A novel differential crossover strategy based on covariance matrix learning with Euclidean neighborhood for solving real-world problems

Solving real-world optimization problems is considered a challenging task. This is due to the variability of the characteristics in objective functions, the presence of enormous number of local optima within the search space and highly nonlinear constraints with large number of variables. The advances on this type of problems are of capital importance for many researchers to develop new efficient evolutionary algorithms to tackle such problems in an efficient manner with better solutions. For this reason, this work proposes a new crossover technique based on covariance learning with Euclidean neighborhood which has been incorporated in the basic L-SHADE algorithm. The goal of this new technique is to help L-SHADE establish a suitable coordinate system for the crossover operator. This helps enhance L-SHADE capability to solve real world problems with difficult characteristics and nonlinear constraints. The proposed algorithm, namely L-covnSHADE, is tested on one of the challenging benchmarks which is the IEEE CEC'11 on real-world numerical optimization problems. This set consists of 22 real-world problems with diverse stimulating characteristics and a dimensionality ranging from 1 to 240 dimensions. The results statistically affirm the efficiency of the proposed approach to obtain better results compared to the L-SHADE algorithm and other state-of-the-art algorithms including the winner of the CEC2011 competition.

[1]  Ponnuthurai N. Suganthan,et al.  A decremental stochastic fractal differential evolution for global numerical optimization , 2016, Inf. Sci..

[2]  Alex S. Fukunaga,et al.  Improving the search performance of SHADE using linear population size reduction , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[3]  Ruhul A. Sarker,et al.  Differential evolution with multiple strategies for solving CEC2011 real-world numerical optimization problems , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[4]  Jason Sheng-Hong Tsai,et al.  A self-optimization approach for L-SHADE incorporated with eigenvector-based crossover and successful-parent-selecting framework on CEC 2015 benchmark set , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[5]  Amit Konar,et al.  Automated emotion recognition employing a novel modified binary quantum-behaved gravitational search algorithm with differential mutation , 2015, Expert Syst. J. Knowl. Eng..

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

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

[8]  Long Li,et al.  Differential evolution based on covariance matrix learning and bimodal distribution parameter setting , 2014, Appl. Soft Comput..

[9]  Robert G. Reynolds,et al.  Leveraged Neighborhood Restructuring in Cultural Algorithms for Solving Real-World Numerical Optimization Problems , 2016, IEEE Transactions on Evolutionary Computation.

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

[11]  Robert G. Reynolds,et al.  An Adaptive Multipopulation Differential Evolution With Dynamic Population Reduction , 2017, IEEE Transactions on Cybernetics.

[12]  Patrick Siarry,et al.  Hybridizing Biogeography-Based Optimization With Differential Evolution for Optimal Power Allocation in Wireless Sensor Networks , 2011, IEEE Transactions on Vehicular Technology.

[13]  Robert G. Reynolds,et al.  A differential evolution algorithm with success-based parameter adaptation for CEC2015 learning-based optimization , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[14]  Ponnuthurai N. Suganthan,et al.  Self-adaptive differential evolution with multi-trajectory search for large-scale optimization , 2011, Soft Comput..

[15]  Tapabrata Ray,et al.  Performance of a hybrid EA-DE-memetic algorithm on CEC 2011 real world optimization problems , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[16]  Ponnuthurai N. Suganthan,et al.  Differential evolution with stochastic fractal search algorithm for global numerical optimization , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[17]  Safaai Deris,et al.  An Evolutionary Firefly Algorithm for the Estimation of Nonlinear Biological Model Parameters , 2013, PloS one.

[18]  Alex S. Fukunaga,et al.  Success-history based parameter adaptation for Differential Evolution , 2013, 2013 IEEE Congress on Evolutionary Computation.

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

[20]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[21]  Qingfu Zhang,et al.  Enhancing the search ability of differential evolution through orthogonal crossover , 2012, Inf. Sci..

[22]  Ruhul A. Sarker,et al.  GA with a new multi-parent crossover for solving IEEE-CEC2011 competition problems , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[23]  Hamid Salimi,et al.  Stochastic Fractal Search: A powerful metaheuristic algorithm , 2015, Knowl. Based Syst..

[24]  Qingfu Zhang,et al.  Differential Evolution With Composite Trial Vector Generation Strategies and Control Parameters , 2011, IEEE Transactions on Evolutionary Computation.

[25]  Robert G. Reynolds,et al.  An ensemble sinusoidal parameter adaptation incorporated with L-SHADE for solving CEC2014 benchmark problems , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).