An effective improved differential evolution algorithm to solve constrained optimization problems

An effective extended differential evolution algorithm is proposed to deal with constrained optimization problems. The proposed algorithm adopts a new mechanism to cope with constrained problems by transforming the equality into inequality first. Then, two kinds of offspring generation approaches are applied to balance the diversity and the convergence speed of the population during evolution, and seven criteria are designed to compare feasible solution over infeasible solution. The performance of the novel algorithm is evaluated on a set of well-known constrained problems from CEC2006. The experimental results are quite competitive when comparing the proposed algorithm against state-of-the-art optimization algorithms.

[1]  Yuren Zhou,et al.  An Adaptive Tradeoff Model for Constrained Evolutionary Optimization , 2008, IEEE Transactions on Evolutionary Computation.

[2]  Xiangtao Li,et al.  Self-adaptive constrained artificial bee colony for constrained numerical optimization , 2012, Neural Computing and Applications.

[3]  B. Babu,et al.  Differential evolution for multi-objective optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[4]  Trade-Diverting Free Trade Agreements, External Tariffs, and Feasibility , 2013 .

[5]  Tapabrata Ray,et al.  An Improved Self-Adaptive Constraint Sequencing approach for constrained optimization problems , 2015, Appl. Math. Comput..

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

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

[8]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[9]  Xin Zhang,et al.  Improving differential evolution by differential vector archive and hybrid repair method for global optimization , 2016, Soft Computing.

[10]  Jun Guo,et al.  Rank B2C e-commerce websites in e-alliance based on AHP and fuzzy TOPSIS , 2011, Expert Syst. Appl..

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

[12]  Sanyang Liu,et al.  A Dual-Population Differential Evolution With Coevolution for Constrained Optimization , 2015, IEEE Transactions on Cybernetics.

[13]  Yong Wang,et al.  Constrained Evolutionary Optimization by Means of ( + )-Differential Evolution and Improved Adaptive Trade-Off Model , 2011, Evolutionary Computation.

[14]  Arthur C. Sanderson,et al.  JADE: Adaptive Differential Evolution With Optional External Archive , 2009, IEEE Transactions on Evolutionary Computation.

[15]  Jianping Li,et al.  Evolution strategies based adaptive Lp LS-SVM , 2011, Inf. Sci..

[16]  Jie Cao,et al.  A novel mutation differential evolution for global optimization , 2015, J. Intell. Fuzzy Syst..

[17]  Harish Sharma,et al.  Fitness based Differential Evolution , 2012, Memetic Computing.

[18]  Tetsuyuki Takahama,et al.  Constrained Optimization by the epsilon Constrained Hybrid Algorithm of Particle Swarm Optimization and Genetic Algorithm , 2005, Australian Conference on Artificial Intelligence.

[19]  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..

[20]  Chih-Hao Lin,et al.  A rough penalty genetic algorithm for constrained optimization , 2013, Inf. Sci..

[21]  Wenyin Gong,et al.  Adaptive Ranking Mutation Operator Based Differential Evolution for Constrained Optimization , 2015, IEEE Transactions on Cybernetics.

[22]  Mohammad Ebrahim Shiri,et al.  An augmented Lagrangian ant colony based method for constrained optimization , 2014, Computational Optimization and Applications.

[23]  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.

[24]  Ali Wagdy Mohamed,et al.  Solving large-scale global optimization problems using enhanced adaptive differential evolution algorithm , 2017 .

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

[26]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[27]  Jing J. Liang,et al.  Comprehensive learning particle swarm optimizer for global optimization of multimodal functions , 2006, IEEE Transactions on Evolutionary Computation.

[28]  Carlos A. Coello Coello,et al.  Modified Differential Evolution for Constrained Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

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

[30]  A. Kai Qin,et al.  Self-adaptive Differential Evolution Algorithm for Constrained Real-Parameter Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[31]  Mehmet Fatih Tasgetiren,et al.  An ensemble of differential evolution algorithms for constrained function optimization , 2010, IEEE Congress on Evolutionary Computation.

[32]  Xinyu Li,et al.  Ε Constrained Differential Evolution with Pre-estimated Comparison Using Gradient-based Approximation for Constrained Optimization Problems , 2016, Expert Syst. Appl..

[33]  Zbigniew Michalewicz,et al.  A Survey of Constraint Handling Techniques in Evolutionary Computation Methods , 1995 .

[34]  Zaiwu Gong,et al.  Risk prediction of low temperature in Nanjing city based on grey weighted Markov model , 2014, Natural Hazards.

[35]  Guo Wei,et al.  Impact of political dispute on international trade based on an international trade Inoperability Input-Output Model: A case study of the 2012 Diaoyu Islands Dispute , 2016 .

[36]  Ivona Brajevic,et al.  Crossover-based artificial bee colony algorithm for constrained optimization problems , 2015, Neural Computing and Applications.

[37]  K. Hameyer,et al.  Adaptive coupling of differential evolution and multiquadrics approximation for the tuning of the optimization process , 2000 .

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

[39]  Tetsuyuki Takahama,et al.  Constrained Optimization by the ε Constrained Differential Evolution with Gradient-Based Mutation and Feasible Elites , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[40]  Sankalap Arora,et al.  Chaotic grey wolf optimization algorithm for constrained optimization problems , 2018, J. Comput. Des. Eng..

[41]  Detong Zhu An affine scaling reduced preconditional conjugate gradient path method for linear constrained optimization , 2007, Appl. Math. Comput..

[42]  Jeng-Shyang Pan,et al.  An improved vector particle swarm optimization for constrained optimization problems , 2011, Inf. Sci..

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

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

[45]  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).

[46]  David W. Coit,et al.  Adaptive Penalty Methods for Genetic Optimization of Constrained Combinatorial Problems , 1996, INFORMS J. Comput..

[47]  Dipti Srinivasan,et al.  A unified differential evolution algorithm for constrained optimization problems , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

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

[49]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[50]  Jonathan M. Garibaldi,et al.  A multi-cycled sequential memetic computing approach for constrained optimisation , 2016, Inf. Sci..

[51]  Carlos García-Martínez,et al.  Global and local real-coded genetic algorithms based on parent-centric crossover operators , 2008, Eur. J. Oper. Res..

[52]  Zhensheng Yu Solving bound constrained optimization via a new nonmonotone spectral projected gradient method , 2008 .

[53]  Mehmet Fatih Tasgetiren,et al.  Differential evolution algorithm with ensemble of parameters and mutation strategies , 2011, Appl. Soft Comput..

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

[55]  Xiaodong Li,et al.  Cooperative coevolutionary differential evolution with improved augmented Lagrangian to solve constrained optimisation problems , 2016, Inf. Sci..

[56]  Yong Wang,et al.  A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization , 2006, IEEE Transactions on Evolutionary Computation.

[57]  Jian Li,et al.  Hybridizing Infeasibility Driven and Constrained-Domination Principle with MOEA/D for Constrained Multiobjective Evolutionary Optimization , 2014, TAAI.

[58]  Xiang Wang,et al.  e -Differential Evolution Algorithm for Constrained Optimization Problems: e -Differential Evolution Algorithm for Constrained Optimization Problems , 2012 .

[59]  T. Saaty,et al.  The Analytic Hierarchy Process , 1985 .

[60]  Xiaodong Li,et al.  Solving Rotated Multi-objective Optimization Problems Using Differential Evolution , 2004, Australian Conference on Artificial Intelligence.

[61]  Harish Garg,et al.  A hybrid PSO-GA algorithm for constrained optimization problems , 2016, Appl. Math. Comput..

[62]  Xin Wang,et al.  Constrained optimization based on improved teaching-learning-based optimization algorithm , 2016, Inf. Sci..

[63]  Zhongping Wan,et al.  An improved artificial bee colony algorithm for solving constrained optimization problems , 2015, International Journal of Machine Learning and Cybernetics.

[64]  Gary G. Yen,et al.  An Adaptive Penalty Formulation for Constrained Evolutionary Optimization , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[65]  Helio J. C. Barbosa,et al.  A new adaptive penalty scheme for genetic algorithms , 2003, Inf. Sci..

[66]  Xuefeng Yan,et al.  Self-Adaptive Differential Evolution Algorithm With Zoning Evolution of Control Parameters and Adaptive Mutation Strategies , 2016, IEEE Transactions on Cybernetics.

[67]  A. Ravindran,et al.  Engineering Optimization: Methods and Applications , 2006 .

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

[69]  Jie Cao,et al.  An Ensemble Differential Evolution for Numerical Optimization , 2015, Int. J. Inf. Technol. Decis. Mak..

[70]  Kalyanmoy Deb,et al.  Optimization for Engineering Design: Algorithms and Examples , 2004 .

[71]  Jing J. Liang,et al.  Dynamic Multi-Swarm Particle Swarm Optimizer with a Novel Constraint-Handling Mechanism , 2006, 2006 IEEE International Conference on Evolutionary Computation.

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

[73]  M. M. Ali,et al.  A local exploration-based differential evolution algorithm for constrained global optimization , 2009, Appl. Math. Comput..

[74]  Chyi Hwang,et al.  A simple and efficient real-coded genetic algorithm for constrained optimization , 2016, Appl. Soft Comput..

[75]  P. N. Suganthan,et al.  Ensemble of Constraint Handling Techniques , 2010, IEEE Transactions on Evolutionary Computation.

[76]  Jianjun Jiao,et al.  A modified augmented Lagrangian with improved grey wolf optimization to constrained optimization problems , 2017, Neural Computing and Applications.

[77]  Yong Wang,et al.  A Dynamic Hybrid Framework for Constrained Evolutionary Optimization , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[78]  Liang Gao,et al.  Backtracking Search Algorithm with three constraint handling methods for constrained optimization problems , 2015, Expert Syst. Appl..

[79]  Wenyin Gong,et al.  Engineering optimization by means of an improved constrained differential evolution , 2014 .

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

[81]  Feng Liu,et al.  Distributed gradient algorithm for constrained optimization with application to load sharing in power systems , 2015, Syst. Control. Lett..

[82]  Yong Wang,et al.  An improved (μ + λ)-constrained differential evolution for constrained optimization , 2013, Inf. Sci..

[83]  Dervis Karaboga,et al.  A modified Artificial Bee Colony (ABC) algorithm for constrained optimization problems , 2011, Appl. Soft Comput..

[84]  Yu Xue,et al.  Prior knowledge guided differential evolution , 2017, Soft Comput..

[85]  Tapabrata Ray,et al.  Infeasibility Driven Evolutionary Algorithm (IDEA) for Engineering Design Optimization , 2008, Australasian Conference on Artificial Intelligence.

[86]  Qiang Long,et al.  A constraint handling technique for constrained multi-objective genetic algorithm , 2014, Swarm Evol. Comput..

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

[88]  P. Suganthan,et al.  Constrained multi-objective optimization algorithm with an ensemble of constraint handling methods , 2011 .

[89]  Yong Wang,et al.  Incorporating Objective Function Information Into the Feasibility Rule for Constrained Evolutionary Optimization , 2016, IEEE Transactions on Cybernetics.

[90]  Ruhul A. Sarker,et al.  A self-adaptive combined strategies algorithm for constrained optimization using differential evolution , 2014, Appl. Math. Comput..