A tree-structured random walking swarm optimizer for multimodal optimization

Abstract This paper develops a novel tree structured random walking swarm optimizer for seeking multiple optima in multimodal landscapes. First, we show that the artificial bee colony algorithm has some distinct advantages over the other swarm intelligence algorithms for accomplishing the multimodal optimization task, from analytical and experimental perspectives. Then, a tree-structured niching strategy is developed to assist the algorithm in exploring multiple optima simultaneously. The strategy constructs a weighted complete graph based on the positions of the food sources (candidate solutions). A minimum spanning tree that encodes the distribution of the food sources is built upon the complete graph to guide the search of the bee swarm. Each artificial bee sets out from a food source and flies along the edges of the tree to gather information about the search space. The dance trajectories of bees are simulated by a random walk model considering both distance and fitness information. Then, mutant vectors are selected from the trajectories to update the food source. This graph-based search method is introduced to simultaneously promote the progress of exploitation and exploration in multimodal environments. Extensive experiments indicate that our proposed algorithm outperforms several state-of-the-art algorithms.

[1]  Dervis Karaboga,et al.  A comprehensive survey: artificial bee colony (ABC) algorithm and applications , 2012, Artificial Intelligence Review.

[2]  Dervis Karaboga,et al.  A comparative study of Artificial Bee Colony algorithm , 2009, Appl. Math. Comput..

[3]  Ronald L. Graham,et al.  On the History of the Minimum Spanning Tree Problem , 1985, Annals of the History of Computing.

[4]  Jun Zhang,et al.  Dual-Strategy Differential Evolution With Affinity Propagation Clustering for Multimodal Optimization Problems , 2018, IEEE Transactions on Evolutionary Computation.

[5]  Xiaodong Li,et al.  Particle Swarm Optimizer with Aging Operator for Multimodal Function Optimization , 2013, Int. J. Comput. Intell. Syst..

[6]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization , 2008, 2008 3rd International Workshop on Genetic and Evolving Systems.

[7]  Alok Singh,et al.  An artificial bee colony algorithm for the leaf-constrained minimum spanning tree problem , 2009, Appl. Soft Comput..

[8]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

[9]  Leslie Pérez Cáceres,et al.  The irace package: Iterated racing for automatic algorithm configuration , 2016 .

[10]  Xiaodong Li,et al.  Efficient differential evolution using speciation for multimodal function optimization , 2005, GECCO '05.

[11]  Aurora Trinidad Ramirez Pozo,et al.  An investigation of the selection strategies impact on MOEDAs: CMA-ES and UMDA , 2018, Appl. Soft Comput..

[12]  Xiaodong Li,et al.  Adaptively Choosing Neighbourhood Bests Using Species in a Particle Swarm Optimizer for Multimodal Function Optimization , 2004, GECCO.

[13]  P. John Clarkson,et al.  Erratum: A Species Conserving Genetic Algorithm for Multimodal Function Optimization , 2003, Evolutionary Computation.

[14]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[15]  María José del Jesús,et al.  KEEL: a software tool to assess evolutionary algorithms for data mining problems , 2008, Soft Comput..

[16]  Swagatam Das,et al.  An Improved Parent-Centric Mutation With Normalized Neighborhoods for Inducing Niching Behavior in Differential Evolution , 2014, IEEE Transactions on Cybernetics.

[17]  René Thomsen,et al.  Multimodal optimization using crowding-based differential evolution , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[18]  Vaishali R. Kulkarni,et al.  ABC and PSO: A comparative analysis , 2016 .

[19]  Swagatam Das,et al.  Synergizing fitness learning with proximity-based food source selection in artificial bee colony algorithm for numerical optimization , 2013, Appl. Soft Comput..

[20]  Pasi Fränti,et al.  Minimum spanning tree based split-and-merge: A hierarchical clustering method , 2011, Inf. Sci..

[21]  Jun Zhang,et al.  Learning Multimodal Parameters: A Bare-Bones Niching Differential Evolution Approach , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Xiaodong Li,et al.  A multimodal particle swarm optimizer based on fitness Euclidean-distance ratio , 2007, GECCO '07.

[23]  Jie Yao,et al.  Bi-Objective Multipopulation Genetic Algorithm for Multimodal Function Optimization , 2010, IEEE Transactions on Evolutionary Computation.

[24]  Jing J. Liang,et al.  Differential Evolution With Neighborhood Mutation for Multimodal Optimization , 2012, IEEE Transactions on Evolutionary Computation.

[25]  Jun Zhang,et al.  Particle Swarm Optimization with Minimum Spanning Tree Topology for Multimodal Optimization , 2015, 2015 IEEE Symposium Series on Computational Intelligence.

[26]  Kay Chen Tan,et al.  Multimodal Optimization Using a Biobjective Differential Evolution Algorithm Enhanced With Mean Distance-Based Selection , 2013, IEEE Transactions on Evolutionary Computation.

[27]  Daniel P. Huttenlocher,et al.  Efficient Graph-Based Image Segmentation , 2004, International Journal of Computer Vision.

[28]  Xiaodong Li,et al.  Benchmark Functions for CEC'2013 Special Session and Competition on Niching Methods for Multimodal Function Optimization' , 2013 .

[29]  Jun Zhang,et al.  Genetic Learning Particle Swarm Optimization , 2016, IEEE Transactions on Cybernetics.

[30]  Xiaodong Yin,et al.  A Fast Genetic Algorithm with Sharing Scheme Using Cluster Analysis Methods in Multimodal Function Optimization , 1993 .

[31]  Dervis Karaboga,et al.  A novel clustering approach: Artificial Bee Colony (ABC) algorithm , 2011, Appl. Soft Comput..

[32]  Yong Wang,et al.  MOMMOP: Multiobjective Optimization for Locating Multiple Optimal Solutions of Multimodal Optimization Problems , 2015, IEEE Transactions on Cybernetics.

[33]  Yangmin Li,et al.  Cooperative particle swarm optimizer with elimination mechanism for global optimization of multimodal problems , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[34]  Arthur C. Sanderson,et al.  Planning multiple paths with evolutionary speciation , 2001, IEEE Trans. Evol. Comput..

[35]  Alain Pétrowski,et al.  A clearing procedure as a niching method for genetic algorithms , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[36]  Ponnuthurai N. Suganthan,et al.  Real-parameter evolutionary multimodal optimization - A survey of the state-of-the-art , 2011, Swarm Evol. Comput..

[37]  Michael G. Epitropakis,et al.  Finding multiple global optima exploiting differential evolution's niching capability , 2011, 2011 IEEE Symposium on Differential Evolution (SDE).

[38]  K. K. Mishra,et al.  Co-variance guided Artificial Bee Colony , 2018, Appl. Soft Comput..

[39]  Jun Zhang,et al.  Toward Fast Niching Evolutionary Algorithms: A Locality Sensitive Hashing-Based Approach , 2017, IEEE Transactions on Evolutionary Computation.

[40]  Xiaodong Li,et al.  A dynamic archive niching differential evolution algorithm for multimodal optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

[41]  Tao Zhu,et al.  Learning enhanced differential evolution for tracking optimal decisions in dynamic power systems , 2017, Appl. Soft Comput..

[42]  Ponnuthurai N. Suganthan,et al.  A Distance-Based Locally Informed Particle Swarm Model for Multimodal Optimization , 2013, IEEE Transactions on Evolutionary Computation.

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

[44]  Kevin Leyton-Brown,et al.  Sequential Model-Based Optimization for General Algorithm Configuration , 2011, LION.

[45]  Sanyang Liu,et al.  Improved artificial bee colony algorithm for global optimization , 2011 .

[46]  Mehmet Fatih Tasgetiren,et al.  A discrete artificial bee colony algorithm for the lot-streaming flow shop scheduling problem , 2011, Inf. Sci..

[47]  Nurhan Karaboga,et al.  A new design method based on artificial bee colony algorithm for digital IIR filters , 2009, J. Frankl. Inst..

[48]  Swagatam Das,et al.  Inducing Niching Behavior in Differential Evolution Through Local Information Sharing , 2015, IEEE Transactions on Evolutionary Computation.

[49]  S. N. Omkar,et al.  Applied Soft Computing Artificial Bee Colony (abc) for Multi-objective Design Optimization of Composite Structures , 2022 .

[50]  Yuhui Shi,et al.  Distributed learning particle swarm optimizer for global optimization of multimodal problems , 2018, Frontiers of Computer Science.

[51]  Xiaodong Li,et al.  Niching Without Niching Parameters: Particle Swarm Optimization Using a Ring Topology , 2010, IEEE Transactions on Evolutionary Computation.

[52]  Jun Zhang,et al.  Adaptive Multimodal Continuous Ant Colony Optimization , 2017, IEEE Transactions on Evolutionary Computation.

[53]  O. Gustafsson,et al.  Implementation of low complexity FIR filters using a minimum spanning tree , 2004, Proceedings of the 12th IEEE Mediterranean Electrotechnical Conference (IEEE Cat. No.04CH37521).

[54]  Xiaodong Li,et al.  Seeking Multiple Solutions: An Updated Survey on Niching Methods and Their Applications , 2017, IEEE Transactions on Evolutionary Computation.

[55]  Jun Zhang,et al.  Multimodal Estimation of Distribution Algorithms , 2017, IEEE Transactions on Cybernetics.

[56]  Tianlong Gu,et al.  Flexible genetic algorithm: A simple and generic approach to node placement problems , 2017, Appl. Soft Comput..

[57]  Ponnuthurai N. Suganthan,et al.  Diversity enhanced particle swarm optimizer for global optimization of multimodal problems , 2009, 2009 IEEE Congress on Evolutionary Computation.

[58]  Sanyang Liu,et al.  A Cluster-Based Differential Evolution With Self-Adaptive Strategy for Multimodal Optimization , 2014, IEEE Transactions on Cybernetics.

[59]  Harish Sharma,et al.  Beer froth artificial bee colony algorithm for job-shop scheduling problem , 2018, Appl. Soft Comput..

[60]  Dervis Karaboga,et al.  Artificial Bee Colony (ABC) Optimization Algorithm for Solving Constrained Optimization Problems , 2007, IFSA.

[61]  Sam Kwong,et al.  Gbest-guided artificial bee colony algorithm for numerical function optimization , 2010, Appl. Math. Comput..

[62]  Dervis Karaboga,et al.  A modified Artificial Bee Colony algorithm for real-parameter optimization , 2012, Inf. Sci..

[63]  Wei-jie Yu,et al.  Artificial bee colony algorithm with an adaptive greedy position update strategy , 2018, Soft Comput..