Reusing the Past Difference Vectors in Differential Evolution—A Simple But Significant Improvement

Differential evolution (DE) has established itself as a simple but efficient population-based, nonconvex optimization algorithm for continuous search spaces. Unlike the conventional real-coded genetic algorithms (GAs) and evolution strategies (ESs), DE uses a mandatory self-referential mutation for its population members, each of which are perturbed with the scaled difference(s) of the individuals from the current generation (iteration). These difference vectors determine the direction of the search moves for the individuals. However, unlike the better individuals, they are not retained in the elitist evolution cycle of DE. In this paper, we show that by archiving the most promising difference vectors from past generations and then by reusing them for generating offspring in the subsequent generations, we can strikingly improve the performance of DE. This strategy can be integrated with any classical or advanced DE variant with no serious overhead in time or space complexity. We demonstrate that when combined with the DE-based winners of the IEEE Congress on Evolutionary Computation (CEC) 2013, 2014, and 2017 competitions on real parameter optimization, the simple reuse strategy leads to a statistically significant performance improvement in the majority of test cases. We further showcase the efficacy of our proposal on a practical optimization problem concerning the design of circular antenna arrays with a prespecified radiation pattern.

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

[2]  Jun Zhang,et al.  Directed differential evolution based on directional derivative for numerical optimization problems , 2011, 2011 11th International Conference on Hybrid Intelligent Systems (HIS).

[3]  Ponnuthurai N. Suganthan,et al.  Recent advances in differential evolution - An updated survey , 2016, Swarm Evol. Comput..

[4]  Cheng Wang,et al.  Differential evolution with individual-dependent topology adaptation , 2018, Inf. Sci..

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

[6]  Yu-Xuan Wang,et al.  Exploring new learning strategies in Differential Evolution algorithm , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

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

[8]  Rainer Storn,et al.  Differential Evolution Research – Trends and Open Questions , 2008 .

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

[10]  Karol R. Opara,et al.  DMEA — An algorithm that combines differential mutation with the fitness proportionate selection , 2011, 2011 IEEE Symposium on Differential Evolution (SDE).

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

[12]  Jing Xiao,et al.  Classification-based self-adaptive differential evolution with fast and reliable convergence performance , 2011, Soft Comput..

[13]  Liang Gao,et al.  Adaptive Differential Evolution With Sorting Crossover Rate for Continuous Optimization Problems , 2017, IEEE Transactions on Cybernetics.

[14]  A. Bellettini,et al.  Theoretical accuracy of synthetic aperture sonar micronavigation using a displaced phase-center antenna , 2002 .

[15]  Shunkai Fu,et al.  Differential Evolution With Adaptive Guiding Mechanism Based on Heuristic Rules , 2019, IEEE Access.

[16]  Shiu Yin Yuen,et al.  A directional mutation operator for differential evolution algorithms , 2015, Appl. Soft Comput..

[17]  Kay Chen Tan,et al.  Multiple Exponential Recombination for Differential Evolution , 2017, IEEE Transactions on Cybernetics.

[18]  Ponnuthurai N. Suganthan,et al.  An Adaptive Differential Evolution Algorithm With Novel Mutation and Crossover Strategies for Global Numerical Optimization , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

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

[21]  R. Storn,et al.  Differential evolution a simple and efficient adaptive scheme for global optimization over continu , 1997 .

[22]  Swagatam Das,et al.  EFFICIENT CIRCULAR ARRAY SYNTHESIS WITH A MEMETIC DIFFERENTIAL EVOLUTION ALGORITHM , 2012 .

[23]  Yiqiao Cai,et al.  Differential Evolution With Neighborhood and Direction Information for Numerical Optimization , 2013, IEEE Transactions on Cybernetics.

[24]  Xin Zhang,et al.  Improving differential evolution by differential vector archive and hybrid repair method for global optimization , 2017, Soft Comput..

[25]  Karol R. Opara,et al.  The contour fitting property of differential mutation , 2019, Swarm Evol. Comput..

[26]  Abbas Ali Heidari,et al.  A Dual-Band Circularly Polarized Stub Loaded Microstrip Patch Antenna for GPS Applications , 2009 .

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

[28]  Jing Hu,et al.  A Diversity-Guided Particle Swarm Optimizer for Dynamic Environments , 2007, LSMS.

[29]  Shu-Mei Guo,et al.  Enhancing Differential Evolution Utilizing Eigenvector-Based Crossover Operator , 2015, IEEE Transactions on Evolutionary Computation.

[30]  Ponnuthurai Nagaratnam Suganthan,et al.  Problem Definitions and Evaluation Criteria for the CEC 2014 Special Session and Competition on Single Objective Real-Parameter Numerical Optimization , 2014 .

[31]  Ponnuthurai N. Suganthan,et al.  Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood for solving CEC2017 benchmark problems , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[32]  Rafal Biedrzycki.  A version of IPOP-CMA-ES algorithm with midpoint for CEC 2017 single objective bound constrained problems , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[33]  Shao Yong Zheng,et al.  An Efficient Multiple Variants Coordination Framework for Differential Evolution , 2017, IEEE Transactions on Cybernetics.

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

[35]  Andrew M. Sutton,et al.  Differential evolution and non-separability: using selective pressure to focus search , 2007, GECCO '07.

[36]  Jason Sheng-Hong Tsai,et al.  Improving Differential Evolution With a Successful-Parent-Selecting Framework , 2015, IEEE Transactions on Evolutionary Computation.

[37]  Janez Brest,et al.  Single objective real-parameter optimization: Algorithm jSO , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

[38]  Murat Akçakaya,et al.  Adaptive MIMO Radar Design and Detection in Compound-Gaussian Clutter , 2011, IEEE Transactions on Aerospace and Electronic Systems.

[39]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

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

[41]  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).

[42]  Dimitris K. Tasoulis,et al.  Enhancing Differential Evolution Utilizing Proximity-Based Mutation Operators , 2011, IEEE Transactions on Evolutionary Computation.