Physical and Physic-Chemical Based Optimization Methods: A Review

Document Type : Regular Article


1 Professor, Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran

2 Ph.D. Student, Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran


Optimization techniques can be divided to two groups: Traditional or numerical methods and methods based on stochastic. The essential problem of the traditional methods, that by searching the ideal variables are found for the point that differential reaches zero, is staying in local optimum points, can not solving the non-linear non-convex problems with lots of constraints and variables, and needs other complex mathematical operations such as derivative. In order to satisfy the aforementioned problems, the scientists become interested on meta-heuristic optimization techniques, those are classified into two essential kinds, which are single and population-based solutions. The method does not require unique knowledge to the problem. By general knowledge the optimal solution can be achieved. The optimization methods based on population can be divided into 4 classes from inspiration point of view and physical based optimization methods is one of them. Physical based optimization algorithm: that the physical rules are used for updating the solutions are:, Lighting Attachment Procedure Optimization (LAPO), Gravitational Search Algorithm (GSA) Water Evaporation Optimization Algorithm, Multi-Verse Optimizer (MVO), Galaxy-based Search Algorithm (GbSA), Small-World Optimization Algorithm (SWOA), Black Hole (BH) algorithm, Ray Optimization (RO) algorithm, Artificial Chemical Reaction Optimization Algorithm (ACROA), Central Force Optimization (CFO) and Charged System Search (CSS) are some of physical methods. In this paper physical and physic-chemical phenomena based optimization methods are discuss and compare with other optimization methods. Some examples of these methods are shown and results compared with other well known methods. The physical phenomena based methods are shown reasonable results.


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[1]       Zarchi DA, Vahidi B. Multi objective self adaptive optimization method to maximize ampacity and minimize cost of underground cables. J Comput Des Eng 2018;5:401–8. doi:10.1016/j.jcde.2018.02.004.
[2]       Rezaie H, Kazemi-Rahbar MH, Vahidi B, Rastegar H. Solution of combined economic and emission dispatch problem using a novel chaotic improved harmony search algorithm. J Comput Des Eng 2019;6:447–67. doi:10.1016/j.jcde.2018.08.001.
[3]       Safaei A, Vahidi B, Askarian-Abyaneh H, Azad-Farsani E, Ahadi SM. A two step optimization algorithm for wind turbine generator placement considering maximum allowable capacity. Renew Energy 2016;92:75–82. doi:10.1016/j.renene.2016.01.093.
[4]       Mirzaei M, Vahidi B. Feasibility analysis and optimal planning of renewable energy systems for industrial loads of a dairy factory in Tehran, Iran. J Renew Sustain Energy 2015;7:063114. doi:10.1063/1.4936591.
[5]       Abootorabi Zarchi D, Vahidi B. Optimal placement of underground cables to maximise total ampacity considering cable lifetime. IET Gener Transm Distrib 2016;10:263–9. doi:10.1049/iet-gtd.2015.0949.
[6]       Vedadi M, Vahidi B, Hosseinian SH. An imperialist competitive algorithm maximum power point tracker for photovoltaic string operating under partially shaded conditions. Sci Int 2015;27:4023–33.
[7]       Kharazi S, Vahidi B, Hosseinian SH. Optimization Design of High Voltage Substation Ground Grid by Using PSO & HS Algorithms. Sci Int 2015;27:4011–8.
[8]       Hosseini SA, Vahidi B, Askarian Abyaneh H, Sadeghi SHH, Karami M. A seven-state Markov model for determining the optimal operating mode of distributed generators. J Renew Sustain Energy 2015;7:033114. doi:10.1063/1.4921658.
[9]       Mohammadi S, Vahidi B, Mirsalim M, Lesani H. Simple nonlinear MEC-based model for sensitivity analysis and genetic optimization of permanent-magnet. COMPEL - Int J Comput Math Electr Electron Eng 2015;34:301–23. doi:10.1108/COMPEL-12-2013-0424.
[10]     Darvishi A, Akhavan Hejazi H, Vahidi B, Hossein Hosseinian S, Abedi M. Co-optimization of Energy and Reserve Considering Demand Response Program. Sci Int 2014;26.
[11]     Darvishi A, Alimardani A, Vahidi B, Hosseinian SH. Bacterial Foraging-based algorithm optimization based on fuzzy multi-objective technique for optimal power flow dispatch. Sci Int(Lahore) 2014;26:1057–64.
[12]     Rahiminejad A, Faramarzi D, Hosseinian SH, Vahidi B. An effective approach for optimal placement of non-dispatchable renewable distributed generation. J Renew Sustain Energy 2017;9:015303. doi:10.1063/1.4976140.
[13]     Shabani H, Vahidi B. A probabilistic approach for optimal power cable ampacity computation by considering uncertainty of parameters and economic constraints. Int J Electr Power Energy Syst 2019;106:432–43. doi:10.1016/j.ijepes.2018.10.030.
[14]     Rahiminejad A, Alimardani A, Vahidi B, Hosseinian SH. Shuffled frog leaping algorithm optimization for AC--DC optimal power flow dispatch. Turkish J Electr Eng Comput Sci 2014;22:874–92.
[15]     Rahiminejad A, Rahmatian M, Gharehpetian GB, Abedi M, Hosseinian SH, Vahidi B. Social welfare maximization in AC-DC power systems based on evolutionary algorithms: a new merit of HVDC links. Int Trans Electr Energy Syst 2015;25:2203–24. doi:10.1002/etep.1957.
[16]     Behnood A, Gharavi H, Vahidi B, Riahy GH. Optimal output power of not properly designed wind farms, considering wake effects. Int J Electr Power Energy Syst 2014;63:44–50. doi:10.1016/j.ijepes.2014.05.052.
[17]     Torabian Esfahani M, Hosseinian SH, Vahidi B. A new optimal approach for improvement of active power filter using FPSO for enhancing power quality. Int J Electr Power Energy Syst 2015;69:188–99. doi:10.1016/j.ijepes.2014.12.078.
[18]     Abarghoei H, Hosseinian SH, Vahidi B, Vand S. Optimal Expansion Planning of Distribution System and DG Placement Using BPSO. J Appl Sci Agric 2014;9:1404–14.
[19]     Darvishi A, Alimardani A, Vahidi B, Hosseinian SH. Shuffled Frog-Leaping Algorithm for Control of Selective and Total Harmonic Distortion. J Appl Res Technol 2014;12:111–21. doi:10.1016/S1665-6423(14)71611-6.
[20]     Haji MM, Zarchi DA, Vahidi B. Optimal configuration of underground cables to maximise total ampacity considering current harmonics. IET Gener Transm Distrib 2014;8:1090–7. doi:10.1049/iet-gtd.2013.0349.
[21]     Irannezhad F, Vahidi B, Abedi M, Dehghani H. Optimal design with considering distributed generation in distribution systems. Sci Int 2014;26.
[22]     Shariatinasab R, Vahidi B, Hosseinian SH, Ametani A. Probabilistic Evaluation of Optimal Location of Surge Arresters on EHV and UHV Networks Due to Switching and Lightning Surges. IEEE Trans Power Deliv 2009;24:1903–11. doi:10.1109/TPWRD.2009.2027477.
[23]     Tabatabaei SM, Vahidi B, Hosseinian SH, Ahadi SM. Locating the effect of switched capacitor in distribution system using support vector machine. Sci Int(Lahore) 2014;26:605–11.
[24]     Hadavi S, Zoghi A, Vahidi B, Gharehpetian GB, Hosseinian SH. Optimal Allocation and Operating Point of DG Units in Radial Distribution Network Considering Load Pattern. Electr Power Components Syst 2017;45:1287–97. doi:10.1080/15325008.2017.1354237.
[25]     Hashemi-Dezaki H, Agheli A, Vahidi B, Askarian-Abyaneh H. Optimized Placement of Connecting the Distributed Generationswork Stand Alone to Improve the Distribution Systems Reliability. J Electr Eng 2013;64:76–83.
[26]     Goudarzi M, Vahidi B, Naghizadeh R-A. Optimum reactive power compensation in distribution networks using imperialistic competitive algorithm. Sci Int 2013;25:27–31.
[27]     Kouhi Jemsi M, Vahidi B, Naghizadeh R, Hossein Hosseinian S. Optimum design of high voltage bushings by rational Bézier curves. COMPEL - Int J Comput Math Electr Electron Eng 2012;31:1901–16. doi:10.1108/03321641211267182.
[28]     Givi H, Noroozi MA, Vahidi B, Moghani JS, Zand MAV. A Novel Approach for Optimization of Z-Matrix Building Process Using Ant Colony Algorithm 2012;2:8932–7.
[29]     Behdashti A, Ebrahimpour M, Vahidi B, Omidipour V, Alizadeh A. Field experiments and technical evaluation of an optimized media evaporative cooler for gas turbine power augmentation. J Appl Res Technol 2012;10:458–71.
[30]     Kavousi A, Vahidi B, Salehi R, Bakhshizadeh MK, Farokhnia N, Fathi SH. Application of the bee algorithm for selective harmonic elimination strategy in multilevel inverters. IEEE Trans Power Electron 2011;27:1689–96.
[31]     Hadji MM, Vahidi B. A solution to the unit commitment problem using imperialistic competition algorithm. IEEE Trans Power Syst 2011;27:117–24.
[32]     Khorsandi A, Alimardani A, Vahidi B, Hosseinian SH. Hybrid shuffled frog leaping algorithm and Nelder–Mead simplex search for optimal reactive power dispatch. IET Gener Transm Distrib 2011;5:249. doi:10.1049/iet-gtd.2010.0256.
[33]     Tabatabaei SM, Vahidi B. Bacterial foraging solution based fuzzy logic decision for optimal capacitor allocation in radial distribution system. Electr Power Syst Res 2011;81:1045–50. doi:10.1016/j.epsr.2010.12.002.
[34]     Vahidi B, Tavakoli MRB, Hosseinian SH. Determining arresters best positions in power system for lightning shielding failure protection using simulation optimization approach. Eur Trans Electr Power 2010;20:255–76. doi:10.1002/etep.309.
[35]     Karami H, Zaker B, Vahidi B, Gharehpetian GB. Optimal Multi-objective Number, Locating, and Sizing of Distributed Generations and Distributed Static Compensators Considering Loadability using the Genetic Algorithm. Electr Power Components Syst 2016;44:2161–71. doi:10.1080/15325008.2016.1214637.
[36]     Hosseinian SH, Vahidi B, Shariatinasab R. Statistical evaluation of lightning-related failures for the optimal location of surge arresters on the power networks. IET Gener Transm Distrib 2009;3:129–44. doi:10.1049/iet-gtd:20070373.
[37]     Shariatinasab R, Vahidi B, Hosseinian SH, Ametani A. Optimization of Surge Arrester’s Location on EHV and UHV Power Networks Using Simulation Optimization Method. IEEJ Trans Power Energy 2008;128:1465–72. doi:10.1541/ieejpes.128.1465.
[38]     Eslamian M, Hosseinian SH, Vahidi B. Bacterial Foraging-Based Solution to the Unit-Commitment Problem. IEEE Trans Power Syst 2009;24:1478–88. doi:10.1109/TPWRS.2009.2021216.
[39]     Vahidi B, Mousavi Aghah SM, Moaddabi Pirkolachahi N. Optimum parameter identification technique of metal oxide surge arrester model using genetic algorithm. Int Rev Autom Control 2008;1.
[40]     Nematollahi AF, Rahiminejad A, Vahidi B. A novel physical based meta-heuristic optimization method known as Lightning Attachment Procedure Optimization. Appl Soft Comput 2017;59:596–621. doi:10.1016/j.asoc.2017.06.033.
[41]     Foroughi Nematollahi A, Rahiminejad A, Vahidi B. A novel multi-objective optimization algorithm based on Lightning Attachment Procedure Optimization algorithm. Appl Soft Comput 2019;75:404–27. doi:10.1016/j.asoc.2018.11.032.
[42]     Hamzeh M, Vahidi B, Nematollahi AF. Optimizing Configuration of Cyber Network Considering Graph Theory Structure and Teaching–Learning-Based Optimization (GT-TLBO). IEEE Trans Ind Informatics 2019;15:2083–90. doi:10.1109/TII.2018.2860984.
[43]     Foroughi Nematollahi A, Rahiminejad A, Vahidi B, Askarian H, Safaei A. A new evolutionary-analytical two-step optimization method for optimal wind turbine allocation considering maximum capacity. J Renew Sustain Energy 2018;10:043312. doi:10.1063/1.5043403.
[44]     Rahiminejad A, Foroughi Nematollahi A, Vahidi B, Shahrooyan S. Optimal Placement of Capacitor Banks Using a New Modified Version of Teaching-Learning-Based Optimization Algorithm. AUT J Model Simul 2018;50:171–80.
[45]     Forooghi Nematollahi A, Dadkhah A, Asgari Gashteroodkhani O, Vahidi B. Optimal sizing and siting of DGs for loss reduction using an iterative-analytical method. J Renew Sustain Energy 2016;8:055301. doi:10.1063/1.4966230.
[46]     Rahiminejad A, Hosseinian SH, Vahidi B, Shahrooyan S. Simultaneous Distributed Generation Placement, Capacitor Placement, and Reconfiguration using a Modified Teaching-Learning-based Optimization Algorithm. Electr Power Components Syst 2016;44:1631–44. doi:10.1080/15325008.2016.1183729.
[47]     Nematollahi AF, Rahiminejad A, Vahidi B. A novel meta-heuristic optimization method based on golden ratio in nature. Soft Comput 2020;24:1117–51. doi:10.1007/s00500-019-03949-w.
[48]     Rahiminejad A, Vahidi B, Hejazi MA, Shahrooyan S. Optimal scheduling of dispatchable distributed generation in smart environment with the aim of energy loss minimization. Energy 2016;116:190–201. doi:10.1016/
[49]     Safavi V, Vahidi B, Abedi M. Optimal DG placement and sizing in distribution network with reconfiguration. Sci Int 2014;26.
[50]     Fassihi M, Vahidi B. Reconfiguration of distribution systems by implementation of shuffled frog leaping algorithm for loss reduction. Sci Int 2014;26.
[51]     Karimyan P, Vahidi B, Abedi M, Ahadi SM. Optimal dispatchable DG allocation in a distribution network considering load growth with a mixed-PSO algorithm. Turkish J Electr Eng Comput Sci 2016;24:3049–65.
[52]     Blum C, Puchinger J, Raidl GR, Roli A. Hybrid metaheuristics in combinatorial optimization: A survey. Appl Soft Comput 2011;11:4135–51. doi:10.1016/j.asoc.2011.02.032.
[53]     Boussaïd I, Lepagnot J, Siarry P. A survey on optimization metaheuristics. Inf Sci (Ny) 2013;237:82–117. doi:10.1016/j.ins.2013.02.041.
[54]     Koza JR, Koza JR. Genetic programming: on the programming of computers by means of natural selection. vol. 1. MIT press; 1992.
[55]     Simon D. Biogeography-Based Optimization. IEEE Trans Evol Comput 2008;12:702–13. doi:10.1109/TEVC.2008.919004.
[56]     Kaveh A, Talatahari S. A novel heuristic optimization method: charged system search. Acta Mech 2010;213:267–89. doi:10.1007/s00707-009-0270-4.
[57]     Formato RA. Central force optimization: a new metaheuristic with applications in applied electromagnetics. Prog Electromagn Res 77: 425–491 2007.
[58]     Alatas B. ACROA: Artificial Chemical Reaction Optimization Algorithm for global optimization. Expert Syst Appl 2011;38:13170–80. doi:10.1016/j.eswa.2011.04.126.
[59]     Hatamlou A. Black hole: A new heuristic optimization approach for data clustering. Inf Sci (Ny) 2013;222:175–84. doi:10.1016/j.ins.2012.08.023.
[60]     Kaveh A, Khayatazad M. A new meta-heuristic method: Ray Optimization. Comput Struct 2012;112–113:283–94. doi:10.1016/j.compstruc.2012.09.003.
[61]     Du H, Wu X, Zhuang J. Small-World Optimization Algorithm for Function Optimization, 2006, p. 264–73. doi:10.1007/11881223_33.
[62]     Shah-Hosseini H. Principal components analysis by the galaxy-based search algorithm: a novel metaheuristic for continuous optimisation. Int J Comput Sci Eng 2011;6:132–40.
[63]     Kaveh A. Water Evaporation Optimization Algorithm. Adv Metaheuristic Algorithms Optim Des Struct, Cham: Springer International Publishing; 2017, p. 489–509. doi:10.1007/978-3-319-46173-1_16.
[64]     Gogna A, Tayal A. Metaheuristics: review and application. J Exp Theor Artif Intell 2013;25:503–26. doi:10.1080/0952813X.2013.782347.
[65]     Mirjalili S, Mirjalili SM, Hatamlou A. Multi-Verse Optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 2016;27:495–513. doi:10.1007/s00521-015-1870-7.
[66]     Rashedi E, Nezamabadi-pour H, Saryazdi S. GSA: A Gravitational Search Algorithm. Inf Sci (Ny) 2009;179:2232–48. doi:10.1016/j.ins.2009.03.004.
[67]     Naka S, Genji T, Yura T, Fukuyama Y. Hybrid particle swarm optimization based distribution state estimation using constriction factor approach. Proc Int Conf SCIS ISIS, vol. 2, 2002, p. 1083–8.
[68]     Yang C, Tu X, Chen J. Algorithm of Marriage in Honey Bees Optimization Based on the Wolf Pack Search. 2007 Int Conf Intell Pervasive Comput (IPC 2007), IEEE; 2007, p. 462–7. doi:10.1109/IPC.2007.104.
[69]     Gandomi AH, Yang X-S, Alavi AH. Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 2013;29:17–35. doi:10.1007/s00366-011-0241-y.
[70]     Yang X-S. Firefly Algorithms for Multimodal Optimization, 2009, p. 169–78. doi:10.1007/978-3-642-04944-6_14.
[71]     Askarzadeh A. Bird mating optimizer: An optimization algorithm inspired by bird mating strategies. Commun Nonlinear Sci Numer Simul 2014;19:1213–28. doi:10.1016/j.cnsns.2013.08.027.
[72]     Mucherino A, Seref O, Seref O, Kundakcioglu OE, Pardalos P. Monkey search: a novel metaheuristic search for global optimization. AIP Conf Proc, vol. 953, AIP; 2007, p. 162–73. doi:10.1063/1.2817338.
[73]     Salcedo-Sanz S, Del Ser J, Landa-Torres I, Gil-López S, Portilla-Figueras JA. The Coral Reefs Optimization Algorithm: A Novel Metaheuristic for Efficiently Solving Optimization Problems. Sci World J 2014;2014:1–15. doi:10.1155/2014/739768.
[74]     Salcedo-Sanz S, Pastor-Sánchez A, Gallo-Marazuela D, Portilla-Figueras A. A Novel Coral Reefs Optimization Algorithm for Multi-objective Problems, 2013, p. 326–33. doi:10.1007/978-3-642-41278-3_40.
[75]     Miettinen K, Preface By-Neittaanmaki P. Evolutionary algorithms in engineering and computer science: recent advances in genetic algorithms, evolution strategies, evolutionary programming, GE. John Wiley & Sons, Inc.; 1999.
[76]     Karaboga D, Basturk B. A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 2007;39:459–71. doi:10.1007/s10898-007-9149-x.
[77]     Mirjalili S. The Ant Lion Optimizer. Adv Eng Softw 2015;83:80–98. doi:10.1016/j.advengsoft.2015.01.010.
[78]     Mirjalili S. Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-Based Syst 2015;89:228–49. doi:10.1016/j.knosys.2015.07.006.
[79]     Mirjalili S, Lewis A. The Whale Optimization Algorithm. Adv Eng Softw 2016;95:51–67. doi:10.1016/j.advengsoft.2016.01.008.
[80]     Mirjalili S. Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 2016;27:1053–73. doi:10.1007/s00521-015-1920-1.
[81]     Kaveh A, Farhoudi N. A new optimization method: Dolphin echolocation. Adv Eng Softw 2013;59:53–70. doi:10.1016/j.advengsoft.2013.03.004.
[82]     Gandomi AH, Alavi AH. Krill herd: A new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 2012;17:4831–45. doi:10.1016/j.cnsns.2012.05.010.
[83]     Rao RV, Savsani VJ, Vakharia DP. Teaching–learning-based optimization: A novel method for constrained mechanical design optimization problems. Comput Des 2011;43:303–15. doi:10.1016/j.cad.2010.12.015.
[84]     Zong Woo Geem, Joong Hoon Kim, Loganathan GV. A New Heuristic Optimization Algorithm: Harmony Search. Simulation 2001;76:60–8. doi:10.1177/003754970107600201.
[85]     Kennedy J. Particle swarm optimization. Encycl Mach Learn, Springer US; 2011, p. 760–766.
[86]     Venkataraman P. Applied optimization with MATLAB programming. John Wiley & Sons; 2009.
[87]     Price K, Storn RM, Lampinen JA. Differential evolution: a practical approach to global optimization. Springer Science & Business Media; 2006.
[88]     Statnikov RB, Matusov JB. Multicriteria optimization and engineering. Springer Science & Business Media; 2012.
[89]     Mirjalili S, Mirjalili SM, Lewis A. Grey Wolf Optimizer. Adv Eng Softw 2014;69:46–61. doi:10.1016/j.advengsoft.2013.12.007.
[90]     Kirkpatrick S, Gelatt CD, Vecchi MP. Optimization by Simulated Annealing. Science (80- ) 1983;220:671–80. doi:10.1126/science.220.4598.671.
[91]     Davis L. Handbook of genetic algorithms 1991.
[92]     Knowles J, Corne D. The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation. Proc 1999 Congr Evol Comput (Cat No 99TH8406), IEEE; n.d., p. 98–105. doi:10.1109/CEC.1999.781913.