Complex-valued encoding metaheuristic optimization algorithm: A comprehensive survey

Abstract The number of publications related to complex-valued encoding metaheuristic optimization research is increasing the area of metaheuristic optimization is gaining in popularity. In this paper, we aim to provide researchers with a comprehensive and extensive overview of complex-valued encoding metaheuristic algorithms and applications for function optimization, engineering optimization design, and combination optimization. Compared with the basic metaheuristic algorithm, which are based on real-valued encoding or binary encoding, the complex-valued encoding metaheuristic algorithm expands the dimension of the search region and efficiently avoids the problem of falling into the local minimum. Finally, eight complex-valued encoding metaheuristic algorithms were used for 29 benchmark test functions and five engineering optimization design problems. Through the analysis and comparison of the results with statistical significance, the superiority of complex-value encoding was proved, and the complex-value encoding metaheuristic algorithm with the best performance was obtained. The purpose of this review is to present a relatively comprehensive list of all the complex-value encoding metaheuristic algorithms in the literature to inspire further research.

[1]  Carlos A. Coello Coello,et al.  An empirical study about the usefulness of evolution strategies to solve constrained optimization problems , 2008, Int. J. Gen. Syst..

[2]  Suash Deb,et al.  Solving 0–1 knapsack problem by a novel binary monarch butterfly optimization , 2017, Neural Computing and Applications.

[3]  Yuhui Shi,et al.  Metaheuristic research: a comprehensive survey , 2018, Artificial Intelligence Review.

[4]  Li Shang,et al.  Palmprint recognition using FastICA algorithm and radial basis probabilistic neural network , 2006, Neurocomputing.

[5]  George W. Irwin,et al.  MISEP Method for Postnonlinear Blind Source Separation , 2007, Neural Computation.

[6]  Vijay Kumar,et al.  Emperor penguin optimizer: A bio-inspired algorithm for engineering problems , 2018, Knowl. Based Syst..

[7]  De-Shuang Huang,et al.  Optimized projections for sparse representation based classification , 2013, Neurocomputing.

[8]  Ganapati Panda,et al.  IIR system identification using cat swarm optimization , 2011, Expert Syst. Appl..

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

[10]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[11]  Arnapurna Panda,et al.  A Symbiotic Organisms Search algorithm with adaptive penalty function to solve multi-objective constrained optimization problems , 2016, Appl. Soft Comput..

[12]  Ashish Kumar Bhandari,et al.  Cuckoo search algorithm and wind driven optimization based study of satellite image segmentation for multilevel thresholding using Kapur's entropy , 2014, Expert Syst. Appl..

[13]  De-Shuang Huang,et al.  Modified constrained learning algorithms incorporating additional functional constraints into neural networks , 2008, Inf. Sci..

[14]  Fariborz Jolai,et al.  Lion Optimization Algorithm (LOA): A nature-inspired metaheuristic algorithm , 2016, J. Comput. Des. Eng..

[15]  Wei Jia,et al.  Palmprint recognition with 2DPCA+PCA based on modular neural networks , 2007, Neurocomputing.

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

[17]  Yongquan Zhou,et al.  A complex encoding flower pollination algorithm for constrained engineering optimisation problems , 2017, Int. J. Math. Model. Numer. Optimisation.

[18]  Al-Attar Ali Mohamed,et al.  Grey Wolf Optimization for Multi Input Multi Output System , 2015 .

[19]  Zhiming Li,et al.  A Novel Complex-Valued Encoding Grey Wolf Optimization Algorithm , 2015, Algorithms.

[20]  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.

[21]  D.-S. Huang,et al.  Radial Basis Probabilistic Neural Networks: Model and Application , 1999, Int. J. Pattern Recognit. Artif. Intell..

[22]  De-shuang Huang,et al.  Computer-Aided Plant Species Identification (CAPSI) Based on Leaf Shape Matching Technique , 2006 .

[23]  Zheng Zhao,et al.  Genetic algorithm based on complex-valued encoding , 2003 .

[24]  Ashok Dhondu Belegundu,et al.  A Study of Mathematical Programming Methods for Structural Optimization , 1985 .

[25]  James L. McClelland,et al.  On the control of automatic processes: a parallel distributed processing account of the Stroop effect. , 1990, Psychological review.

[26]  Harish Sharma,et al.  Spider Monkey Optimization algorithm for numerical optimization , 2014, Memetic Computing.

[27]  Victor O. K. Li,et al.  A social spider algorithm for global optimization , 2015, Appl. Soft Comput..

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

[29]  Christian Blum,et al.  Hybrid metaheuristics in combinatorial optimization: A survey , 2011, Appl. Soft Comput..

[30]  Xin-She Yang,et al.  A New Metaheuristic Bat-Inspired Algorithm , 2010, NICSO.

[31]  Salim Chikhi,et al.  Solving 0-1 knapsack problems by a discrete binary version of cuckoo search algorithm , 2012, Int. J. Bio Inspired Comput..

[32]  Reza Tavakkoli-Moghaddam,et al.  The Social Engineering Optimizer (SEO) , 2018, Eng. Appl. Artif. Intell..

[33]  Yuxiang Zhou,et al.  A Novel Complex-Valued Social Spider Optimization Algorithm , 2016 .

[34]  B. Maddock,et al.  FROM DESIGN TO IMPLEMENTATION , 1982 .

[35]  Kazuyuki Murase,et al.  Using complex-valued Levenberg-Marquardt algorithm for learning and recognizing various hand gestures , 2012, The 2012 International Joint Conference on Neural Networks (IJCNN).

[36]  De-Shuang Huang,et al.  An improved approximation approach incorporating particle swarm optimization and a priori information into neural networks , 2010, Neural Computing and Applications.

[37]  Meng Joo Er,et al.  Face recognition with radial basis function (RBF) neural networks , 2002, IEEE Trans. Neural Networks.

[38]  Michael Collins,et al.  Discriminative Training Methods for Hidden Markov Models: Theory and Experiments with Perceptron Algorithms , 2002, EMNLP.

[39]  Yongquan Zhou,et al.  Complex-valued encoding symbiotic organisms search algorithm for global optimization , 2018, Knowledge and Information Systems.

[40]  Xin-She Yang,et al.  Flower pollination algorithm: A novel approach for multiobjective optimization , 2014, ArXiv.

[41]  Erik Cuevas,et al.  Social Spider Optimization Algorithm: Modifications, Applications, and Perspectives , 2018, Mathematical Problems in Engineering.

[42]  Xing-Ming Zhao,et al.  Classifying protein sequences using hydropathy blocks , 2006, Pattern Recognit..

[43]  Ling Wang,et al.  An effective co-evolutionary particle swarm optimization for constrained engineering design problems , 2007, Eng. Appl. Artif. Intell..

[44]  De-Shuang Huang,et al.  Genetic Optimization Of Radial Basis Probabilistic Neural Networks , 2004, Int. J. Pattern Recognit. Artif. Intell..

[45]  Siamak Talatahari,et al.  An improved ant colony optimization for constrained engineering design problems , 2010 .

[46]  Xiaofeng Wang,et al.  Shape recognition based on neural networks trained by differential evolution algorithm , 2007, Neurocomputing.

[47]  Xiaofeng Wang,et al.  A Novel Multi-Layer Level Set Method for Image Segmentation , 2008, J. Univers. Comput. Sci..

[48]  Suash Deb,et al.  Solving IIR system identification by a variant of particle swarm optimization , 2016, Neural Computing and Applications.

[49]  Kalyanmoy Deb,et al.  Optimal design of a welded beam via genetic algorithms , 1991 .

[50]  Yongquan Zhou,et al.  A novel complex-valued bat algorithm , 2014, Neural Computing and Applications.

[51]  De-Shuang Huang,et al.  Cancer classification using Rotation Forest , 2008, Comput. Biol. Medicine.

[52]  De-Shuang Huang,et al.  A new constrained learning algorithm for function approximation by encoding a priori information into feedforward neural networks , 2008, Neural Computing and Applications.

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

[54]  De-Shuang Huang,et al.  Linear and Nonlinear Feedforward Neural Network Classifiers: A Comprehensive Understanding , 1999 .

[55]  De-Shuang Huang,et al.  A constructive approach for finding arbitrary roots of polynomials by neural networks , 2004, IEEE Transactions on Neural Networks.

[56]  Dean J. Krusienski,et al.  Particle swarm optimization for adaptive IIR filter structures , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[57]  Paolo Toth,et al.  New trends in exact algorithms for the 0-1 knapsack problem , 2000, Eur. J. Oper. Res..

[58]  Iztok Fister,et al.  Cuckoo Search: A Brief Literature Review , 2014, ArXiv.

[59]  De-Shuang Huang,et al.  A New Constrained Independent Component Analysis Method , 2007, IEEE Transactions on Neural Networks.

[60]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[61]  Yang Zhao,et al.  Completed Local Binary Count for Rotation Invariant Texture Classification , 2012, IEEE Transactions on Image Processing.

[62]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.

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

[64]  Hossam Faris,et al.  Grasshopper optimization algorithm for multi-objective optimization problems , 2017, Applied Intelligence.

[65]  Yongquan Zhou,et al.  A complex-valued encoding satin bowerbird optimization algorithm for global optimization , 2019, ICIC.

[66]  Aboul Ella Hassanien,et al.  Binary grey wolf optimization approaches for feature selection , 2016, Neurocomputing.

[67]  De-Shuang Huang,et al.  Determining the centers of radial basis probabilistic neural networks by recursive orthogonal least square algorithms , 2005, Appl. Math. Comput..

[68]  De-peng Du,et al.  Greedy Strategy Based Self-adaption Ant Colony Algorithm for 0/1 Knapsack Problem , 2015 .

[69]  Erik Valdemar Cuevas Jiménez,et al.  A swarm optimization algorithm inspired in the behavior of the social-spider , 2013, Expert Syst. Appl..

[70]  Sen Zhang,et al.  A complex-valued encoding wind driven optimization for the 0-1 knapsack problem , 2017, Applied Intelligence.

[71]  Amir Hossein Gandomi,et al.  Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems , 2011, Engineering with Computers.

[72]  Xiaofeng Wang,et al.  Classification of plant leaf images with complicated background , 2008, Appl. Math. Comput..

[73]  Vahid Khatibi Bardsiri,et al.  Satin bowerbird optimizer: A new optimization algorithm to optimize ANFIS for software development effort estimation , 2017, Eng. Appl. Artif. Intell..

[74]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[75]  Andrew Lewis,et al.  Grasshopper Optimisation Algorithm: Theory and application , 2017, Adv. Eng. Softw..

[76]  Jagadeeswar Reddy Chintam,et al.  Real-Power Rescheduling of Generators for Congestion Management Using a Novel Satin Bowerbird Optimization Algorithm , 2018 .

[77]  Xin-She Yang,et al.  Multiobjective cuckoo search for design optimization , 2013, Comput. Oper. Res..

[78]  Q. H. Wu,et al.  A heuristic particle swarm optimizer for optimization of pin connected structures , 2007 .

[79]  Xiaofeng Wang,et al.  An efficient local Chan-Vese model for image segmentation , 2010, Pattern Recognit..

[80]  De-Shuang Huang,et al.  A General CPL-AdS Methodology for Fixing Dynamic Parameters in Dual Environments , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[81]  Erik Valdemar Cuevas Jiménez,et al.  A new algorithm inspired in the behavior of the social-spider for constrained optimization , 2014, Expert Syst. Appl..

[82]  T. Martínez,et al.  Competitive Hebbian Learning Rule Forms Perfectly Topology Preserving Maps , 1993 .

[83]  Hae Chang Gea,et al.  STRUCTURAL OPTIMIZATION USING A NEW LOCAL APPROXIMATION METHOD , 1996 .

[84]  Hossam Faris,et al.  Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems , 2017, Adv. Eng. Softw..

[85]  Chao Wang,et al.  Supervised feature extraction based on orthogonal discriminant projection , 2009, Neurocomputing.

[86]  Min-Yuan Cheng,et al.  Symbiotic Organisms Search: A new metaheuristic optimization algorithm , 2014 .

[87]  Satvir Singh,et al.  Butterfly optimization algorithm: a novel approach for global optimization , 2018, Soft Computing.

[88]  Zhang Cui-jun,et al.  Greedy genetic algorithm for solving knapsack problems and its applications , 2007 .

[89]  V. Mukherjee,et al.  A novel symbiotic organisms search algorithm for congestion management in deregulated environment , 2017, J. Exp. Theor. Artif. Intell..

[90]  K. M. Ragsdell,et al.  Optimal Design of a Class of Welded Structures Using Geometric Programming , 1976 .

[91]  Mohamed Abdel-Baset,et al.  A New Hybrid Flower Pollination Algorithm for Solving Constrained Global Optimization Problems , 2014 .

[92]  De-Shuang Huang,et al.  The nearest-farthest subspace classification for face recognition , 2013, Neurocomputing.

[93]  Xiaofeng Wang,et al.  A Novel Density-Based Clustering Framework by Using Level Set Method , 2009, IEEE Transactions on Knowledge and Data Engineering.

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

[95]  De-Shuang Huang,et al.  A mended hybrid learning algorithm for radial basis function neural networks to improve generalization capability , 2007 .

[96]  Min-Yuan Cheng,et al.  A novel Multiple Objective Symbiotic Organisms Search (MOSOS) for time-cost-labor utilization tradeoff problem , 2016, Knowl. Based Syst..

[97]  Li Zheng,et al.  Particle swarm optimization based on complex-valued encoding and application in function optimization , 2009 .

[98]  Hossein Nezamabadi-pour,et al.  GSA: A Gravitational Search Algorithm , 2009, Inf. Sci..

[99]  Yongquan Zhou,et al.  Flower Pollination Algorithm with Dimension by Dimension Improvement , 2014 .

[100]  De-Shuang Huang,et al.  Extracting nonlinear features for multispectral images by FCMC and KPCA , 2005, Digit. Signal Process..

[101]  De-Shuang Huang,et al.  Using FCMC, FVS, and PCA techniques for feature extraction of multispectral images , 2005, IEEE Geosci. Remote. Sens. Lett..

[102]  Z. Shayfull,et al.  Recent studies on optimisation method of Grey Wolf Optimiser (GWO): a review (2014–2017) , 2019, Artificial Intelligence Review.

[103]  D. Werner,et al.  Wind Driven Optimization (WDO): A novel nature-inspired optimization algorithm and its application to electromagnetics , 2010, 2010 IEEE Antennas and Propagation Society International Symposium.

[104]  Douglas H. Werner,et al.  The Wind Driven Optimization Technique and its Application in Electromagnetics , 2013, IEEE Transactions on Antennas and Propagation.

[105]  David Casasent,et al.  A classifier neural net with complex-valued weights and square-law nonlinearities , 1995, Neural Networks.

[106]  Michael R. Lyu,et al.  Nonnegative independent component analysis based on minimizing mutual information technique , 2006, Neurocomputing.

[107]  Carlos A. Coello Coello,et al.  Use of a self-adaptive penalty approach for engineering optimization problems , 2000 .

[108]  Chao Wang,et al.  Feature extraction using constrained maximum variance mapping , 2008, Pattern Recognit..

[109]  Xin-She Yang,et al.  Bat algorithm: a novel approach for global engineering optimization , 2012, 1211.6663.

[110]  Heitor Silvério Lopes,et al.  Particle Swarm Optimization for the Multidimensional Knapsack Problem , 2007, ICANNGA.

[111]  De-Shuang Huang,et al.  Zeroing polynomials using modified constrained neural network approach , 2005, IEEE Transactions on Neural Networks.

[112]  Henry Leung,et al.  The complex backpropagation algorithm , 1991, IEEE Trans. Signal Process..

[113]  Yuxin Zhao,et al.  Swarm intelligence: past, present and future , 2017, Soft Computing.

[114]  Wen Jiang,et al.  Random Walk-Based Solution to Triple Level Stochastic Point Location Problem , 2016, IEEE Transactions on Cybernetics.

[115]  De-Shuang Huang,et al.  Improved extreme learning machine for function approximation by encoding a priori information , 2006, Neurocomputing.

[116]  Kenneth Morgan,et al.  Modified cuckoo search: A new gradient free optimisation algorithm , 2011 .

[117]  Xin-She Yang,et al.  Flower Pollination Algorithm for Global Optimization , 2012, UCNC.

[118]  Azlan Mohd Zain,et al.  Potential ANN prediction model for multiperformances WEDM on Inconel 718 , 2016, Neural Computing and Applications.

[119]  Li Shang,et al.  Optimal selection of time lags for TDSEP based on genetic algorithm , 2006, Neurocomputing.

[120]  Michael R. Lyu,et al.  A novel adaptive sequential niche technique for multimodal function optimization , 2006, Neurocomputing.

[121]  De-Shuang Huang,et al.  A novel full structure optimization algorithm for radial basis probabilistic neural networks , 2006, Neurocomputing.

[122]  De-Shuang Huang,et al.  Locally linear discriminant embedding: An efficient method for face recognition , 2008, Pattern Recognit..

[123]  Philipp Slusallek,et al.  Introduction to real-time ray tracing , 2005, SIGGRAPH Courses.

[124]  Li Shang,et al.  Feature selection in independent component subspace for microarray data classification , 2006, Neurocomputing.

[125]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[126]  De-Shuang Huang,et al.  A Constructive Hybrid Structure Optimization Methodology for Radial Basis Probabilistic Neural Networks , 2008, IEEE Transactions on Neural Networks.

[127]  Li Shang,et al.  Noise removal using a novel non-negative sparse coding shrinkage technique , 2006, Neurocomputing.

[128]  Andrew Lewis,et al.  Adaptive gbest-guided gravitational search algorithm , 2014, Neural Computing and Applications.

[129]  K. Lee,et al.  A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice , 2005 .