Differential Evolution (DE) is a simple, yet highly competitive real parameter optimizer in the family of evolutionary algorithms. A significant contribution of its robust performance is attributed to its control parameters, and mutation strategy employed, proper settings of which, generally lead to good solutions. Finding the best parameters for a given problem through the trial and error method is time consuming, and sometimes impractical. This calls for the development of adaptive parameter control mechanisms. In this work, we investigate the impact and efficacy of adapting mutation strategies with or without adapting the control parameters, and report the plausibility of this scheme. Backed with empirical evidence from this and previous works, we first build a case for strategy adaptation in the presence as well as in the absence of parameter adaptation. Afterwards, we propose a new mutation strategy, and an adaptive variant SA-SHADE which is based on a recently proposed self-adaptive memory based variant of Differential evolution, SHADE. We report the performance of SA-SHADE on 28 benchmark functions of varying complexity, and compare it with the classic DE algorithm (DE/Rand/1/bin), and other state-of-the-art adaptive DE variants including CoDE, EPSDE, JADE, and SHADE itself. Our results show that adaptation of mutation strategy improves the performance of DE in both presence, and absence of control parameter adaptation, and should thus be employed frequently.
If the inline PDF is not rendering correctly, you can download the PDF file here.
 A. E. Eiben R. Hinterding Z. Michalewicz Parameter control in evolutionary algorithms IEEE Transactions on Evolutionary Computation 3 (2) 124–141 1999.
 G. Beni J. Wang Swarm Intelligence in Cellular Robotic Systems in: Proceedings of the NATO Advanced Workshop on Robots and Biological Systems. Tuscany Italy 1989.
 P.J. Angeline Adaptive and self-adaptive evolutionary computation in: M. Palaniswami Y. Attikiouzel R.J. Marks D.B. Fogel T. Fukuda (Eds.) Computational Intelligence: A Dynamic System Perspective IEEE Press pp. 152–161 1995.
 J. Gomez D. Dasgupta F. Gonazalez Using adaptive operators in genetic search in: Proceedings of the Genetic and Evolutionary Computation Conference 2003 (GECCO03) Chicago Illinois USA pp. 1580–1581 2003.
 B. R. Julstrom What have you done for me lately? Adapting operator probabilities in a steady-state genetic algorithm in: Proceedings of the 6th International Conference on Genetic Algorithms Pittsburgh PA USA pp. 81-87 1995.
 J. E. Smith T.C. Fogarty Operator and parameter adaptation in genetic algorithms Soft Computing 1 pp. 81-87 1997.
 A. Tuson P. Ross Adapting operator settings in genetic algorithms Evolutionary Computation 6 pp. 161-184 1998.
 R. M. Storn K. V. Price Differential evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces International Computer Science Institute Berkeley CA USA ICSI Technical Report 95-012 1995.
 S. Das P. N. Suganthan Differential evolution - A survey of the state-of-the-art IEEE Transactions on Evolutionary Computation 15 (1) pp. 4–31 2011.
 R. M. Storn K. V. Price Minimizing the real functions of the ICEC 1996 contest by differential evolution in: Proceedings of IEEE International Conference on Evolutionary Computation pp. 842–844 1996.
 J. Liu J. Lampinen On setting the control parameter of the differential evolution method in: Proceedings of 8th Int. Conference Soft Computing (MENDEL) pp. 11–18 2002.
 R. Gamperle S. D. Muller P. Koumoutsakos A parameter study for differential evolution NNAFSFS-EC 2002 Interlaken Switzerland WSEAS pp. 11–15 2002.
 A. E. Eiben J. E. Smith Introduction to Evolutionary Computing Natural Computing. Berlin Germany: Springer-Verlag 2003.
 K. Price R. Storn J. Lampinen Differential Evolution - A Practical Approach to Global Optimization Berlin Germany: Springer 2005.
 S. Das A. Konar U. K. Chakraborty Two improved Differential Evolution schemes for faster global search in Proceedings of ACM-SIGEVO GECCO pp. 991–998 2005.
 H. A. Abbass The self-adaptive pareto differential evolution algorithm in Proceedings of the 2002 IEEE Congress on Evolutionary Computation Honolulu Hawaii USA 1 pp. 831–836 2002.
 J. Brest S. Greiner B. Boskovic M. Mernik V. Zumer Self adapting control parameters in differential evolution: A comparative study on numerical benchmark problems IEEE Transactions on Evolutionary Computation 10 (6) pp. 646–657 2006.
 A. Zamuda J. Brest Self-adaptive control parameters randomization frequency and propagations in differential evolution. Swarm and Evolutionary Computation 25(1) pp. 72–99 2015.
 A. K. Qin V. L. Huang P. N. Suganthan Differential evolution algorithm with strategy adaptation for global numerical optimization IEEE Transactions on Evolutionary Computation 13 pp. 398–417 2009.
 M. G. H. Omran A. Salman A. P. Engelbrecht Self-adaptive differential evolution in: Computational Intelligence and Security PT 1 Proceedings Lecture Notes in Artificial Intelligence pp. 192-199 2005.
 D. Zaharie Control of population diversity and adaptation in differential evolution algorithms in: Proceedings of the 9th International Conference on Soft Computing Brno pp. 41-46 2003.
 J. Tvrdik Adaptation in differential evolution: a numerical comparison Applied Soft Computing 9 pp. 1149–1155 2009.
 R. Mallipeddi P. N. Suganthana Q. K. Pan M. F. Tasgetiren Differential evolution algorithm with ensemble of parameters and mutation strategies Applied Soft Computing 11 (2) pp. 1679–1696 2011.
 R. Storn K. Price Differential evolution A simple and efficient heuristic for global optimization over continuous spaces Journal of Global Optimization 11 pp. 341–359 1997.
 J. Lampinen I. Zelinka On stagnation of the differential evolution algorithm in: Proceedings of MENDEL 2000 6th International Mendel Conference on Soft Computing pp. 76–83 2000.
 J. Ronkkonen S. Kukkonen K. V. Price Real parameter optimization with differential evolution in Proceedings of IEEE Congress on Evolutionary Computation 1 pp. 506–513 2005.
 J. Liu J. Lampinen A Fuzzy Adaptive Differential Evolution Algorithm in: Soft Computing A Fusion of Foundations Methodologies and Applications 9 (6) pp. 448–462 2005.
 F. Neri V. Tirronen Recent advances in differential evolution: a survey and experimental analysis Artificial Intelligence Review 33 (1-2) pp. 61–106 2010.
 J. Ronkkonen J. Lampinen On using normally distributed mutation step length for the differential evolution algorithm in: Proceedings of the 9th Int. Conf. on Soft Computuing MENDEL Brno Czech Republic pp. 11–18 2003.
 A. K. Qin P. N. Suganthan Self-adaptive Differential Evolution Algorithm for Numerical Optimization in: Proceedings of the IEEE Congress on Evolutionary Computation 2005.
 M. M. Ali A. Trn Population set based global optimization algorithms: Some modifications and numerical studies Journal of Computers and Operations Research 31 (10) pp. 1703–1725 2004.
 U. K. Chakraborty Advances in Differential Evolution in: Differential Evolution Research-Trends and Open Questions Springer pp. 11–12 2008.
 D. Dawar S. A. Ludwig Differential evolution with dither and annealed scale factor in: Proceedings of the IEEE Symposium Series on Computational Intelligence Orlando Florida U.S.A. pp. 1–8 2014.
 J. Teo Exploring dynamic self-adaptive populations in differential evolution Soft Computing - A Fusion of Foundations Methodologies and Applications 10 (8) pp. 673–686 2006.
 J. Brest M. S. Mauec Population size reduction for the differential evolution algorithm Applied Intelligence 29 (3) pp. 228–247 2008.
 J. Zhang A. C. Sanderson JADE: Adaptive differential evolution with optional external archive IEEE Transaction on Evolutionary Computation 13 (5) pp. 945-958 2009.
 E. Mezura-Montes J. Velazquez-Reyes C. A. Coello Coello A comparative study of differential evolution variants for global optimization in GECCO pp. 485–492 2006.
 F. Peng K. Tang G. Chen X. Yao Multi-start JADE with knowledge transfer for numerical optimization in: Proceedings of the IEEE CEC pp. 1889–1895 2009.
 Z. Yang J. Zhang K. Tang X. Yao A. C. Sanderson An adaptive coevolutionary differential evolution algorithm for large-scale optimization in: Proceedings of the IEEE CEC pp. 102–109 2009.
 W. Gong Z. Cai C. X. Ling H. Li Enhanced differential evolution with adaptive strategies for numerical optimization IEEE Transactions on Systems Man and Cybernetics PartB 41 (2) pp. 397–413 2011.
 J. Zhang V. Avasarala A. C. Sanderson T. Mullen Differential evolution for discrete optimization: An experimental study on combinatorial auction problems in: Proceedings of the IEEE CEC pp. 2794–2800 2008.
 J. Zhang A. C. Sanderson Self-adaptive multiobjective differential evolution with direction information provided by archived inferior solutions in: Proceedings of the IEEE CEC pp. 2801–2810 2008.
 R. Tanabe A. Fukunaga Success-History Based Parameter Adaptation for Differential Evolution in: Proceedings of the IEEE CEC pp. 71–78 2013.
 R. Tanabe A. Fukunaga Evaluating the performance of SHADE on CEC 2013 benchmark problems in: Proceedings of the IEEE CEC pp. 1952–1959 2013.
 A. Auger N. Hansen A Restart CMA Evolution Strategy With Increasing Population Size in: Proceedings of the IEEE CEC pp. 1769–1776 2005.
 C. Garca-Martnez M. Lozano F. Herrera D. Molina A. M. Sanchez Global and local real-coded genetic algorithms based on parent-centric crossover operators European Journal of Operations Research 185 (3) pp. 1088–1113 2008.
 M. A. M. de Oca T. Stutzle K. V. den Enden M. Dorigo Incremental Social Learning in Particle Swarms IEEE Transactions on Systems Man and Cybernetics PartB 41 (2) pp. 368–384 2011.
 J. L. J. Laredo C. Fernandes J. J. M. Guervos C. Gagne Improving Genetic Algorithms Performance via Deterministic Population Shrinkage in: Proceedings of the GECCO pp. 819–826 2009.
 R. Tanabe A. Fukunaga Improving the Search Performance of SHADE Using Linear Population Size Reduction in: Proceedings of the IEEE CEC pp. 1658–1665 2014.
 J. Brest A. Zamuda B. Boskovic M. S. Maucec V. Zumer Highdimensional real-parameter optimization using self-adaptive differential evolution algorithm with population size reduction in: Proceedings of the IEEE Congress on Evolutionary Computation pp. 2032–2039 2008.
 A. Zamuda J. Brest. Population Reduction Differential Evolution with Multiple Mutation Strategies in Real World Industry Challenges. Artificial Intelligence and Soft Computing – ICAISC 2012 7269 pp. 154–161 2012.
 J. J. Liang B.Y. Qu P. N. Suganthan A. G. Hernandez-Daz Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization Computational Intelligence Laboratory Zhengzhou University Zhengzhou China and Nanyang 2013.
 A. K. Qin Xiaodong Li Differential Evolution on the CEC-2013 Single-Objective Continuous Optimization Testbed IEEE Congress on Evolutionary Computation Cancun Mexico June 20-23 2013.
 M. Friedman The use of ranks to avoid the assumption of normality implicit in the analysis of variance Journal of the American Statistical Association 32 pp. 674–701 1937.
 D. J. Sheskin Handbook of Parametric and Nonparametric Statistical Procedures 4th ed. Chapman and Hall/CRC 2006.
 J. H. Zar Biostatistical Analysis Prentice Hall 2009.
 Y. Hochberg A sharper Bonferroni procedure for multiple tests of significance Biometrika pp. 800–803 1988.
 J. Derrac S. Garca D. Molina F. Herrera A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms Swarm and Evolutionary Computation vol 1 pp. 3–18 2011.
 B. V. Babu S. A. Munawar Optimal design of shell-and-tube heat exchangers bu different strategies of Differential Evolution Technical Report PILANI -333 031 Department of chemical engineering BITS Rajasthan India 2001.
 J. Vesterstrom R. A. Thomson Comparative study of differential evolution particle swarm optimization and evolutionary algorithms on numerical benchmark problems in: Proceedings of the IEEE Congress on Evolutionary Computation 1980–1987 2004.
 X. F. Xie W. J. Zhang. SWAF: Swarm algorithm framework for numerical optimization in: Proceedings of the Genetic Evolutionary Computation Conference Part I pp. 238–250 2004.
 A. Zamuda J. Brest B. Bokovic V. umer. Large scale global optimization using differential evolution with self-adaptation and cooperative coevolution in: Proceedings of the 2008 IEEE World Congress on Computational Intelligence pp. 3719–3726 2008.
 Z. Yang K. Tang X. Yao. Self-adaptive differential evolution with neighborhood search. In Proceedings of the IEEE Congress on Evolutionary Computation pp. 1110–1116 2008.
 A. Iorio X. Li Solving rotated multi-objective optimization problems using differential evolution in: Australian Conference on Artificial Intelligence Cairns Australia pp. 861–872 2004.
 S. Das A. Abraham U.K. Chakraborthy Differential evolution using a neighborhood-based mutation operator IEEE Transactions on Evolutionary Computation 13 pp. 526–553 2009.
 D. H. Wolpert W. G. Macready No Free Lunch Theorems for Optimization IEEE Transactions on Evolutionary Computation vol. 1 no. 1 pp. 67–82 1997.