Distributed minimum spanning tree differential evolution for multimodal optimization problems

Multimodal optimization problem (MMOP) requires to find optima as many as possible for a single problem. Recently, many niching techniques have been proposed to tackle MMOPs. However, most of the niching techniques are either sensitive to the niching parameters or causing a waste of fitness evaluations. In this paper, we proposed a novel niching technique based on minimum spanning tree (MST) and applied it into differential evolution (DE), termed as MSTDE, to solve MMOPs. In every generation, an MST is built based on the distance information among the individuals. After that, we cut the M largest weighted edges of the MST to form some subtrees, so-called subpopulations. The DE operators are executed within the subpopulations. Besides, a dynamic pruning ratio (DPR) strategy is proposed to determine M with an attempt to reduce its sensitivity, so as to enhance the niching performance. Meanwhile, the DPR strategy can achieve a good balance between diversity and convergence. Besides, taking the advantage of fast availability in time from virtual machines (VMs), a distributed model is applied in MSTDE, where different subpopulations run concurrently on distributed VMs. Experiments have been conducted on the CEC2013 multimodal benchmark functions to test the performance of MSTDE, and the experimental results show that MSTDE can outperform many existed multimodal optimization algorithms.

[1]  Hossein Sharifi Noghabi,et al.  A novel mutation operator based on the union of fitness and design spaces information for Differential Evolution , 2017, Soft Comput..

[2]  Jie Zhang,et al.  Coevolutionary Particle Swarm Optimization With Bottleneck Objective Learning Strategy for Many-Objective Optimization , 2019, IEEE Transactions on Evolutionary Computation.

[3]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[4]  Kalyanmoy Deb,et al.  Multimodal Optimization by Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations , 2017, Evolutionary Computation.

[5]  Jun Zhang,et al.  A Discrete Multiobjective Particle Swarm Optimizer for Automated Assembly of Parallel Cognitive Diagnosis Tests , 2019, IEEE Transactions on Cybernetics.

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

[7]  Grant Dick,et al.  Weighted local sharing and local clearing for multimodal optimisation , 2010, Soft Comput..

[8]  Erik Valdemar Cuevas Jiménez,et al.  An optimization algorithm for multimodal functions inspired by collective animal behavior , 2013, Soft Comput..

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

[10]  Guo Li,et al.  A niching chaos optimization algorithm for multimodal optimization , 2018, Soft Comput..

[11]  Jun Zhang,et al.  An Improved Method for Comprehensive Learning Particle Swarm Optimization , 2015, 2015 IEEE Symposium Series on Computational Intelligence.

[12]  Zhi-hui Zhan,et al.  Parallel multi-strategy evolutionary algorithm using massage passing interface for many-objective optimization , 2016, 2016 IEEE Symposium Series on Computational Intelligence (SSCI).

[13]  Jun Zhang,et al.  An Evolutionary Algorithm with Double-Level Archives for Multiobjective Optimization , 2015, IEEE Transactions on Cybernetics.

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

[15]  Jun Zhang,et al.  Cloudde: A Heterogeneous Differential Evolution Algorithm and Its Distributed Cloud Version , 2017, IEEE Transactions on Parallel and Distributed Systems.

[16]  Jun Zhang,et al.  Cloud Computing Resource Scheduling and a Survey of Its Evolutionary Approaches , 2015, ACM Comput. Surv..

[17]  Dong-Kyun Woo,et al.  A Novel Multimodal Optimization Algorithm Applied to Electromagnetic Optimization , 2011, IEEE Transactions on Magnetics.

[18]  Xiaodong Li,et al.  A framework for generating tunable test functions for multimodal optimization , 2011, Soft Comput..

[19]  C. Shunmuga Velayutham,et al.  Distributed heterogeneous mixing of differential and dynamic differential evolution variants for unconstrained global optimization , 2014, Soft Comput..

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

[21]  Mike Preuss,et al.  Improved Topological Niching for Real-Valued Global Optimization , 2012, EvoApplications.

[22]  Enrique Alba,et al.  Efficiently finding the optimum number of clusters in a dataset with a new hybrid differential evolution algorithm: DELA , 2016, Soft Comput..

[23]  José Rui Figueira,et al.  Graph partitioning by multi-objective real-valued metaheuristics: A comparative study , 2011, Appl. Soft Comput..

[24]  Kwong-Sak Leung,et al.  Protein structure prediction on a lattice model via multimodal optimization techniques , 2010, GECCO '10.

[25]  Cheng-Hung Chen,et al.  A knowledge-based cooperative differential evolution for neural fuzzy inference systems , 2013, Soft Comput..

[26]  Ville Tirronen,et al.  Scale factor inheritance mechanism in distributed differential evolution , 2009, Soft Comput..

[27]  Erik Valdemar Cuevas Jiménez,et al.  Multi-ellipses detection on images inspired by collective animal behavior , 2013, Neural Computing and Applications.

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

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

[30]  Tianlong Gu,et al.  Historical and Heuristic-Based Adaptive Differential Evolution , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[31]  Jun Zhang,et al.  Differential Evolution with an Evolution Path: A DEEP Evolutionary Algorithm , 2015, IEEE Transactions on Cybernetics.

[32]  Xin Zhang,et al.  Improving differential evolution by differential vector archive and hybrid repair method for global optimization , 2016, Soft Computing.

[33]  Mike Preuss,et al.  Niching the CMA-ES via nearest-better clustering , 2010, GECCO '10.

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

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

[36]  Jun Zhang,et al.  Neural Network for Change Direction Prediction in Dynamic Optimization , 2018, IEEE Access.

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

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

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

[40]  Smriti Srivastava,et al.  Multimodal biometric system based on information set theory and refined scores , 2017, Soft Comput..

[41]  Craig A. Knoblock,et al.  A Survey of Digital Map Processing Techniques , 2014, ACM Comput. Surv..

[42]  Ponnuthurai N. Suganthan,et al.  Ensemble and Arithmetic Recombination-Based Speciation Differential Evolution for Multimodal Optimization , 2016, IEEE Transactions on Cybernetics.

[43]  Zhiwen Yu,et al.  Orthogonal learning particle swarm optimization with variable relocation for dynamic optimization , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

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

[45]  R. K. Ursem.  Multinational evolutionary algorithms , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[46]  Nguyen Ngoc Son,et al.  Adaptive neural model optimized by modified differential evolution for identifying 5-DOF robot manipulator dynamic system , 2018, Soft Comput..

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

[48]  Shikha Agrawal,et al.  FRPSO: Fletcher–Reeves based particle swarm optimization for multimodal function optimization , 2014, Soft Comput..