Abstract
Novel metaheuristic algorithms are now considered an appealing collection of methods for solving complex optimization problems, in which the challenging objective is to find a better solution in a shorter computation time. Focusing on the same objective, this paper proposes a novel metaheuristic optimization algorithm inspired by heat transfer relationships based on the second law of thermodynamics. Imitating the heat transfer behavior of solid objects, the proposed method is called the heat transfer relation-based optimization algorithm (HTOA). This behavior was modeled on a heat transfer function used to measure temperature differences between the selected solutions and the best solution. This function was employed to determine and add the heat capacity transferred between those solutions. Finally, all the solutions were heat-exchanged with the best solution to select the fittest solution and exclude the rest. This procedure continued until the best solution or solutions were found. The proposed method is challenged by many famous benchmark problems in two categories as well as two real-world problems (PID controller and linear regression). The HTOA was then compared with a number of well-known and state-of-the-art optimization algorithms. Selecting better solutions and requiring shorter computation time, the proposed HTOA outperformed the other algorithms.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Abbass HA MBO: Marriage in honey bees optimization-A haplometrosis polygynous swarming approach. In: Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No. 01TH8546), 2001. IEEE, pp 207–214
Alatas B (2011) ACROA: artificial chemical reaction optimization algorithm for global optimization. Expert Syst Appl 38:13170–13180
Arora S, Singh S (2019) Butterfly optimization algorithm: a novel approach for global optimization. Soft Comput 23:715–734
Askarzadeh A, Rezazadeh A (2013) A new heuristic optimization algorithm for modeling of proton exchange membrane fuel cell: bird mating optimizer. Int J Energy Res 37:1196–1204
Bárdossy A (1990) Note on fuzzy regression. Fuzzy Sets Syst 37:65–75
Basturk B (2006) An artificial bee colony (ABC) algorithm for numeric function optimization. In: IEEE swarm intelligence symposium, Indianapolis, IN, USA.
Beni G, Wang J (1993) Swarm intelligence in cellular robotic systems. In: Robots and biological systems: towards a new bionics? Springer, pp 703–712
Bonabeau E, Marco DdRDF, Dorigo M, Theraulaz G (1999) Swarm intelligence: from natural to artificial systems, vol 1. Oxford University Press, Oxford
Chen S-F (2007) Particle swarm optimization for PID controllers with robust testing. In: 2007 international conference on machine learning and cybernetics, IEEE, pp 956–961
Dhiman G, Kumar V (2017) Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Adv Eng Softw 114:48–70
Dhiman G, Kumar V (2018) Emperor penguin optimizer: A bio-inspired algorithm for engineering problems. Knowl-Based Syst 159:20–50
Digalakis JG, Margaritis KG (2001) On benchmarking functions for genetic algorithms. Int J Comput Math 77:481–506
Dorigo AM, Birattari M (2006) Thomas St utzle, Ant Colony Optimization, Artificial Ants as a Computational Intelligence Technique IEEE CIM
Dorigo M, Birattari M (2010) Ant colony optimization. Springer
Du H, Wu X, Zhuang J (2006) Small-world optimization algorithm for function optimization. In: International Conference on Natural Computation, Springer, pp 264-273
Dukhan N, Quinones-Ramos PD, Cruz-Ruiz E, Vélez-Reyes M, Scott EP (2005) One-dimensional heat transfer analysis in open-cell 10-ppi metal foam. Int J Heat Mass Transf 48:5112–5120
Erol OK, Eksin I (2006) A new optimization method: big bang–big crunch. Adv Eng Softw 37:106–111
Formato RA (2007) Central force optimization. Prog Electromagn Res 77(1):425–491
Gandomi AH, Alavi HA (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845
Hansen N, Müller SD, Koumoutsakos P (2003) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evolutionary Comput 11:1–18
Hatamlou A (2013) Black hole: A new heuristic optimization approach for data clustering. Inf Sci 222:175–184
He S, Wu Q, Saunders J A novel group search optimizer inspired by animal behavioural ecology. In: 2006 IEEE international conference on evolutionary computation, 2006. IEEE, pp 1272–1278
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: Algorithm and applications. Futur Gener Comput Syst 97:849–872
Holland J (1992) Genetic Algorithms Scientific American 267:66–72. https://doi.org/10.1038/scientificamerican0792-66
Jamil M, Yang X-S (2013) A literature survey of benchmark functions for global optimization problems arXiv preprint https://arxiv.org/abs/1308.4008
Jones A, Oliveira P (1995) “Genetic auto-tuning of PID controllers”. In: Proceedings of international conference on genetic algorithms in engineering systems: innovations and applications, pp 141–145
Karaboga D, Basturk B (2007) Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems. International fuzzy systems association world congress. Springer, pp 789–798
Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112:283–294
Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213:267–289
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, Piscataway NJ, IEEE Service Center, pp 1942–1948
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680
Koza JR, Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection, vol 1. MIT press, Cambridge
Koza JR, Rice JP (1992) Automatic programming of robots using genetic programming. In: AAAI, Citeseer, pp 194–207
Lam AYS, Li VOK (2009) Chemical-reaction-inspired metaheuristic for optimization. IEEE Trans Evol Comput 14:381–399
Li X (2003) A new intelligent optimization-artificial fish swarm algorithm Doctor thesis. Zhejiang University of Zhejiang, China
Li Z, Al-Rashed AA, Rostamzadeh M, Kalbasi R, Shahsavar A, Afrand M (2019) Heat transfer reduction in buildings by embedding phase change material in multi-layer walls: Effects of repositioning, thermophysical properties and thickness of PCM. Energy Conv Manag 195:43–56
Lienhard JH (2019) A heat transfer textbook. Dover Publications
Lu X, Zhou Y (2008) A novel global convergence algorithm: bee collecting pollen algorithm. In: International conference on intelligent computing, Springer, pp 518-525
Maučec MS, Brest J, Bošković B, Kačič Z (2018) Improved differential evolution for large-scale black-box optimization IEEE. Access 6:29516–29531. https://doi.org/10.1109/ACCESS.2018.2842114
Mech LD (1999) Alpha status, dominance, and division of labor in wolf packs. Canadian J Zool 77:1196–1203
Mirjalili S, Lewis A (2013) S-shaped versus V-shaped transfer functions for binary particle swarm optimization. Swarm Evolut Comput 9:1–14
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Mirjalili S, Mirjalili SM, Lewis A (2014a) Grey wolf optimizer. Adv Eng Softw 69:46–61
Mirjalili S, Mirjalili SM, Yang X-S (2014b) Binary bat algorithm. Neural Comput Appl 25:663–681
Moghaddam FF, Moghaddam RF, Cheriet M (2012) Curved space optimization: a random search based on general relativity theory arXiv preprint https://arxiv.org/abs/1208.2214
Mucherino A, Seref O (2007) Monkey search: a novel metaheuristic search for global optimization. In: AIP conference proceedings, vol 1. AIP, pp 162–173
Muro C, Escobedo R, Spector L, Coppinger R (2011) Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations. Behav Process 88:192–197
Murrill PW (1991) Fundamentals of process control theory. Instrument Society of America Research Triangle Park, NC
Nash JC, Walker-Smith M (1987) Nonlinear parameter estimation Dekker. New York 5:5014–5019
Omran MG (2016) A novel cultural algorithm for real-parameter optimization. Int J Comput Math 93:1541–1563
Pan W-T (2012) A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowl-Based Syst 26:69–74
Park J-H, Choi Y-K (1996) An on-line PID control scheme for unknown nonlinear dynamic systems using evolution strategy. In: Proceedings of IEEE international conference on evolutionary computation. IEEE, pp 759–763
Pinto PC, Runkler TA, Sousa JM (2007) Wasp swarm algorithm for dynamic MAX-SAT problems. In: International conference on adaptive and natural computing algorithms, Springer, pp 350-357
Price K, Awad NH, Ali MZ, Suganthan P (2019) The 2019 100-Digit Challenge on Real-Parameter, Single Objective Optimization: Analysis of Results; Technical Report 2019. https://www.ntu.edu.sg/home/epnsugan/index_files/CEC2019/CEC2019.htm. Accessed 12 April 2020
Rashedi E, Hossein N-P, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf sci 179(13):2232–2248
Rechenberg I (1994) Evolutionsstrategie’94, volume 1 of Werkstatt Bionik und Evolutionstechnik Frommann Holzboog, Stuttgart
Roth M, Stephen W (2005) Termite: A swarm intelligent routing algorithm for mobile wireless ad-hoc networks. In: Stigmergic Optimization, vol 31. Springer, Berlin, Heidelberg, pp 155–184. doi:https://doi.org/10.1007/978-3-540-34690-6_7
Shah-Hosseini H (2011) Principal components analysis by the galaxy-based search algorithm: a novel metaheuristic for continuous optimisation. Int J Comput Sci Eng 6:132–140
Shiqin Y, Jianjun J, Guangxing Y (2009) A dolphin partner optimization. In: 2009 WRI Global Congress on Intelligent Systems, IEEE, pp 124–128
Simon D (2008) Biogeography-based optimization. IEEE Trans Evolut Comput 126:702–713
Slowik A, Kwasnicka H (2017) Nature inspired methods and their industry applications—Swarm intelligence algorithms. IEEE Trans Ind Inf 14:1004–1015
Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359
Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y-P, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization KanGAL report 2005005:2005
Thermal Conductivity of selected Materials and Gases (2003) [online] Available at: https://www.engineeringtoolbox.com/thermal-conductivity-d_429.html. 2019
Truong Tung Khac, Li Kenli, Yuming Xu (2013) Chemical reaction optimization with greedy strategy for the 0–1 knapsack problem. Appl Soft Comput 13(4):1774–1780
Van den Bergh F, Engelbrecht AP (2006) A study of particle swarm optimization particle trajectories. Inf Sci 176:937–971
Watts DG (1984) Nonlinear regression modeling: a unified practical approach (Statistics: Textbooks and Monographs Series), vol 48. Taylor & Francis Group, UK
Webster B, Bernhard PJ (2003) A local search optimization algorithm based on natural principles of gravitation.
Wikipedia Contributors PID controller. Wikipedia, The Free Encyclopedia. https://en.wikipedia.org/w/index.php?title=PID_controller&oldid=925590136. Accessed 11 November 2019 02:10 UTC
Wikimedia Commons Contributors Linear regression.svg. Wikimedia Commons, the free media repository. https://commons.wikimedia.org/w/index.php?title=File:Linear_regression.svg&oldid=343115066. Accessed 26 November 2019 20:16 UTC
Xu Yuming et al (2013) A DAG scheduling scheme on heterogeneous computing systems using double molecular structure-based chemical reaction optimization. J Parallel Distrib Comput 73(9):1306–1322
Xu Yuming et al (2014) A hybrid chemical reaction optimization scheme for task scheduling on heterogeneous computing systems. IEEE Trans Parallel and Distributed Syst 26(12):3208–3222
Yan X, Su X (2009) Linear regression analysis: theory and computing. World Scientific
Yang X-S (2010a) Firefly algorithm, stochastic test functions and design optimisation arXiv preprint https://arxiv.org/abs/1003.1409
Yang X-S (2010b) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, pp 65–74
Yang X-S, Deb S (2009) Cuckoo search via Lévy flights. In: 2009 world congress on nature & biologically inspired computing (NaBIC), IEEE, pp 210–214
Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster IEEE Transactions on. Evol Comput 3:82–102
Zhang J, Zhuang J, Du H (2009) Self-organizing genetic algorithm based tuning of PID controllers. Inf Sci 179:1007–1018
Funding
No funding was received for this work.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no competing interests
Ethical approval
We further confirm that any aspect of the work covered in this manuscript that has involved human patients has been conducted with the ethical approval of all relevant bodies and that such approvals are acknowledged within the manuscript.
IRB approval was obtained (required for studies and series of 3 or more cases)
Written consent to publish potentially identifying information, such as details or the case and photographs, was obtained from the patient(s) or their legal guardian(s).
Human and animal rights
This article does not contain any studies with human participants or animals performed by any of the authors.
Informed consent
Informed consent was obtained from all individual participants included in the study
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
Asef, F., Majidnezhad, V., Feizi-Derakhshi, MR. et al. Heat transfer relation-based optimization algorithm (HTOA). Soft Comput 25, 8129–8158 (2021). https://doi.org/10.1007/s00500-021-05734-0
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-021-05734-0