Abstract
Swarm intelligence algorithms are stochastic algorithms, i.e. they perform some random movement. This random movement imparts the algorithms with exploration capabilities and allows them to escape local optima. Exploration at the start of execution helps with thorough inspection of the search/solution space. However, as the algorithm progresses, the focus should ideally shift from exploration to exploitation. This shift would help the algorithm to enhance existing solutions and improve its convergence capabilities. Hence if the range of random movement is not kept in check, it may limit an algorithm’s convergence capabilities and overall efficiency. To ensure that the convergence of an algorithm is not compromised, an improved search technique to reduce range of uniform random movement was recently proposed for bat algorithm. Uniform distribution and levy distribution are the most commonly used random distributions in swarm algorithms. In this paper, the applicability of the improved search technique over different swarm algorithms employing uniform and levy distributions, as well as Cauchy distribution has been studied. The selected algorithms are firefly algorithm, cuckoo search algorithm, moth search algorithm, whale optimization algorithm, earthworm optimization algorithm and elephant herding optimization algorithm. The resultant variants of each of these algorithms show improvement upon inclusion of the improved search technique. Hence results establish that the improved search technique has positive influence over swarm algorithms employing different random distributions.
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References
Abraham A, Grosan C, Ramos V (eds) (2006) Swarm intelligence in data mining, vol 34. Studies in computational intelligence. Springer, Berlin. https://doi.org/10.1007/978-3-540-34956-3
Banati H, Chaudhary R (2017) Multi-modal bat algorithm with improved search (MMBAIS). J Comput Sci 23:130–144. https://doi.org/10.1016/j.jocs.2016.12.003
Banzhaf W, Nordin P, Keller RE, Francone FD (1998) Genetic programming: an introduction. Morgan Kaufmann, San Francisco
Beyer HG, Schwefel HP (2002) Evolution strategies: a comprehensive introduction. Nat Comput 1(1):3–52. https://doi.org/10.1023/A:1015059928466
Bonabeau E, Dorigo M, Theraulaz G (1999) Swarm intelligence: from natural to artificial systems. Oxford University Press, Oxford
Boussaïd I, Lepagnot J, Siarry P (2013) A survey on optimization metaheuristics. Inf Sci 237:82–117. https://doi.org/10.1016/j.ins.2013.02.041
Cagnina LC, Esquivel SC, Coello CAC (2008) Solving engineering optimization problems with the simple constrained particle swarm optimizer. Informatica 32:319–326
Chakri A, Khelif R, Benouaret M, Yang XS (2017) New directional bat algorithm for continuous optimization problems. Expert Syst Appl 69:159–175. https://doi.org/10.1016/j.eswa.2016.10.050
Chaudhary R, Banati H (2018) Modified shuffled multi-population bat algorithm. In: Proceedings of the 2018 international conference on advances in computing, communications and informatics (ICACCI), Bangalore, pp 943–951. https://doi.org/10.1109/icacci.2018.8554926
Chaudhary R, Banati H (2019a) Peacock algorithm. In: Proceedings of IEEE congress on evolutionary computation (IEEE CEC 2019), Wellington, New Zealand, pp 2331–2338. https://doi.org/10.1109/cec.2019.8790371
Chaudhary R, Banati H (2019b) Swarm bat algorithm with improved search (SBAIS). Soft Comput 23(22):11461–11491. https://doi.org/10.1007/s00500-018-03688-4
Chaudhary R, Banati H (2020a) Adaptive multi-swarm bat algorithm (AMBA). In: Das K, Bansal J, Deep K, Nagar A, Pathipooranam P, Naidu R (eds) Soft computing for problem solving. Advances in intelligent systems and computing, vol 1048. Springer, Singapore. https://doi.org/10.1007/978-981-15-0035-0_66
Chaudhary R, Banati H (2020b) Weighted multi-modal bat algorithm with improved search. Int J Hybrid Intell 1(4):326–361. https://doi.org/10.1504/IJHI.2020.10028083
Coelho LDS, Mariani VC (2008) Use of chaotic sequences in a biologically inspired algorithm for engineering design optimization. Expert Syst Appl 34(3):1905–1913. https://doi.org/10.1016/j.eswa.2007.02.002
Coello CAC (2006) Evolutionary multi-objective optimization: a historical view of the field. IEEE Comput Intell Mag 1(1):28–36. https://doi.org/10.1109/MCI.2006.1597059
Crepinsek M, Liu SH, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv 45(3):33. https://doi.org/10.1145/2480741.2480752
Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the art. IEEE Trans Evolut Comput 15(1):4–31. https://doi.org/10.1109/TEVC.2010.2059031
De Jong KA (2006) Evolutionary computation: a unified approach. The MIT Press, Cambridge
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 1:3–18. https://doi.org/10.1016/j.swevo.2011.02.002
Dorigo M, Caro GD (1999) The ant colony optimization meta-heuristic. In: Corne D, Dorigo M, Glover F (eds) New ideas in optimization. McGraw-Hill, London
Eberhart RC, Shi Y (2004) Guest editorial special issue on particle swarm optimization. IEEE Trans Evolut Comput 8(3):201–203. https://doi.org/10.1109/TEVC.2004.830335
El-Abd M, Kamel M (2005) A taxonomy of cooperative search algorithms. In: Proceeding of international workshop on hybrid metaheuristics, Barcelona, Spain, pp 32–41
Emmerich MTM, Deutz AH (2018) A tutorial on multiobjective optimization: fundamentals and evolutionary methods. Nat Comput 17:585–609. https://doi.org/10.1007/s11047-018-9685-y
Fogel DB (1991) System identification through simulated evolution: a machine learning approach to modeling. Ginn Press, New York
Fogel DB (1995) Evolutionary computation: toward a new philosophy of machine intelligence. IEEE Press, Piscataway
Fogel LJ, Owens AJ, Walsh MJ (1966) Artificial intelligence through simulated evolution. Wiley, Chichester
Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simulat 17:4831–4845. https://doi.org/10.1016/j.cnsns.2012.05.010
Ghosh A, Tsutsui S (eds) (2003) Advances in evolutionary computation: theory and applications. Springer, Berlin
Gomes J, Mariano P, Christensen AL (2019) Challenges in cooperative coevolution of physically heterogeneous robot teams. Nat Comput 18:29–46. https://doi.org/10.1007/s11047-016-9582-1
Hashmi A, Goel N, Goel S, Gupta D (2013) Firefly algorithm for unconstrained optimization. IOSR J Comput Eng 11(1):75–78
Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor
Horváth T, de Carvalho ACPLF (2017) Evolutionary computing in recommender systems: a review of recent research. Nat Comput 16:441–462. https://doi.org/10.1007/s11047-016-9540-y
Hsieh T-J (2014) A bacterial gene recombination algorithm for solving constrained optimization problems. Appl Math Comput 231:187–204. https://doi.org/10.1016/j.amc.2013.12.178
Jain M, Singh V, Rani A (2018) A novel nature-inspired algorithm for optimization: squirrel search algorithm. Swarm Evolut Comput. https://doi.org/10.1016/j.swevo.2018.02.013
Jones DF, Mirrazavi SK, Tamiz M (2002) Multi-objective meta-heuristics: an overview of the current state-of-the-art. Eur J Oper Res 137(1):1–9
Jun L, Liheng L, Xianyi W (2015) A double-subpopulation variant of the bat algorithm. Appl Math Comput 263:361–377. https://doi.org/10.1016/j.amc.2015.04.034
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95—international conference on neural networks, Perth, WA, Australia, vol 4, pp 1942–1948. IEEE. https://doi.org/10.1109/icnn.1995.488968
Koza JR (1994) Introduction to genetic programming. In: Kinnear KE Jr (ed) Advances in genetic programming. MIT Press, Cambridge, pp 21–42
Lanzi PL (2008) Learning classifier systems: then and now. Evolut Intell 1:63–82. https://doi.org/10.1007/s12065-007-0003-3
Lee KS, Geem ZW (2005) A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194(36–38):3902–3933. https://doi.org/10.1016/j.cma.2004.09.007
Lung RI, Dumitrescu D (2010) Evolutionary swarm cooperative optimization in dynamic environments. Nat Comput 9:83–94. https://doi.org/10.1007/s11047-009-9129-9
Ma H, Simon D, Fei M, Chen Z (2013) On the equivalences and differences of evolutionary algorithms. Eng Appl Artif Intell 26(10):2397–2407. https://doi.org/10.1016/j.engappai.2013.05.002
Ma H, Ye S, Simon D, Fei M (2017) Conceptual and numerical comparisons of swarm intelligence optimization algorithms. Soft Comput 21(11):3081–3100. https://doi.org/10.1007/s00500-015-1993-x
Mirjalili S (2015) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl. https://doi.org/10.1007/s00521-015-1920-1
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007
Mitchell M (1996) Introduction to genetic algorithms. MIT Press, Cambridge
Price KV (1999) An introduction to differential evolution. In: Corne D, Dorigo M, Glover V (eds) New ideas in optimization. McGraw-Hill, London, pp 79–108
Rao SS (2009) Engineering optimization: theory and practice, 4th edn. Wiley, New York
Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2013) Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl Soft Comput 13(5):2592–2612. https://doi.org/10.1016/j.asoc.2012.11.026
Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47. https://doi.org/10.1016/j.advengsoft.2017.01.004
Simon D (2013) Evolutionary optimization algorithms. Wiley Press, New York
Souza E, Santos D, Oliveira G, Silva A, Oliveira ALI (2018) Swarm optimization clustering methods for opinion mining. Nat Comput. https://doi.org/10.1007/s11047-018-9681-2
Srivastava S, Sahana SK (2019) A survey on traffic optimization problem using biologically inspired techniques. Nat Comput. https://doi.org/10.1007/s11047-019-09731-z
Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical Report TR-95-012, ICSI, Berkeley
Urbanowicz RJ, Moore JH (2009) Learning classifier systems: a complete introduction, review, and roadmap. J Artif Evolut Appl. https://doi.org/10.1155/2009/736398
Wang GG (2018) Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Memetic Comput 10:151–164. https://doi.org/10.1007/s12293-016-0212-3
Wang GG, Deb S, Cui Z (2015) Monarch butterfly optimization. Neural Comput Appl 31(7):1995–2014. https://doi.org/10.1007/s00521-015-1923-y
Wang GG, Deb S, Gao XZ, Coelho LDS (2016) A new metaheuristic optimization algorithm motivated by elephant herding behaviour. Int J Bio-Inspired Comput. https://doi.org/10.1504/ijbic.2016.10002274
Wang GG, Deb S, Coelho L (2018) Earthworm optimisation algorithm: a bio-inspired metaheuristic algorithm for global optimisation problems. Int J Bio-Inspired Comput. https://doi.org/10.1504/IJBIC.2018.093328
Yang XS (2005) Engineering optimizations via nature-inspired virtual bee algorithms. In: Mira J, Álvarez JR (eds) Artificial intelligence and knowledge engineering applications: a bioinspired approach, vol 3562. IWINAC 2005. Lecture notes in computer science. Springer, Berlin. https://doi.org/10.1007/11499305_33
Yang XS (2009) Firefly algorithms for multimodal optimization. In: Watanabe O, Zeugmann T (eds) Stochastic algorithms: foundations and appplications, vol 5792. SAGA 2009, Lecture notes in computer science. Springer, Berlin, pp 169–178. https://doi.org/10.1007/978-3-642-04944-6_14
Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Gonzalez et al JR (eds) Proceedings of nature inspired cooperative strategies for optimization (NISCO 2010). Studies in computational intelligence, vol 284. Springer, Berlin, pp 65–74. https://doi.org/10.1007/978-3-642-12538-6_6
Yang XS (2012) Flower pollination algorithm for global optimization. In: Durand-Lose J, Jonoska N (eds) Unconventional computation and natural computation, vol 7445. UCNC 2012. Lecture notes in computer science. Springer, Berlin, pp 240–249. https://doi.org/10.1007/978-3-642-32894-7_27
Yang XS (2014) Swarm intelligence based algorithms: a critical analysis. Evolut Intell 7:17–28. https://doi.org/10.1007/s12065-013-0102-2
Yang XS (2016) Nature-inspired optimization algorithms. Elsevier Press, Amsterdam
Yang XS, Deb S (2009) Cuckoo search via lévy flights. In: Proceedings of 2009 world congress on nature and biologically inspired computing (NaBIC), Coimbatore, pp 210–214. https://doi.org/10.1109/nabic.2009.5393690
Yang XS, Deb S, Zhao YX, Fong S, He XS (2017) Swarm intelligence: past, present and future. Soft Comput. https://doi.org/10.1007/s00500-017-2810-5
Yu X, Gen M (2010) Introduction to evolutionary algorithms, 2nd edn. Springer, Berlin
Zhao W, Wang L, Zhang Z (2019) Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowl Based Syst 163:283–304. https://doi.org/10.1016/j.knosys.2018.08.030
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Chaudhary, R., Banati, H. Improving convergence in swarm algorithms by controlling range of random movement. Nat Comput 20, 513–560 (2021). https://doi.org/10.1007/s11047-020-09826-y
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DOI: https://doi.org/10.1007/s11047-020-09826-y