Abstract
This paper combines Artificial Physics and Base Optimization Algorithms to propose a Modified Artificial Physics Optimization for multi-parameter function minimization. Prominent features of Base Optimization lies in using standard arithmetic operators with displacement parameters to reach the optimal solution. Artificial Physics benefit from the success of physicomimetics and shows an evident predominance in search of global optima. This study uses distinctive advantages of two algorithms to propose an efficient optimization for multi-parameter functions. In order to reveal effects of mass function approach of Artificial Physics and cost functions of the optimization process, the proposed method executes various mass–cost function combinations synchronously. The effectiveness of the proposed algorithm is demonstrated on integer-order and fractional-order controller tunings for integer- and fractional-order models. Priority of the proposed optimization method is presented by comparing with known optimization algorithms.
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Alagoz BB, Ates A, Yeroglu C (2013) Auto-tuning of PID controller according to fractional order reference model approximation for DC rotor control. Mechatronics 23:789–797. https://doi.org/10.1016/j.mechatronics.2013.05.001
Ameli K, Alfi A, Aghaebrahimi M (2016) A fuzzy discrete harmony search algorithm applied to annual cost reduction in radial distribution systems. Eng Optim 48(9):1529–1549. https://doi.org/10.1080/0305215X.2015.1120299
Åström KJ, Hägglund T (1995) PID controllers: theory, design and tuning. Instrument Society of America, Nort Carolina
Ates A, Yeroglu C (2014) Tabu Search algorithm for fractional order PID via nonlinear multi objective functions. In: IEEE 2014 international conference on fractional differentiation and its applications. IEEE, Catania, Italy, pp 1–6. https://doi.org/10.1109/icfda.2014.6967387
Ates A, Yeroglu C (2016) Optimal fractional order PID design via Tabu Search based algorithm. ISA Trans 60:109–118. https://doi.org/10.1016/j.isatra.2015.11.015
Ates A, Yeroglu C, Alagoz BB, Senol B (2014) Tuning of fractional order PID with master-slave stochastic multi-parameter divergence optimization method. In: IEEE 2014 international conference on fractional differentiation and its applications. IEEE, Catania, Italy, pp 1–6. https://doi.org/10.1109/icfda.2014.6967388
Beni G, Hackwood S (1992) Stationary waves in cyclic swarms. In: 1992 international symposium on intelligent control. IEEE, Glasgow, England, pp 234–242. https://doi.org/10.1109/isic.1992.225097
Beni G, Wang J (1989) Swarm intelligence. In: Proceedings of the seventh annual meeting of the Robotics Society of Japan, Tokyo, Japan, pp 425–428
Biswas A, Das S, Abraham A, Dasgupta S (2009) Design of fractional-order PIλDμ controllers with an improved differential evolution. Eng Appl Artif Intell 22:343–350
Bonabeau E, Dorigo M, Theraulaz G (1999) Swarm intelligence: from natural to artificial intelligence. Oxford University Press, New York
Chen YQ, Vinagre BM, Podlubny I (2004) Continued fraction expansion approaches to discretizing fractional order derivatives an expository review. Nonlinear Dyn 38:155–170. https://doi.org/10.1007/s11071-004-3752-x
Chevalier PY, Hendrickx JM, Jungers RM (2014) Efficient algorithms for the consensus decision problem. SIAM J Control Optim 53:3104–3119. https://doi.org/10.1137/140988024
Črepinšek M, Liu SH, Mernik L, Mernik M (2016) Is a comparison of results meaningful from the inexact replications of computational experiments? Soft Comput 20:223–235. https://doi.org/10.1007/s00500-014-1493-4
Davendra D, Zelinka I, Senkerik R (2010) Chaos driven evolutionary algorithms for the task of PID control. Comput Math Appl 60:1088–1104. https://doi.org/10.1016/j.camwa.2010.03.066
Dorigo M, Maniezzo V, Colorni A (1996) The ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern 26:29–41. https://doi.org/10.1109/3477.484436
Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, Nagoya, Japan, pp 39–43
Erol OK, Eksin I (2006) New optimization method: big bang–big crunch. Adv Eng Softw 37:106–111. https://doi.org/10.1016/j.advengsoft.2005.04.005
Fogel LJ, Owens AJ, Walsh MJ (1966) Artificial intelligence through simulated evolution. Wiley, Chichester
Glover F, Laguna M (1997) Tabu Search. Kluwer, Norwell
Gutiérrez RE, Rosário JM, Machado JAT (2010) Fractional order calculus: basic concepts and engineering applications. Math Probl Eng 2010:1–9. https://doi.org/10.1155/2010/375858
Hayes A, Martinoli A, Goodman R (2001) Swarm robotic odor localization. In: IEEE 2001 international conference on intelligent robots and systems. IEEE, Maui, HI, USA, pp 1073–1078. https://doi.org/10.1109/iros.2001.976311
Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor
Kang N, Kokkolaras M, Papalambros PY (2014) Solving multiobjective optimization problems using quasi-separable MDO formulations and analytical target cascading. Struct Multidiscip Optim 50:849–859. https://doi.org/10.1007/s00158-014-1144-5
Kaveh A, Talatahari S (2010) An improved ant colony optimization for constrained engineering design problems. Eng Comput 1:155–182. https://doi.org/10.1108/02644401011008577
Kirkpatrick S, Gelatt C, Vecchi M (1983) Optimization by simulated annealing. Science 4598:671–680
Li HS, Luo Y, Chen YQ (2010) A fractional order proportional and derivative (FOPD) motion controller: tuning rule and experiments. IEEE Trans Control Syst Technol 18:516–520. https://doi.org/10.1109/TCST.2009.2019120
Lin MH, Tsai J (2014) A deterministic global approach for mixed-discrete structural optimization. Eng Optim 46:863–879. https://doi.org/10.1080/0305215X.2013.806918
Misener R, Smadbeck JB, Floudas CA (2015) Dynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2. Optim Methods Softw 30:215–249. https://doi.org/10.1080/10556788.2014.916287
Mohammadi SD, Rais-Rohani M (2013) Exponential penalty function formulation for multilevel optimization using the analytical target cascading framework. Struct Multidiscip Optim 47:599–612. https://doi.org/10.1007/s00158-012-0861-x
Mousavi Y, Alfi A (2017) A memetic algorithm applied to trajectory control by tuning of fractional order proportional-integral-derivative controllers. Appl Soft Comput 36:599–617. https://doi.org/10.1016/j.asoc.2015.08.009
Noorbin SFH, Alfi A (2017) Adaptive parameter control of search group algorithm using fuzzy logic applied to networked control systems. Soft Comput. https://doi.org/10.1007/s00500-017-2742-0
Pahnehkolaei SMA, Alfi A, Sadollah A, Kim JH (2017) Gradient-based water cycle algorithm with evaporation rate applied to chaos suppression. Appl Soft Comput 53:420–440. https://doi.org/10.1016/j.asoc.2016.12.030
Panda S, Sahu BK, Mohanty PK (2012) Design and performance analysis of PID controller for an automatic voltage regulator system using simplified particle swarm optimization. J Franklin Inst 349:2609–2625. https://doi.org/10.1016/j.jfranklin.2012.06.008
Podlubny I (1999) Fractional order systems and PIλDμ controller. Proc IEEE Trans Autom Control 44:208–214
Podlubny I, Petraš I, Vinagre BM, O’leary P, Dorčák L (2009) Analogue realizations of fractional-order controllers. Nonlinear Dyn 29:281–296
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232–2248. https://doi.org/10.1016/j.ins.2009.03.004
Salem SA (2012) BOA: a novel optimization algorithm. In IEEE 2012 international conference on engineering and technology; 10–11 October 2012. IEEE, Cairo, Egypt, pp 1–5. https://doi.org/10.1109/icengtechnol.2012.6396156
Spears WM, Gordon DF (1999) Using artificial physics to control agents. In: IEEE 1999 international conference on information intelligence and systems. IEEE, Bethesda, MD, USA, pp 281–288. https://doi.org/10.1109/iciis.1999.810278
Spears WM, Spears DF (2012) Physicomimetics: physics-based swarm intelligence. Springer, Berlin
Spears WM, Spears DF, Hamann JC, Heil R (2004a) Distributed, physics-based control of swarms of vehicles. Auton Robots 17:137–162. https://doi.org/10.1023/B:AURO.0000033970.96785.f2
Spears WM, Spears DF, Heil R, Kerr W, Hettiarachchi S (2004b) An overview of physicomimetics. Springer, Berlin, pp 84–97
Spears DF, Kerr W, Hettiarachchi S (2005) An overview of physicomimetics. Lect Notes Comput Sci State Art Ser 3324:84–97
Tepljakov A, Petlenkov E, Belikov J, Halas M (2013) Design and implementation of fractional-order PID controllers for a fluid tank system. In: IEEE 2013 American control conference. IEEE, Washington, DC, USA, pp 1777–1782. https://doi.org/10.1109/acc.2013.6580093
Valerio D (2005) Ninteger v. 2.3 fractional control toolbox for Matlab. Technical University of Lisboa, Lisboa
Wachsmuth D, Wurst JE (2015) An interior point method designed for solving linear quadratic optimal control problems with hp finite elements. Optim Methods Softw 30:1276–1302. https://doi.org/10.1080/10556788.2015.1045067
Weise T (2009) Global optimization algorithms theory and application. Self Published. http://www.it-weise.de/projects/book.pdf. Accessed 23 June 2018
Xie LP, Zeng J (2009) An extended artificial physics optimization algorithm for global optimization problems. In: IEEE 2009 innovative computing, information and control conference. IEEE, Kaohsiung, Taiwan, pp 881–884. https://doi.org/10.1109/icicic.2009.86
Xie LP, Zeng JC, Cui ZH (2009) General framework of artificial physics optimization algorithm. In: IEEE 2009 the World Congress on nature and biologically inspired computing, IEEE, Coimbatore, Indian, pp 1321–1326. https://doi.org/10.1109/nabic.2009.5393736
Xie L, Zeng J, Cai X (2011a) A hybrid vector artificial physics optimization with multi-dimensional search method. In: IEEE 2011 second international conference on innovations in bio-inspired computing and applications. IEEE, Shenzhan, China, pp 116–119. https://doi.org/10.1109/ibica.2011.33
Xie L, Zeng J, Formato RA (2011b) Convergence analysis and performance of the extended artificial physics optimization algorithm. Appl Math Comput 218:4000–4011. https://doi.org/10.1016/j.amc.2011.02.062
Xie LP, Tan Y, Zeng J (2011c) The convergence analysis and parameter selection of artificial physics optimization algorithm. Int J Intell Inf Database Syst 5:536–554
Xue D, Chen YQ, Atherton DP (2007) Linear feedback control analysis and design with MATLAB. Advances in design and control. SIAM, Breckenridge
Yeroglu C, Ates A (2014) A stochastic multi-parameters divergence method for online auto-tuning of fractional order PID controllers. J Franklin Inst 351:2411–2429. https://doi.org/10.1016/j.jfranklin.2013.12.006
Yeroglu C, Kavuran G (2014) Sliding mode controller design with fractional order differentiation: applications on unstable time delay systems. Turk J Electr Eng Comput 22:1270–1286. https://doi.org/10.3906/elk-1212-149
Yeroglu C, Tan N (2011) Note on fractional-order proportional–integral–differential controller design. IET Control Theory Appl 5:1978–1989. https://doi.org/10.1049/iet-cta.2010.0746
Zelinka I, Celikovský S, Richter H, Chen G (2010) Evolutionary algorithms and chaotic systems. Studies computational intelligence, vol 267. Springer, Berlin
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Ateş, A., Yeroğlu, C. Modified Artificial Physics Optimization for Multi-parameter Functions. Iran J Sci Technol Trans Electr Eng 42, 465–478 (2018). https://doi.org/10.1007/s40998-018-0082-4
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DOI: https://doi.org/10.1007/s40998-018-0082-4