Extensions of Firefly Algorithm for Nonsmooth Nonconvex Constrained Optimization Problems

Firefly Algorithm (FA) is a stochastic population-based algorithm based on the flashing patterns and behavior of fireflies. Original FA was created and successfully applied to solve bound constrained optimization problems. In this paper we present extensions of FA for solving nonsmooth nonconvex constrained global optimization problems. To handle the constraints of the problem, feasibility and dominance rules and a fitness function based on the global competitive ranking, are proposed. To enhance the speed of convergence, the proposed extensions of FA invoke a stochastic local search procedure. Numerical experiments to validate the proposed approaches using a set of well know test problems are presented. The results show that the proposed extensions of FA compares favorably with other stochastic population-based methods.

[1]  Zong Woo Geem,et al.  A New Heuristic Optimization Algorithm: Harmony Search , 2001, Simul..

[2]  Milan Tuba,et al.  Swarm intelligence algorithms parameter tuning , 2012 .

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

[4]  M. Fernanda P. Costa,et al.  Heuristic-Based Firefly Algorithm for Bound Constrained Nonlinear Binary Optimization , 2014, Adv. Oper. Res..

[5]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[6]  Shu-Cherng Fang,et al.  An Electromagnetism-like Mechanism for Global Optimization , 2003, J. Glob. Optim..

[7]  Janez Brest,et al.  A comprehensive review of firefly algorithms , 2013, Swarm Evol. Comput..

[8]  Xin-She Yang,et al.  Multiobjective firefly algorithm for continuous optimization , 2012, Engineering with Computers.

[9]  Xin-She Yang,et al.  Firefly Algorithms for Multimodal Optimization , 2009, SAGA.

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

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

[12]  Jonathan A. Wright,et al.  Self-adaptive fitness formulation for constrained optimization , 2003, IEEE Trans. Evol. Comput..

[13]  Jing J. Liang,et al.  Problem Deflnitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization , 2006 .

[14]  Xiaodong Li,et al.  Swarm Intelligence in Optimization , 2008, Swarm Intelligence.

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

[16]  Carlos A. Coello Coello,et al.  Constraint-handling in nature-inspired numerical optimization: Past, present and future , 2011, Swarm Evol. Comput..

[17]  Xin-She Yang,et al.  Firefly Algorithm: Recent Advances and Applications , 2013, ArXiv.

[18]  N. Hansen,et al.  Markov Chain Analysis of Cumulative Step-Size Adaptation on a Linear Constrained Problem , 2015, Evolutionary Computation.

[19]  Edite M. G. P. Fernandes,et al.  Firefly penalty-based algorithm for bound constrained mixed-integer nonlinear programming , 2016 .

[20]  Ming-Huwi Horng,et al.  Multilevel minimum cross entropy threshold selection based on the firefly algorithm , 2011, Expert Syst. Appl..

[21]  Xin Yao,et al.  Constrained Evolutionary Optimization , 2003 .

[22]  Helio J. C. Barbosa,et al.  An adaptive constraint handling technique for differential evolution with dynamic use of variants in engineering optimization , 2011 .

[23]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[24]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization , 1999, Evolutionary Computation.

[25]  Amir Hossein Gandomi,et al.  Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect , 2012, Appl. Soft Comput..

[26]  M. M. Ali,et al.  A penalty function-based differential evolution algorithm for constrained global optimization , 2012, Computational Optimization and Applications.

[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]  Gary G. Yen,et al.  A Self Adaptive Penalty Function Based Algorithm for Constrained Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[29]  A. Gandomi,et al.  Mixed variable structural optimization using Firefly Algorithm , 2011 .

[30]  X. Yao,et al.  Constrained Evolutionary Optimization - the penalty function approach , 2002 .

[31]  Afonso C. C. Lemonge,et al.  An Adaptive Penalty Method for Genetic Algorithms in Constrained Optimization Problems , 2008 .

[32]  Heder S. Bernardino,et al.  Variants of an adaptive penalty scheme for steady-state genetic algorithms in engineering optimization , 2015 .

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