A comprehensive study of phase based optimization algorithm on global optimization problems and its applications

Inspired by the completely different motional features of individuals in three different phases of nature, i.e. gas phase, liquid phase and solid phase, this paper presents a phase based evolutionary model. Based on the proposed model, a specific implementation termed Phase Based Optimization (PBO) was systematically given. Meanwhile, the search behavior analysis and the evolution process of population are provided to further understand the search mechanisms of PBO. To evaluate the performance of PBO, numerical experiments are carried out on twenty-three benchmark test functions consisting of different types of unimodal and multimodal functions. The obtained results demonstrate the better performance of PBO compared with eight state-of-the-art nature-inspired optimization algorithms. Besides, the effects of population size on PBO and the performance comparison of PBO under different problem dimensions are systematically investigated, respectively. Finally, PBO is applied to two application problems which are parameter estimation for frequency modulated sound waves synthesis and large scale transmission pricing problem, and the promising results indicate the applicability of PBO in both low and high dimensional real-world optimization problems.

[1]  Feng Zou,et al.  Teaching-learning-based optimization with dynamic group strategy for global optimization , 2014, Inf. Sci..

[2]  Pinar Çivicioglu,et al.  Backtracking Search Optimization Algorithm for numerical optimization problems , 2013, Appl. Math. Comput..

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

[4]  Grzegorz Rozenberg,et al.  Handbook of Natural Computing , 2011, Springer Berlin Heidelberg.

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

[6]  James Jeans,et al.  An Introduction to the Kinetic Theory of Gases: Index of Subjects , 2009 .

[7]  Yuhui Shi,et al.  Particle Swarm Optimization With Interswarm Interactive Learning Strategy , 2016, IEEE Transactions on Cybernetics.

[8]  N. Nachtrieb,et al.  Principles of Modern Chemistry , 1986 .

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

[10]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[11]  E. Afjei,et al.  Reactive power dispatch using Big Bang-Big Crunch optimization algorithm for voltage stability enhancement , 2012, 2012 IEEE International Conference on Power and Energy (PECon).

[12]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[13]  Roger J.-B. Wets,et al.  Minimization by Random Search Techniques , 1981, Math. Oper. Res..

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

[15]  Kevin M. Passino,et al.  Biomimicry of bacterial foraging for distributed optimization and control , 2002 .

[16]  Xin-She Yang,et al.  Chapter 10 – Bat Algorithms , 2014 .

[17]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[18]  Victor O. K. Li,et al.  Chemical-Reaction-Inspired Metaheuristic for Optimization , 2010, IEEE Transactions on Evolutionary Computation.

[19]  Peter J. Angeline,et al.  Genetic programming: On the programming of computers by means of natural selection,: John R. Koza, A Bradford Book, MIT Press, Cambridge MA, 1992, ISBN 0-262-11170-5, xiv + 819pp., US$55.00 , 1994 .

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

[21]  M. Hoare.  Structure and Dynamics of Simple Microclusters , 2007 .

[22]  Noah Webster,et al.  Webster's new collegiate dictionary , 1936 .

[23]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[24]  Alireza Askarzadeh,et al.  Bird mating optimizer: An optimization algorithm inspired by bird mating strategies , 2014, Commun. Nonlinear Sci. Numer. Simul..

[25]  Yu Liu,et al.  A new bio-inspired optimisation algorithm: Bird Swarm Algorithm , 2016, J. Exp. Theor. Artif. Intell..

[26]  Yujun Zheng.  Water wave optimization: A new nature-inspired metaheuristic , 2015, Comput. Oper. Res..

[27]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[28]  Istvan Erlich,et al.  Performance assessment of evolutionary algorithms in power system optimization problems , 2015, 2015 IEEE Eindhoven PowerTech.

[29]  Hamed Shah-Hosseini,et al.  The intelligent water drops algorithm: a nature-inspired swarm-based optimization algorithm , 2009, Int. J. Bio Inspired Comput..

[30]  Seyed Mohammad Mirjalili.  How effective is the Grey Wolf optimizer in training multi-layer perceptrons , 2014, Applied Intelligence.

[31]  Mansoureh Maadi,et al.  Modified Cuckoo Optimization Algorithm (MCOA) to solve Precedence Constrained Sequencing Problem (PCSP) , 2017, Applied Intelligence.

[32]  Ardeshir Bahreininejad,et al.  Water cycle algorithm - A novel metaheuristic optimization method for solving constrained engineering optimization problems , 2012 .

[33]  Xinghuo Yu,et al.  Conditions for the convergence of evolutionary algorithms , 2001, J. Syst. Archit..

[34]  Yuhui Shi,et al.  Brain Storm Optimization Algorithm , 2011, ICSI.

[35]  Q. Henry Wu,et al.  Group Search Optimizer: An Optimization Algorithm Inspired by Animal Searching Behavior , 2009, IEEE Transactions on Evolutionary Computation.

[36]  Rainer Storn,et al.  Differential Evolution-A simple evolution strategy for fast optimization , 1997 .

[37]  Xiao Fan Wang,et al.  A phase based optimization algorithm for big optimization problems , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

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

[39]  Pinar Civicioglu,et al.  Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm , 2012, Comput. Geosci..

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

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

[42]  Xin-She Yang,et al.  Nature-Inspired Optimization Algorithms: Challenges and Open Problems , 2020, J. Comput. Sci..

[43]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[44]  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..

[45]  Rémi Monasson,et al.  Statistical mechanics methods and phase transitions in optimization problems , 2001, Theor. Comput. Sci..

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

[47]  P. N. Suganthan,et al.  Problem Definitions and Evaluation Criteria for CEC 2011 Competition on Testing Evolutionary Algorithms on Real World Optimization Problems , 2011 .

[48]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

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

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

[51]  Ziying Zhang,et al.  Differential evolution algorithm with multiple mutation strategies based on roulette wheel selection , 2018, Applied Intelligence.