Constrained Optimization Problems Solving Using Evolutionary Algorithms: A Review

Solving Constrained Optimization Problems (COPs) is challenging task in the field of computer optimization. Many researchers have put efforts to solve COPs using techniques such as Dynamic Programming, Non Linear Programming etc. These methods are generally trapped in local optima. The solution to this lacuna is Evolutionary Algorithms (EAs), which work as a promising technique for wide range of Constrained Optimization Problems. This paper reviews established Evolutionary Algorithms specifically, Genetic Algorithm (GA), Artificial Bee Colony (ABC), Differential Evolution (DE), Particle Swarm Optimization (PSO), Teaching Learning Based Optimization (TLBO) and variants of above Evolutionary algorithms which have solved Constrained Optimization Problems. This review will help new researchers to know about various Evolutionary Algorithms and their potential strengths and weaknesses to solve COPs.

[1]  Zhihua Cui,et al.  Artificial Plant Optimization Algorithm for Constrained Optimization Problems , 2011, 2011 Second International Conference on Innovations in Bio-inspired Computing and Applications.

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

[3]  Qing Hui,et al.  A numerical gradient based technique and directed neighborhood structure for Constrained Particle Swarm Optimization , 2013, 2013 American Control Conference.

[4]  Sana Ben Hamida,et al.  An Adaptive Algorithm for Constrained Optimization Problems , 2000, PPSN.

[5]  Hu Peng,et al.  Dynamic Neighborhood Hybrid Particle Swarm Optimization for Constrained Optimization , 2010, 2010 International Conference on Computational and Information Sciences.

[6]  Michael M. Skolnick,et al.  Using Genetic Algorithms in Engineering Design Optimization with Non-Linear Constraints , 1993, ICGA.

[7]  Takashi Okamoto,et al.  Constrained optimization using the lagrangian method and the improved discrete gradient chaos model , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

[8]  Yuren Zhou,et al.  Multi-objective and MGG evolutionary algorithm for constrained optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[9]  Tetsuyuki Takahama,et al.  Efficient constrained optimization by the ε constrained adaptive differential evolution , 2010, IEEE Congress on Evolutionary Computation.

[10]  Aijia Ouyang,et al.  A hybrid immune PSO for constrained optimization problems , 2010, 2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA).

[11]  Gunar E. Liepins,et al.  Some Guidelines for Genetic Algorithms with Penalty Functions , 1989, ICGA.

[12]  Jonathan A. Wright,et al.  Genetic algorithms: a fitness formulation for constrained minimization , 2001 .

[13]  Madhuri S. Joshi,et al.  Dual Population Genetic Algorithm for Solving Constrained Optimization Problems , 2015 .

[14]  Zbigniew Michalewicz,et al.  Evolutionary algorithms , 1997, Emerging Evolutionary Algorithms for Antennas and Wireless Communications.

[15]  Haiyan Lu,et al.  Self-adaptive velocity particle swarm optimization for solving constrained optimization problems , 2008, J. Glob. Optim..

[16]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[17]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .

[18]  Yunping Chen,et al.  A Hybrid Evolutionary Algorithm by Combination of PSO and GA for Unconstrained and Constrained Optimization Problems , 2007, 2007 IEEE International Conference on Control and Automation.

[19]  Marco Tomassini,et al.  Evolutionary Algorithms , 1995, Towards Evolvable Hardware.

[20]  Keigo Watanabe,et al.  Evolutionary Optimization of Constrained Problems , 2004 .

[21]  Hyun Myung,et al.  Preliminary Investigations into a Two-State Method of Evolutionary Optimization on Constrained Problems , 1995, Evolutionary Programming.

[22]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

[23]  Madhuri S. Joshi,et al.  OpenMP Dual Population Genetic Algorithm for Solving Constrained Optimization Problems , 2015 .

[24]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[25]  Chengen Wang,et al.  A genetic algorithm with constrained sorting method for constrained optimization problems , 2009, 2009 IEEE International Conference on Intelligent Computing and Intelligent Systems.

[26]  Jian Li,et al.  Solving Constrained Optimization via Dual Particle Swarm Optimization with Stochastic Ranking , 2008, CSSE.

[27]  Yun-ping Chen,et al.  A Master-Slave Particle Swarm Optimization Algorithm for Solving Constrained Optimization Problems , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[28]  Zhiwen Yu,et al.  Nearest neighbor evolutionary algorithm for constrained optimization problem , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

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

[30]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .

[31]  Marc Schoenauer,et al.  Constrained GA Optimization , 1993, ICGA.

[32]  Paul T. Boggs,et al.  Sequential Quadratic Programming , 1995, Acta Numerica.

[33]  Carlos A. Coello Coello,et al.  A simple multimembered evolution strategy to solve constrained optimization problems , 2005, IEEE Transactions on Evolutionary Computation.

[34]  Michael N. Vrahatis,et al.  Particle Swarm Optimization Method for Constrained Optimization Problems , 2002 .

[35]  Bingyan Zhao,et al.  Modified Differential Evolution for Hard Constrained Optimization , 2009, 2009 International Conference on Computational Intelligence and Software Engineering.

[36]  Zbigniew Michalewicz,et al.  Using Cultural Algorithms for Constraint Handling in GENOCOP , 1995, Evolutionary Programming.

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

[38]  Ruhul A. Sarker,et al.  Improved genetic algorithm for constrained optimization , 2011, The 2011 International Conference on Computer Engineering & Systems.

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

[40]  Xiaojun Bi,et al.  Constrained Optimization Based on Epsilon Constrained Biogeography-Based Optimization , 2012, 2012 4th International Conference on Intelligent Human-Machine Systems and Cybernetics.

[41]  Wenyin Gong,et al.  A multiobjective differential evolution algorithm for constrained optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[42]  Xin Yao,et al.  Search biases in constrained evolutionary optimization , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[43]  Ruhul A. Sarker,et al.  On an evolutionary approach for constrained optimization problem solving , 2012, Appl. Soft Comput..

[44]  Atidel B. Hadj-Alouane,et al.  A dual genetic algorithm for bounded integer programs James C. Bean, Atidel Ben Hadj-Alouane. , 1993 .

[45]  Renato A. Krohling,et al.  Hierarchical bare bones particle swarm for solving constrained optimization problems , 2013, 2013 IEEE Congress on Evolutionary Computation.

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

[47]  Zbigniew Michalewicz,et al.  Handling Constraints in Genetic Algorithms , 1991, ICGA.

[48]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[49]  Z. Michalewicz,et al.  Genocop III: a co-evolutionary algorithm for numerical optimization problems with nonlinear constraints , 1995, Proceedings of 1995 IEEE International Conference on Evolutionary Computation.

[50]  Takashi Okamoto,et al.  Constrained optimization using the quasi-chaotic optimization method with the exact penalty function and the sequential quadratic programming , 2011, 2011 IEEE International Conference on Systems, Man, and Cybernetics.

[51]  Gary G. Yen,et al.  A generic framework for constrained optimization using genetic algorithms , 2005, IEEE Transactions on Evolutionary Computation.

[52]  Yuren Zhou,et al.  Multiobjective Optimization and Hybrid Evolutionary Algorithm to Solve Constrained Optimization Problems , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[53]  Vivek Patel,et al.  An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems , 2012 .

[54]  Chengen Wang,et al.  An Archived Differential Evolution Algorithm for Constrained Global Optimization , 2008, 2008 International Conference on Smart Manufacturing Application.

[55]  Yong Wang,et al.  Combining Multiobjective Optimization With Differential Evolution to Solve Constrained Optimization Problems , 2012, IEEE Transactions on Evolutionary Computation.

[56]  Marc Schoenauer,et al.  ASCHEA: new results using adaptive segregational constraint handling , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[57]  Jan Paredis,et al.  Co-evolutionary Constraint Satisfaction , 1994, PPSN.

[58]  Zbigniew Michalewicz,et al.  Evolutionary optimization of constrained problems , 1994 .

[59]  Yanda Li,et al.  Constrained Optimization Using Triple Spaces Cultured Genetic Algorithm , 2008, 2008 Fourth International Conference on Natural Computation.

[60]  Kalyanmoy Deb,et al.  An evolutionary algorithm based pattern search approach for constrained optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.