Adaptive gbest-guided gravitational search algorithm

Abstract One heuristic evolutionary algorithm recently proposed is the gravitational search algorithm (GSA), inspired by the gravitational forces between masses in nature. This algorithm has demonstrated superior performance among other well-known heuristic algorithms such as particle swarm optimisation and genetic algorithm. However, slow exploitation is a major weakness that might result in degraded performance when dealing with real engineering problems. Due to the cumulative effect of the fitness function on mass in GSA, masses get heavier and heavier over the course of iteration. This causes masses to remain in close proximity and neutralise the gravitational forces of each other in later iterations, preventing them from rapidly exploiting the optimum. In this study, the best mass is archived and utilised to accelerate the exploitation phase, ameliorating this weakness. The proposed method is tested on 25 unconstrained benchmark functions with six different scales provided by CEC 2005. In addition, two classical, constrained, engineering design problems, namely welded beam and tension spring, are also employed to investigate the efficiency of the proposed method in real constrained problems. The results of benchmark and classical engineering problems demonstrate the performance of the proposed method.

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

[2]  Xinsheng Lai,et al.  An efficient ensemble of GA and PSO for real function optimization , 2009, 2009 2nd IEEE International Conference on Computer Science and Information Technology.

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

[4]  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..

[5]  Germano Lambert-Torres,et al.  Hybrid Evolutionary Algorithm Based on PSO and GA Mutation , 2006, 2006 Sixth International Conference on Hybrid Intelligent Systems (HIS'06).

[6]  Manuel López-Ibáñez,et al.  Ant colony optimization , 2010, GECCO '10.

[7]  Ling Wang,et al.  An effective co-evolutionary differential evolution for constrained optimization , 2007, Appl. Math. Comput..

[8]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[9]  Junying Chen,et al.  Particle Swarm Optimization with Local Search , 2005, 2005 International Conference on Neural Networks and Brain.

[10]  Jasbir S. Arora,et al.  Introduction to Optimum Design , 1988 .

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

[12]  Marco Dorigo,et al.  Ant Colony Optimization and Stochastic Gradient Descent , 2002, Artificial Life.

[13]  Zheng Tang,et al.  Hybrid Gravitational Search Algorithm with Random-key Encoding Scheme Combined with Simulated Annealing , 2011 .

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

[15]  Ying Zhang,et al.  Immune Gravitation Inspired Optimization Algorithm , 2011, ICIC.

[16]  M. Fesanghary,et al.  An improved harmony search algorithm for solving optimization problems , 2007, Appl. Math. Comput..

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

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

[19]  Hitoshi Iba,et al.  Accelerating Differential Evolution Using an Adaptive Local Search , 2008, IEEE Transactions on Evolutionary Computation.

[20]  Kang-Hyun Jo,et al.  Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence , 2008, Lecture Notes in Computer Science.

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

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

[23]  Carlos A. Coello Coello,et al.  Constraint-handling in genetic algorithms through the use of dominance-based tournament selection , 2002, Adv. Eng. Informatics.

[24]  Saman Sinaie,et al.  SOLVING SHORTEST PATH PROBLEM USING GRAVITATIONAL SEARCH ALGORITHM AND NEURAL NETWORKS , 2010 .

[25]  Alex Alves Freitas,et al.  A hybrid PSO/ACO algorithm for classification , 2007, GECCO '07.

[26]  Andrew Lewis,et al.  S-shaped versus V-shaped transfer functions for binary Particle Swarm Optimization , 2013, Swarm Evol. Comput..

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

[28]  Salwani Abdullah,et al.  Gravitational search algorithm with heuristic search for clustering problems , 2011, 2011 3rd Conference on Data Mining and Optimization (DMO).

[29]  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..

[30]  Jianzhong Zhou,et al.  Parameters identification of hydraulic turbine governing system using improved gravitational search algorithm , 2011 .

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

[32]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[33]  Minzhou Luo,et al.  Identification of Nonlinear System Based on a New Hybrid Gradient-Based PSO Algorithm , 2007, 2007 International Conference on Information Acquisition.

[34]  Alex A. Freitas,et al.  A hybrid PSO/ACO algorithm for discovering classification rules in data mining , 2008 .

[35]  C. Coello,et al.  CONSTRAINT-HANDLING USING AN EVOLUTIONARY MULTIOBJECTIVE OPTIMIZATION TECHNIQUE , 2000 .

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

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

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

[39]  Hossein Nezamabadi-pour,et al.  BGSA: binary gravitational search algorithm , 2010, Natural Computing.

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

[41]  Tony J. Dodd,et al.  Why ‘GSA: a gravitational search algorithm’ is not genuinely based on the law of gravity , 2011, Natural Computing.

[42]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[43]  Xiao-Feng Xie,et al.  DEPSO: hybrid particle swarm with differential evolution operator , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[44]  Ben Niu,et al.  A Novel PSO-DE-Based Hybrid Algorithm for Global Optimization , 2008, ICIC.

[45]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

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

[47]  Sakti Prasad Ghoshal,et al.  A novel opposition-based gravitational search algorithm for combined economic and emission dispatch problems of power systems , 2012 .

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

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

[50]  Xin-She Yang,et al.  Nature-Inspired Metaheuristic Algorithms: Second Edition , 2010 .

[51]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[52]  S. Mirjalili,et al.  A new hybrid PSOGSA algorithm for function optimization , 2010, 2010 International Conference on Computer and Information Application.

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

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

[55]  R. Storn,et al.  Differential Evolution , 2004 .

[56]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

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

[58]  Seyed Mohammad Mirjalili,et al.  Chaotic krill herd optimization algorithm , 2014 .

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