based Optimization for Feature Selection Using Gene Expression Data , 2013, IEEE Transactions on NanoBioscience.

[60]  Andrew Lewis,et al.  Grey Wolf Optimizer , 2014, Adv. Eng. Softw..

[61]  Siti Zaiton Mohd Hashim,et al.  Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm , 2012, Appl. Math. Comput..

[62]  Xiangtao Li,et al.  A particle swarm inspired cuckoo search algorithm for real parameter optimization , 2015, Soft Computing.

[63]  Andrew Lewis,et al.  Biogeography-based optimisation with chaos , 2014, Neural Computing and Applications.

[64]  Jianhua Wu,et al.  Novel global harmony search algorithm for unconstrained problems , 2010, Neurocomputing.

[65]  Amir Hossein Gandomi,et al.  A hybrid method based on krill herd and quantum-behaved particle swarm optimization , 2015, Neural Computing and Applications.

[66]  Seyedali Mirjalili,et al.  Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems , 2015, Neural Computing and Applications.

[67]  Xinchao Zhao,et al.  A perturbed particle swarm algorithm for numerical optimization , 2010, Appl. Soft Comput..

[68]  Xin-She Yang,et al.  Cuckoo Search via Lévy flights , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[69]  Fei Xue,et al.  Optimal parameter settings for bat algorithm , 2015, Int. J. Bio Inspired Comput..

[70]  S. Baluja An Empirical Comparison of Seven Iterative and Evolutionary Function Optimization Heuristics , 1995 .

[71]  Andrew Lewis,et al.  Autonomous Particles Groups for Particle Swarm Optimization , 2014 .

[72]  Hans-Georg Beyer,et al.  The Theory of Evolution Strategies , 2001, Natural Computing Series.

[73]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[74]  Leandro dos Santos Coelho,et al.  Binary optimization using hybrid particle swarm optimization and gravitational search algorithm , 2014, Neural Computing and Applications.

[75]  Xiangtao Li,et al.  Modified cuckoo search algorithm with self adaptive parameter method , 2015, Inf. Sci..

[76]  Jianhua Wu,et al.  Solving 0-1 knapsack problem by a novel global harmony search algorithm , 2011, Appl. Soft Comput..

[77]  Xin-She Yang,et al.  Firefly algorithm, stochastic test functions and design optimisation , 2010, Int. J. Bio Inspired Comput..

[78]  Amir Hossein Alavi,et al.  Krill herd: A new bio-inspired optimization algorithm , 2012 .