Constrained Dynamic Differential Evolution using a novel hybrid constraint handling technique

In this paper, a Constrained Dynamic Differential Evolution (CDDE) algorithm is proposed to solve constrained optimization problems. In CDDE, the crossover rate CR and scale factor F are dynamically changed and selected randomly from the range [0.5,1]. This way, CDDE has degrees of exploration abilities for the landscape of the constrained optimization problems and can be able to discover the search space and reach the feasible regions. Also, a novel hybrid simple constraint handling technique is suggested, which combines two well-known techniques: feasible rules and adaptive penalty function. Near convergence, CDDE uses the Sequential quadratic programming (SQP) method to enhance its local search ability. CDDE performance has been tested on the constrained benchmark functions of the CEC 2010 competition. The results demonstrate that CDDE outperforms other state-of-the-art algorithms and consistently reaches feasible solutions.

[1]  Masaharu Munetomo,et al.  An adaptive resolution hybrid binary-real coded genetic algorithm , 2011, Artificial Life and Robotics.

[2]  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.

[3]  Biao Yang,et al.  Computing Nonlinear $\tau$-Estimation Based on Dynamic Differential Evolution Strategy , 2006, IEEE Signal Processing Letters.

[4]  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).

[5]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[6]  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.

[7]  Tetsuyuki Takahama,et al.  Constrained optimization by the ε constrained differential evolution with an archive and gradient-based mutation , 2010, IEEE Congress on Evolutionary Computation.

[8]  Mehmet Fatih Tasgetiren,et al.  A Multi-Populated Differential Evolution Algorithm for Solving Constrained Optimization Problem , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[9]  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.

[10]  Randy L. Haupt,et al.  Practical Genetic Algorithms , 1998 .

[11]  Carlos A. Coello Coello,et al.  Boundary Search for Constrained Numerical Optimization Problems With an Algorithm Inspired by the Ant Colony Metaphor , 2009, IEEE Transactions on Evolutionary Computation.

[12]  Chellapilla Patvardhan,et al.  A novel hybrid constraint handling technique for evolutionary optimization , 2009, 2009 IEEE Congress on Evolutionary Computation.

[13]  Francisco Herrera,et al.  Tackling Real-Coded Genetic Algorithms: Operators and Tools for Behavioural Analysis , 1998, Artificial Intelligence Review.

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

[15]  P. Suganthan,et al.  Problem Definitions and Evaluation Criteria for the CEC 2010 Competition on Constrained Real- Parameter Optimization , 2010 .

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

[17]  James Montgomery Crossover and the different faces of differential evolution searches , 2010, IEEE Congress on Evolutionary Computation.

[18]  Masaharu Munetomo,et al.  An adaptive parameter binary-real coded genetic algorithm for constraint optimization problems: Performance analysis and estimation of optimal control parameters , 2013, Inf. Sci..

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

[20]  Zhigang Shang,et al.  Coevolutionary Comprehensive Learning Particle Swarm Optimizer , 2010, IEEE Congress on Evolutionary Computation.

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

[22]  Amit Konar,et al.  Two improved differential evolution schemes for faster global search , 2005, GECCO '05.

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

[24]  Athanasios V. Vasilakos,et al.  Modified estimation of Distribution algorithm with differential mutation for constrained optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

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

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