Abstract
This paper introduces two novel lightweight algorithms based on a single non-uniform mutation (SNUM) operator: a single solution algorithm and a SNUM-based compact Genetic Algorithm. The first algorithm, called also SNUM with reference to the operator, performs the search by an iterative process that perturbs one design variable selected randomly from a single solution. The latter, called compact SNUM (cSNUM), incorporates the SNUM mechanism into the compact Genetic Algorithm scheme, that replaces a population of solutions with a probabilistic model. Both approaches are characterised by a purposely simple and highly generic algorithmic structure. These two attractive features make it possible to readily employ the core part of each algorithm and combine it with other techniques for extended complexity. The results obtained from applying the two proposed algorithms on the BBOB and CEC-2017 benchmarks reveal that the use of SNUM is largely beneficial. Not only the two algorithms (in particular cSNUM) are able to deal with separable functions, especially when the problem dimensionality increases, but they also prove to be competitive on other classes of functions, displaying very good performances compared to other methods from the literature, also on non-separable functions
Similar content being viewed by others
Availability of data and material
The raw data are available upon request.
Code availability
The code is available upon request.
Notes
Complete numerical results are available at: https://drive.google.com/drive/folders/1yYm3Q4sYpp2kx-lMTPu-8SH-8_RLPAU-?usp=sharing.
References
Ahn CW, Ramakrishna RS (2003) Elitism-based compact genetic algorithms. IEEE Trans Evolut Comput 7(4):367–385
Awad NH, Ali MZ, Qu BY, Liang JJ, Suganthan PN (2016) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective bound constrained real-parameter numerical optimization. Tech. rep., Nanyang Technological University, Singapore
Banitalebi A, Aziz MIA, Bahar A, Aziz ZA (2015) Enhanced compact artificial bee colony. Inf Sci 298:491–511
Bansal JC, Singh PK, Pal NR (2019) Evolutionary and swarm intelligence algorithms. Springer, Berlin
Biedrzycki R (2017) A version of IPOP-CMA-ES algorithm with midpoint for CEC 2017 single objective bound constrained problems. In: 2017 IEEE congress on evolutionary computation (CEC). IEEE, pp 1489–1494
Brest J, Maučec MS, Bošković B (2017) Single objective real-parameter optimization: algorithm jSO. In: 2017 IEEE congress on evolutionary computation (CEC). IEEE, pp 1311–1318
Caraffini F, Iacca G, Neri F, Mininno E (2012) Three variants of three stage optimal memetic exploration for handling non-separable fitness landscapes. In: 2012 12th UK workshop on computational intelligence (UKCI). IEEE, pp 1–8
Caraffini F, Neri F, Iacca G, Mol A (2013a) Parallel memetic structures. Inf Sci 227:60–82
Caraffini F, Neri F, Passow BN, Iacca G (2013b) Re-sampled inheritance search: high performance despite the simplicity. Soft Comput 17(12):2235–2256
Caraffini F, Neri F, Iacca G (2017) Large scale problems in practice: the effect of dimensionality on the interaction among variables. In: European conference on the applications of evolutionary computation. Springer, pp 636–652
Dao TK, Chu SC, Shieh CS, Horng MF et al (2014a) Compact artificial bee colony. In: International conference on industrial, engineering and other applications of applied intelligent systems. Springer, pp 96–105
Dao TK, Pan JS, Chu SC, Shieh CS et al (2014b) Compact bat algorithm. In: Intelligent data analysis and its applications, vol II. Springer, pp 57–68
Dao TK, Pan TS, Nguyen TT, Chu SC (2015) A compact artificial bee colony optimization for topology control scheme in wireless sensor networks. J Inf Hiding Multimed Signal Process 6(2):297–310
Dao TK, Pan TS, Nguyen TT, Chu SC, Pan JS (2016) A compact flower pollination algorithm optimization. In: 2016 Third international conference on computing measurement control and sensor network (CMCSN). IEEE, pp 76–79
Deb K, Goyal M (1996) A combined genetic adaptive search (GeneAS) for engineering design. Comput Sci Inform 26:30–45
Deep K, Thakur M (2007) A new mutation operator for real coded genetic algorithms. Appl Math Comput 193(1):211–230
Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evolut Comput 1(1):3–18
Ferigo A, Iacca G (2020) A GPU-enabled compact genetic algorithm for very large-scale optimization problems. Mathematics 8(5):758
García S, Fernández A, Luengo J, Herrera F (2009) A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft Comput 13(10):959
Hansen N, Müller SD, Koumoutsakos P (2003) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evolut Comput 11(1):1–18
Hansen N, Ros R, Mauny N, Schoenauer M, Auger A (2008) PSO facing non-separable and ill-conditioned problems. Tech. Rep. RR-6447, INRIA
Hansen N, Ros R, Mauny N, Schoenauer M, Auger A (2011) Impacts of invariance in search: when CMA-ES and PSO face ill-conditioned and non-separable problems. Appl Soft Comput 11(8):5755–5769
Hansen N, Auger A, Finck S, Ros R (2012) Real-parameter black-box optimization benchmarking: experimental setup. Tech. rep., Orsay, France: Université Paris Sud, Institut National de Recherche en Informatique et en Automatique (INRIA) Futurs, Équipe TAO, Tech. Rep
Hansen N, Auger A, Brockhoff D, Tušar D, Tušar T (2016) COCO: Performance assessment. arXiv preprint arXiv:1605.03560
Harik GR, Lobo FG, Goldberg DE (1999a) The compact genetic algorithm. IEEE Trans Evolut Comput 3(4):287–297
Harik GR, Lobo FG et al (1999b) A parameter-less genetic algorithm. In: GECCO, vol 99. pp 258–267
Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6(2):65–70
Iacca G (2011) Memory-saving optimization algorithms for systems with limited hardware. Ph.D. thesis, University of Jyväskylä
Iacca G (2013) Distributed optimization in wireless sensor networks: an Island-model framework. Soft Comput 17(12):2257–2277
Iacca G, Caraffini F (2019) Compact optimization algorithms with re-sampled inheritance. In: International conference on the applications of evolutionary computation (Part of EvoStar). Springer, pp 523–534
Iacca G, Caraffini F (2020) Re-sampled inheritance compact optimization. Knowl Based Syst 208:106416
Iacca G, Caraffini F, Neri F (2012a) Compact differential evolution light: high performance despite limited memory requirement and modest computational overhead. J Comput Sci Technol 27(5):1056–1076
Iacca G, Neri F, Mininno E (2012b) Compact bacterial foraging optimization. In: Swarm and evolutionary computation. Springer, pp 84–92
Iacca G, Neri F, Mininno E, Ong YS, Lim MH (2012c) Ockham’s razor in memetic computing: three stage optimal memetic exploration. Inf Sci 188:17–43
Iacca G, Caraffini F, Neri F (2013a) Memory-saving memetic computing for path-following mobile robots. Appl Soft Comput 13(4):2003–2016
Iacca G, Caraffini F, Neri F (2013b) Multi-strategy coevolving aging particle optimization. Int J Neural Syst 24(01):1450008 (19 pages)
Iacca G, Caraffini F, Neri F, Mininno E (2013c) Single particle algorithms for continuous optimization. In: 2013 IEEE congress on evolutionary computation. IEEE, pp 1610–1617
Jewajinda Y (2016) Covariance matrix compact differential evolution for embedded intelligence. In: 2016 IEEE region 10 symposium (TENSYMP). IEEE, pp 349–354
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95-international conference on neural networks, vol 4. IEEE, pp 1942–1948
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680
Kommadath R, Kotecha P (2017) Teaching learning based optimization with focused learning and its performance on CEC 2017 functions. In: 2017 IEEE congress on evolutionary computation (CEC). IEEE, pp 2397–2403
Kumar A, Misra RK, Singh D (2017) Improving the local search capability of effective butterfly optimizer using covariance matrix adapted retreat phase. In: 2017 IEEE congress on evolutionary computation (CEC). IEEE, pp 1835–1842
Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evolut Comput 10(3):281–295
Li X, Tang K, Omidvar MN, Yang Z, Qin K, China H (2013) Benchmark functions for the CEC 2013 special session and competition on large-scale global optimization. Tech. Rep. 33, IEEE
Mahdavi S, Shiri ME, Rahnamayan S (2015) Metaheuristics in large-scale global continues optimization: a survey. Inf Sci 295:407–428
Michalewicz Z (1996) Genetic algorithms + data structures = evolution programs. Springer, Berlin
Mininno E, Cupertino F, Naso D (2008) Real-valued compact genetic algorithms for embedded microcontroller optimization. IEEE Trans Evolut Comput 12(2):203–219
Mininno E, Neri F, Cupertino F, Naso D (2011) Compact differential evolution. IEEE Trans Evolut Comput 15(1):32–54
Mohamed AW, Hadi AA, Fattouh AM, Jambi KM (2017) LSHADE with semi-parameter adaptation hybrid with CMA-ES for solving CEC 2017 benchmark problems. In: 2017 IEEE congress on evolutionary computation (CEC). IEEE, pp 145–152
Neri F, Mininno E (2010) Memetic compact differential evolution for cartesian robot control. IEEE Comput Intell Mag 5(2):54–65
Neri F, Cotta C, Moscato P (2011a) Handbook of memetic algorithms, vol 379. Springer, Berlin
Neri F, Iacca G, Mininno E (2011b) Disturbed exploitation compact differential evolution for limited memory optimization problems. Inf Sci 181(12):2469–2487
Neri F, Iacca G, Mininno E (2013a) Compact optimization. In: Handbook of optimization. Springer, pp 337–364
Neri F, Mininno E, Iacca G (2013b) Compact particle swarm optimization. Inf Sci 239:96–121
Prügel-Bennett A (2010) Benefits of a population: five mechanisms that advantage population-based algorithms. IEEE Trans Evolut Comput 14(4):500–517
Rao SS (2019) Engineering optimization: theory and practice. Wiley, Hoboken
Sergio A, Carvalho S, Marco R (2014) On the use of compact approaches in evolution strategies. Adv Distrib Comput Artif Intell J 3(4):13–23
Shi Yj, Teng Hf, Li Zq (2005) Cooperative co-evolutionary differential evolution for function optimization. In: International conference on natural computation. Springer, pp 1080–1088
Song PC, Pan JS, Chu SC (2020) A parallel compact cuckoo search algorithm for three-dimensional path planning. Appl Soft Comput 94:106443
Tang PH, Tseng MH (2013) Adaptive directed mutation for real-coded genetic algorithms. Appl Soft Comput 13(1):600–614
Tangherloni A, Rundo L, Nobile MS (2017) Proactive particles in swarm optimization: a settings-free algorithm for real-parameter single objective optimization problems. In: 2017 IEEE congress on evolutionary computation (CEC). IEEE, pp 1940–1947
Tian AQ, Chu SC, Pan JS, Cui H, Zheng WM (2020) A compact pigeon-inspired optimization for maximum short-term generation mode in cascade hydroelectric power station. Sustainability 12(3):767
Tighzert L, Fonlupt C, Mendil B (2018) A set of new compact firefly algorithms. Swarm Evolut Comput 40:92–115
Wilcoxon F (1992) Individual comparisons by ranking methods. In: Breakthroughs in statistics. Springer, pp 196–202
Xinchao Z (2011) Simulated annealing algorithm with adaptive neighborhood. Appl Soft Comput 11(2):1827–1836
Yaman A, Iacca G, Caraffini F (2019) A comparison of three differential evolution strategies in terms of early convergence with different population sizes. In: International global optimization workshop
Yaman A, Iacca G, Coler M, Fletcher G, Pechenizkiy M (2018) Multi-strategy differential evolution. In: International conference on the applications of evolutionary computation. Springer, Cham, pp 617–633
Yang XS (2010) Engineering optimization: an introduction with metaheuristic applications. Wiley, Hoboken
Yang Z, Li K, Guo Y, Ma H, Zheng M (2018) Compact real-valued teaching-learning based optimization with the applications to neural network training. Knowl Based Syst 159:51–62
Yang Z, Li K, Guo, Y (2014) A new compact teaching-learning-based optimization method. In: International conference on intelligent computing. Springer, pp 717–726
Zhang J, Sanderson AC (2009) JADE: Adaptive differential evolution with optional external archive. IEEE Trans Evolut Comput 13(5):945–958
Zhao X, Gao XS, Hu ZC (2007) Evolutionary programming based on non-uniform mutation. Appl Math Comput 192(1):1–11
Zhao M, Pan JS, Chen ST (2017) Compact cat swarm optimization algorithm. In: International conference on security with intelligent computing and big-data services. Springer, pp 33–43
Zhou J, Ji Z, Shen L (2008) Simplified intelligence single particle optimization based neural network for digit recognition. In: 2008 Chinese conference on pattern recognition. IEEE, pp 1–5
Funding
Not applicable.
Author information
Authors and Affiliations
Contributions
All authors contributed to the design of this study. Experiments and data collection were performed by SK and AD. The analysis was performed by all authors. The first draft of the manuscript was written by SK. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Khalfi, S., Iacca, G. & Draa, A. On the use of single non-uniform mutation in lightweight metaheuristics. Soft Comput 26, 2259–2275 (2022). https://doi.org/10.1007/s00500-021-06495-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-021-06495-6